Feedback Control Circuit For Magnetic Suspension And Propulsion System

Abstract

A linear motor uses the same magnetic flux for suspension and propulsion of a high speed tracked vehicle and operates below a support rail without physical contact therewith. Displacement and inertial sensors carried by the vehicle sense the length of the motor-to-rail gap and any acceleration of the vehicle causing changes in the gap. A non-linear feedback circuit responds to the sensor signals and controls the voltage applied to the phased windings of the motor to maintain the selected gap. The feedback circuit provides uniform stability and dynamic response over a wide range of gap, maintains the selected gap substantially constant notwithstanding track irregularities and variations in vehicle loading, and gradually corrects for unevenness. The inertial sensor is made to be sensitive to vertical acceleration of the vehicle and insensitive to irregularities of the rail thereby assuring a "smooth" or "easy" ride notwithstanding irregularities of the rail. The frequency of the applied voltage is varied upwards from zero to adjust the linear speed of the motor, and the voltage is increased with the frequency to compensate for the increase in inductive reactance of the windings. A wide dynamic range of motor control voltage is provided to cover the propulsion range from standstill to high speed without requiring a wide dynamic range in the feedback control elements.

Parent Case Text

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of the U.S. Pat. application of James A. Ross for "Magnetic Suspension and Propulsion System," Ser. No. 131,041, filed Apr. 16, 1971, now U.S. Pat. No. 3,638,093, hereinafter sometimes referred to as the "parent application."

Description

BACKGROUND OF THE INVENTION

Heretofore others have suggested linear motors utilizing the same magnetic flux for suspension and propulsion of tracked vehicles. United States Pat. No. 782,312 (1905) to Alfred Zehden and French Pat. No. 1,537,842 (1968) to Jeumont-Schneider Electromechanical Construction Company, for example, teach combined propulsion and suspension of a linear induction motor by magnetic attraction of the motor upwardly toward its support rail which also serves as the reaction rail. Zehden discloses triphase windings, and the French patent teaches changes in power frequency to effect changes in propulsion speed. The French patent further teaches the use of gap sensing operative in an electronic feedback circuit for maintaining suspension of the motor below its support rail at a controlled air gap therebetween, thereby to avoid physical contact with the rail both at standstill and during propulsion along the rail. Zehden employs a rail engaging wheel support and does not disclose a feedback control circuit.

German Pat. Nos. 643,316 (1937), 44,302 (1938), and 707,032 (1941) to Hermann Kemper disclose the suspension of tracked vehicles by use of electromagnets disposed below a support rail and magnetically attracted thereto while maintaining a controlled air gap therebetween, thus avoiding physical contact of the electromagnets with the rail.

The 1941 Kemper patent and the French patent disclose similar arrangements utilizing magnetic attraction for guidance and switching of the magnetically suspended vehicle.

The 1937 Kemper patent suggests that the electromagnets used for suspension can be configured for polyphase operation for propulsion of the vehicle along the track, operating for this purpose in the manner of polyphase induction motors. Recent developments of German industry in the transportation field, however, while apparently following the teachings of Kemper with respect to achieving magnetic suspension, tend to follow Kemper's suggested alternative propulsion arrangement of using separate electromagnets operative with their own reaction rail in a conventional polyphased linear induction motor mode.

The suspension arrangement of the 1938 Kemper patent (Addition to the 1937 patent), in common with the teaching of the 1937 patent, senses motor position with respect to the rail (gap), but further senses rate of change of that position (motor velocity), and change in motor energy state (motor suspension current) to provide a motor control voltage which is operative over a wide range of gap X (twice normal gap a). The motor voltage may be d.c. or a.c. and is characterized as being positive or negative over-voltages for achieving arbitrarily high acceleration of the energy level contained in the motor windings.

The 1938 Kemper patent is concerned with providing feedback for preventing oscillations of the suspended vehicle caused by the kinetic energy acquired by the vehicle in response to a correction of position and, further, in preventing high acceleration of change of motor energy level from causing further changes in energy level when the correct level is reached. The position feedback voltage e.sub.x produces a directing magnetic force to return the suspended vehicle to the correct location relative to the rails, and the damping or velocity feedback voltage e.sub.d assures that the correcting movement can be made to a more or less damped oscillation. A report feedback potential e.sub.r is made to be proportional to the motor current and, in turn, provides a measure of the momentary energy state of the motor magnet. The sum of the position feedback voltage e.sub.x and the damping voltage e.sub.d constitutes a command voltage e.sub.b which starts the energy addition or reduction when a change in gap is sensed. The report potential e.sub.r opposes the command potential e.sub.b to prevent further changes in the energy state as soon as the correct level is reached.

The feedback provided by the Kemper Addition Patent is made to produce a smooth ride of the suspended vehicle by designing a pull force curve (curve III of FIG. 4) wherein position feedback voltage e.sub.x is caused to fall off for increasing gap distance, the directional pull force being sufficient, however, to return the vehicle to the correct location but being limited to a desirable maximum value which results in limiting the tracking of the vehicle in relation to the rail track when moving rapidly. Additional absorption of rail nonuniformities is achieved by avoiding excessive suppression of the electrical inertia characteristics of the feedback regulator circuits, the smooth ride resulting because the feedback is not required to force distance corrections for deviations which exist only in short sections of the rail track whereby the vehicle is caused to follow only the average from a number of different regulation impulses.

Automotive News for October 1970 describes an active spring-hydraulic suspension system for an air cushion supported tracked vehicle which employs vertical and lateral acceleration sensor inputs to a computer which calculates the forces necessary to maintain the vehicle body on a smooth path and with banking on turns.

In the aforesaid copending parent application, Ser. No. 131,041, of James A. Ross there is disclosed a tracked vehicular transportation system employing polyphased linear motors both for suspension and propulsion in which each motor is magnetically attracted upwardly by its magnetic field toward a support rail with a controlled air gap maintained therebetween, and its suspension magnetic field is also used to translate the motor and its supported vehicle along the track at a speed related to the frequency of the polyphase alternating current applied to the motor.

Although any number of phases could be used, a three phase design is disclosed because it is the simplest motor construction having the desirable characteristic of providing nearly constant pole attraction as a function of phase rotation. The propulsion system is a variable reluctance, synchronous speed type wherein the rail is provided with repetitive magnetic discontinuities (notches), or alternatively, the propulsion system is a linear induction motor type wherein the rail is provided with either a continuous conductive reaction strip or a squirrel cage winding (shorted rotor). Other disclosed propulsion systems are of the wound rotor and hysteresis types.

The terminal voltage applied to the polyphased motor windings to produce the attractive suspension force as well as the moving field for propulsion is controlled by a non linear-feedback circuit which uses signals from displacement and inertial sensors carried on the vehicle for maintaining a selected air gap. The feedback is non linear in order to compensate for the nonlinearity of the motor characteristic as a function of gap length and of feedback operating frequency. The attractive force produced by the magnetic field of the motor is proportional to the square of the motor current and inversely proportional to the square of the gap length. The motor impedance, moreover, is resistive at zero frequency and largely inductive at frequencies such as 10 to 30 hertz which are relatively high for the feedback apparatus.

The circuit elements of the feedback circuit provide the motor terminal voltage in accordance with the following equation which expresses the relationship between the motor terminal voltage and the resulting attractive magnetic force produced between the motor and its support rail:

E = K.sub.3 .sqroot.F (lr + jK.sub.4 .omega.) where

.omega. = 2.pi.f

E = terminal voltage

l = air gap length

f = frequency in hertz (cycles/second)

K.sub.1, K.sub.2 = constants

F = attractive magnetic force

j = reaction symbol.

In order to provide stable suspension of the vehicle, whether at standstill or some propulsive speed, and at a selective gap which may range from substantially zero to one-half inches, the motor terminal voltage E, whether d.c. at standstill or a.c. at the propulsive speed, produces an attractive magnetic force F which is opposite to the gravitational and inertial forces acting on the vehicle and sufficient to restore and maintain the same in stable suspension. The feedback circuit responds to signals from the displacement and inertial sensors to produce various voltages indicative of these gravitational and inertial forces. For example, in a specific circuit arrangement, a voltage input of -4 volts to the square rooter element of the circuit indicates a gravitational force of 1 g which, of course, is the weight of the vehicle including its support motors. When this is the only force on the vehicle, the magnetic attractive force F produced by the motor terminal voltage E is just sufficient to support the vehicle against gravity at the selected gap.

Signals from the displacement and inertial sensors pass in parallel paths through displacement and accelerometer channels in the input portion of the feedback circuit. The displacement channel produces displacement signals indicative of the length of the gap, velocity signals which are derived from differentiated displacement and are indicative of the rate of change of displacement, and change in loading signals which are derived from integrated displacement. The velocity signals range in frequency from 1.2 to 5 hertz. The change in loading signals range in frequency from d.c. to 1.2 hertz. The range of frequencies of maximum interest in the displacement channel thus extends from d.c. to 5 hertz.

Signals from the displacement channel are algebraically summed with signals from the accelerometer channel which has a frequency range of maximum interest extending from 0.3 to 30 hertz. Partial integration of the accelerometer feedback signal provides a quasi-velocity feedback which is effective from a frequency of the order of 10 hertz down to 4 hertz below which the differentiated displacement signal provides the velocity feedback.

The square rooter element of the feedback circuit takes the square root of the combined displacement and accelerometer channel signals to produce a voltage corresponding to the equation quantity .sqroot.F which is thereafter multiplied by the displacement function (lR) and the frequency function (jK.sub.4 .omega.), respectively, these equation functions being performed by mutliplier and amplifier-differentiator circuit elements. These circuit elements respectively provide d.c. and a.c. paths for their inputs, the d.c. path providing a voltage which increases with the gap and the a.c. path providing a voltage which increases with increasing feedback frequency, as is required to linearize the motor response with frequency. The a.c. path includes a perfect differentiator which provides a first derivative of the input over a frequency range of from essentially zero to 200 hertz.

The combined outputs of the multiplier and amplifier-differentiator elements produce a unidirectional feedback voltage which represents the equation quantity .sqroot.F (lR + jK.sub.4 .omega.). The combined circuit gain required to produce suspension against gravity accounts for the constant K.sub.3 in the equation.

The varying frequency voltage required for propulsion at speeds upward from zero is provided by a constant amplitude variable frequency three phase oscillator, the amplitude of each phase of which is increased as a function of the frequency by an imperfect differentiator for each phase to compensate for the increase in motor impedance due to the increase in inductive reactance with frequency. The differentiation is imperfect to assure an output at zero frequency and thus provide the magnetic flux required in the motor-to-rail gap to establish suspension when the system is in operation at standstill.

The unidirectional variations of the feedback voltage are made essentially to modulate the imperfect differentiator outputs for each phase, it being a first input to each of three multipliers for the three phases, the other input for each of the multipliers being one of the differentiator outputs. Each of the multiplier outputs gives the product of the feedback voltage and the instantaneous value of each of the phased voltages in accordance with the three-phase variation thereof.

The output from each multiplier for each phase passes into a controllable power supply having three outputs, one for each of the phased windings of the motor, the voltage output of each being controlled according to the variation of three phase electrical energy with time, including the special case of zero frequency wherein the phased outputs constitute "frozen" instantaneous values which do not vary with time until a frequency variation is again produced to provide propulsion. Highly efficient controllable amplifiers of high power capabilities such as the Class D type or the gated-silicon-controlled-rectifier type are employed to provide propulsive power for passenger-carrying railroad car type vehicles weighing thousands of pounds.

An inertial or accelerometer type sensor which senses any acceleration in the vertical direction of the motor and its supported mass as the same moves up and down in space is preferred since it provides signals indicative of such movements without regard to the motor-rail spacial relationship. Thus, the accelerometer sensor is not sensitive to irregularities in the track and does not pass them on to the passengers in the form of vibrations or jolts. On the other hand, the gain of the displacement channel is reduced as a function of gap change frequency and only a mean gap is maintained by the displacement sensor. An alternative acceleration feedback sensor which senses relative acceleration of the suspended mass with respect to the rail is suggested for use as a substitute for the inertial-reference accelerometer in the feedback circuit when it is desired that the vehicle closely follow the rail for technical reasons or to avoid the higher costs of the inertial accelerometer. Hall-effect transducers which sense the flux in the air gap are suggested as a suitable sensor for such purpose.

The feedback loop that includes the inertial sensor makes a second order correction to the overall feedback network of the order of 10db of feedback over the frequency of interest which is from 0.5 to 5 hertz. This makes the system insensitive to second order variations such as changes in coil resistance with temperature and variations in the d.c. gain and a.c. gain of the feedback network which may change from day to day with weather changes, and for other reasons.

As aforementioned, the force exerted magnetically by the motor to provide suspension varies as the square of the motor current and inversely as the square of the gap length. This is a non-linear relation. However, the d.c. flux in the air gap remains the same for different gap lengths when the current to gap ratio remains constant as it does, for example, when the current is doubled when the gap is doubled, the magnetizing force or ampere turns per unit length of gap remaining the same. Non-linear elements in the feedback circuit, such as the square-rooter circuit, linearize the voltage vs. force function for all gap lengths and thus allows the dynamic response of the feedback signals to be constant and provides constant stability for the system. The resultant linearization of the feedback circuit also provides constant gain at all operating frequencies of the polyphase power and corresponding propulsive speeds. This assures a smooth ride at all vehicle speeds. The smoothness of the ride, moreover, can be adjusted by adjustment of the feedback circuit, it being unnecessary to change the motor or any related parts of the structure.

The feedback circuit assures the stability of the vehicle with respect to the track, compensates for varying passenger loading and thrust due to wind, and gradually corrects for unevenness of the track. The feedback circuit also inherently maintains lateral stability and any lateral perturbation is restored in a damped manner without overshoot.

SUMMARY OF THE INVENTION

The present invention relates generally to the transportation field and more particularly to a high speed tracked transport vehicle which uses the same linear electric motors for both suspension and propulsion, such as disclosed in the aforesaid copending parent application of James A. Ross, and which additionally may use such motors for vehicle guidance and banking.

The present invention follows the basic principles and incorporates the fundamental features of the parent application while providing improvements in the composition and functioning of the non-linear feedback circuit which controls both the magnitude and frequency of the motor terminal voltage to achieve suspension and propulsion at selected propulsion speeds, or suspension alone at standstill.

Specifically, the feedback control circuit of the present invention, while employing circuit elements for performing the multiplications and summations of the voltage vs. force function equation:

E = K.sub.3 .sqroot.F (Rl + jK.sub.4 .omega.)

as in the parent application, expresses this equation in the form

E = K.sub.1 .sqroot.F (lR + jK.sub.2 f)

where:

F is the attractive magnetic force

E is the terminal voltage

l is the air gap length

R is the winding resistance

f is the propulsion frequency in hertz

K.sub.1, K.sub.2 are constants

j is the reaction symbol.

The square root function .sqroot.F is developed from the sensor signal paths, as in the parent application. The multiplication of this function times displacement and propulsion frequency, however, are performed in the propulsion frequency control channel.

A first multiplier produces the product of the .sqroot.F function times each phase of a constant applitude three phase voltage of selected frequency which may be zero at standstill or a specific frequency corresponding to a desired propulsion speed. This product which represents K.sub.1 .sqroot.F in the equation is the input to a second multiplier operating in parallel with a perfect differentiator. The second multiplier produces the product K.sub.1 .sqroot.F lR and the differentiator produces the product K.sub.1 .sqroot.F K.sub.2 f, and these products are summed and provided as the input to the three phase controllable power amplifiers which supply the terminal voltages to the three phase motor windings.

This improved feedback circuit arrangement eliminates the imperfect differentiator of the parent application which increased the amplitude of the oscillator signal, of each phase as the oscillator frequency increased. This required that the following multipliers be operated over an extremely wide dynamic range. A perfect differentiator which in the circuit arrangement of the instant case provides the voltage vs. frequency function, follows the multipliers and thus permits the motor terminal voltage to be increased with frequency for any desired propulsion speed without exceeding the dynamic operating range of the multipliers.

The non-linear feedback circuit disclosed and claimed in the parent application is a species of the generic invention herein disclosed and claimed wherein an electroresponsive force field generator and a coacting member separated or spaced therefrom are attracted toward each other by the force field set up between them and are held separated from each other at a selected gap by an opposing force, it being the function of the non-linear feedback circuit to so adjust the voltage of the electroresponsive force field generator that the force produced by it is at all times sufficient relative to the opposing force to restore and maintain stable equilibrium at the selected gap.

In the species of the invention disclosed and claimed in the parent application, the magnetic force field and feedback circuit arrangements are made to be responsive to opposing force relationships wherein the opposing force is gravity and other acceleration forces tending to upset the stable equilibrium of the suspended vehicle and its support motors.

In the present invention, force field and feedback circuit arrangements embodying the generic invention are also made to be responsive to laterally directed displacement and acceleration forces on the vehicle such as may be caused by wind loads or may occur during turning movements, to thus accomplish controlled magnetic guidance and banking of the vehicle.

The foregoing and other features of the invention will become more fully apparent from the following detailed description with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a force field generator embodying the voltage vs. force functions employed in the present invention;

FIG. 2 is a schematic view of a tracked vehicle and its support motors for achieving magnetic suspension and banking in accordance with the feedback principles of the present invention;

FIG. 3 is a schematic view of a tracked vehicle and its linear motors for achieving suspension and guidance of the vehicle;

FIG. 4 is a block diagram of a feedback control circuit for supplying the motor terminal voltages E.sub.1 and E.sub.2 of FIG. 2;

FIG. 4A is a schematic circuit diagram of one embodiment of the block diagram of FIG. 4;

FIG. 5 is a complete block diagram of the electrical system for achieving suspension and propulsion of a tracked vehicle and its linear electric support motors;

FIGS. 6A and 6B, taken together, constitute a schematic circuit diagram of one embodiment of the block diagram of FIG. 5;

FIGS. 7A and 7B are graphs showing speed vs. frequency relationships for synchronous relucatance and inductance motors respectively;

FIG. 8 is a plot of the open loop response of the system of FIGS. 6A and 6B to a disturbing force; and

FIGS. 9 and 10 are graphs showing curves which represent the characteristic response of the system to load and track disturbances.

DETAILED DESCRIPTION

Referring to FIG. 1, an electroresponsive force generator M and a member R are separated physically by the air gap distance or length l. Generator M and member R are mutually attracted toward each other as indicated by the force field f set up therebetween by generator M when a voltage E supplies a I thereto, the attractive force being designated F.sub.M . Assuming the member R to be fixed, that is, nonmovable, the force F.sub.M is directed to depict that the generator M is attracted toward member R.

When the generator M, for example, is an electromagnet, or an electric linear motor, and the member R, for example, is a ferromagnetic rail, the force F.sub.M varies as the square of the current flowing in the winding of the electromagnetic device M and inversely as the square of the air gap length l between the device M and the rail R in accordance with the equation:

F.sub.M = K.sub.1 (I.sup.2 /l.sup. 2) (1)

where:

K.sub.1 = [ A/(8 .times. 981)] (4.pi.N/10).sup.2 (1.sub.1)

where:

A is the area of attraction in square centimeters

N is the number of turns in the winding of electromagnetic device M

Equation (1) is derived from two basic equations expressing magnetic circuit principles, one being that the magnetic force F.sub.M between two parts of a magnetic circuit varies as the product of their area of attraction A and the square of the magnetic flux density B at their interface:

F.sub.M = AB.sup.2 /(8.pi. .times. 981) (1.sub.2)

where:

B is the flux density in gauss

F.sub.M is the force in grams

and the second principle being that the magnetizing force H required to set up a flux in an air gap l between the parts is equal to the flux density B:

B = H = 4 .pi. NI/10l (1.sub.3)

where:

NI/l is ampere turns per centimeter

l is air gap length in centimeters

B is flux density in gauss

Combining equations (1.sub.2) and (1.sub.3):

F.sub.M = [ A/(8.pi. .times. 981)] (4.pi.NI/10l ).sup.2

= [A/(8.pi. .times. 981)] (4.pi. N/10).sup.2 (I/l).sup.2

= K.sub.1 (I/l).sup.2 = K.sub.1 (I.sup.2 /l.sup.2) (1)

It will be noted that the magnetic force F.sub.M is the same for any air gap within a wide range of air gaps as long as the ampere turns per unit length or the air gap, namely, the ratio NI/l, is constant. Thus, for example, the attractive force will remain the same if the current is doubled when the gap length is doubled.

The linear relationship between the current and gap length is apparent from a re-write of equation (1):

I =(.sqroot.F.sub.M l)/.sqroot.K.sub.1 (1.sub.4)

where the current varies directly with the air gap and as the square root of the force F.sub.M. The current varies directly as the voltage E across the winding of the electromagnetic device M and can be changed by changing the voltage:

I = E/(R + j.omega. L) (2)

where:

R + j.omega.L is the winding impedance

R is the winding resistance

L is the winding inductance

j is the reactive symbol

.omega. is 2.pi.f

f is frequency in hertz (cps)

E is the voltage across the impedance.

Combining equations (1.sub.4) and (2):

E= [(.sqroot.F.sub.M l/.sqroot. K.sub.1) ] (R + j.omega.L) (2.sub.1)

the inductance of an electromagnetic device M separated from a ferromagnetic member R in a magnetic circuit the therewith having an air gap 1 therebetween varies inversely as the length of the air gap:

L = K.sub.2 /l (3)

Combining equations (2.sub.1) and (3):

E = K.sub.3 .sqroot.F.sub.M (lR + K.sub.4 j.omega.) (4)

or

E = K.sub.3 .sqroot.F.sub.M lR + K.sub.3 .sqroot.F.sub.M K.sub.4 j.omega. (4.sub.1)

In order to keep equation (4.sub.1) in balance, any changes in F.sub.M and/or in l in magnitude and rate must be accompanied by a change in E, and any such changes in E must be both in magnitude and rate of change, the latter giving rise to a frequency component in E, and this, in turn, causing the reactive voltage component K.sub.3 .sqroot.F.sub.M K.sub.4 j.omega. to increase directly in proportion to the increase in the frequency. The voltage E, of course, must increase, as required, to compensate for the increase in the winding impedance due to the increase in inductive reactance with frequency. At zero, or very low frequencies, the winding impedance is substantially resistive, and the voltage E is substantially equal to the resistive voltage component K.sub.3.sqroot.F.sub.M lR, the voltage E in such case being characterized only by its magnitude, being essentially d.c.

Referring again to FIG. 1; assume that an opposing force F.sub.O is acting on the force generator M in a direction opposite to the attractive force F.sub.M. If the attractive force F.sub.M is made to equal the opposing force F.sub.O, the separation distance l will be constant and the generator mass M will be in a state of stable equilibrium.

In the aforesaid parent application Ser. No. 131,041, a tracked, high speed vehicle is disclosed having four linear electric motors mounted at the four corners thereof for suspension and propulsion of the vehicle from and along the track by magnetic attraction. This arrangement is disclosed, in part, in FIG. 2, wherein the rear motors M.sub.1 and M.sub.2 are shown in spaced dependent relation to their respective support rails R.sub.1 and R.sub.2 , being separated therefrom by the air gaps l.sub.1 and l.sub.2. The rails are supported in fixed relation on the track generally designated T.

The vehicle V which moves along the track T is supported by and secured to the front and rear motors of which the rear motors M.sub.1 and M.sub.2 are shown secured to the vehicle as by the mounting brackets schematically designated b.sub.1 and b.sub.2.

The magnetic attractive forces F.sub.M1 and F.sub.M2 respectively of the motors M.sub.1 and M.sub.2 are opposed by the forces F.sub.O1 and F.sub.O2. These opposing forces may be considered generally to be acceleration forces expressed by the equation:

F = Ma (5)

where:

F is the acceleration force

M is the mass of the body acted upon by the force F

a is the acceleration of the body represent W

When the air gaps l.sub.1 and l.sub.2 are static, there being no change in the gaps, the corresponding forces F.sub.O1 and F.sub.O2 represent the weights supported respectively by the magnetic forces F.sub.M1 and F.sub.M2 of motors M.sub.1 and M.sub.2. Weight W is the force which gravitation exerts upon a body and is equal to the mass of the body times the local acceleration of gravity g, thus:

F = Ma

as before set forth in equation (5). Now with g substituted for a, and W substituted for F:

W = Mg

and

M = W/g (6)

Motors M.sub.1 and M.sub.2 by their attractive forces F.sub.M1 and F.sub.M2 support their own weights W.sub.M1 and W.sub.M2 and one fourth the weight Wv/4of the vehicle, thus: ##SPC1## 4

Vehicle V carries a pair of position or placement sensors S.sub.P1 and S.sub.P2 which respectively sense the length of the air gaps l.sub.1 and l.sub. 2 associated with motors M.sub.1 and M.sub.2. Signals from these sensors operate in their respective feedback circuits, subsequently to be described, to produce voltages therein which represent the attractive forces F.sub.M1 and F.sub.M2 required to produce the voltages E.sub.1 and E.sub.2 for support of the motors M.sub.1 and M.sub.2 at selected gaps l.sub.1 and l.sub.2, such representative voltages corresponding to the voltage component F.sub.M of equation (4).

When it is desired to maintain constant motor gaps notwithstanding changes in passenger loading, or wind loading, on the vehicle, such changes will, in turn, change the opposing forces and the gaps. The position sensors, however, sense the gap changes and produces signals which are integrated to produce appropriate adjustment in the feedback voltages representing the forces F.sub.M1 and F.sub.M2. These signals, moreover, are differentiated to provide velocity feedback for dampening adjustment of these voltages.

Vehicle V further carries accelerometer sensors S.sub.A1 and S.sub.A2 which are made to sense up and down accelerations of the vehicle caused, for example, by variations in the vertical radius of curvature of the track to thus produce signals for the further adjustment of the feedback voltages representing the magnetic forces F.sub.M1 and F.sub.M2 and, further, by the integration of such signals, to develop velocity feedback voltages for the development of the reactive voltage component of equation (4).

A second pair of accelerometers S.sub.A4 and S.sub.A5 are carried on the vehicle and directed to sense lateral accelerations occuring during turning movements of the vehicle so that signals therefrom may be used to produce relative adjustments of the gaps l.sub.1 and l.sub.2 for banking purposes, thereby obviating the need for banking the track and rails R.sub.1 and R.sub.2. Thus, for example, referring again to FIG. 2, and assuming that the vehicle V is caused to move in a turn to the left, the sensors S.sub.A4 and S.sub.A5 will sense acceleration forces directed to the right of the vehicle, and signals from sensor S.sub.A4 associated with motor M.sub.1 will cause a decrease in gap l.sub.1 and sensor S.sub.A5 associated with motor M.sub.2 will cause an increase in gap l.sub.2, thereby to effect the desired banking to negotiate the left turn.

Referring now to FIG. 3, there is shown thereon a vehicle V.sup.1 having three linear electric motors M.sub.3, M.sub.4 and M.sub.5 of which M.sub.3 is used for suspension and propulsion, or for suspension alone, and motors M.sub.4 and M.sub.5 are used for guidance and propulsion, or for guidance alone. Their respective force fields are designated f.sub.3, f.sub.4 and f.sub.5, and are generated in relation to their associated fixed rails R.sub.3, R.sub.4 and R.sub.5 in the same manner as the force fields f.sub.1 and f.sub. 2 of motors M.sub.1 and M.sub.2 of FIG. 2.

The gaps l.sub.4 and l.sub.5 will normally be equal so that the magnetic attractive forces F.sub.M4 and F.sub.M5 will also be equal and, being opposite, will present the required opposing force, each to the other, to maintain balance. In this case, the attractive forces, at equal gap lengths l.sub.4, l.sub.5, may be set at any desired strength upwards from zero. At zero force setting, of course, there would be no force fields f.sub.4 and f.sub.5.

Considering first the zero force field setting at equal gaps, it will be presumed that provision is made, as subsequently described, for producing either of the forces F.sub.M4 and F.sub.M5 as its associated motor M.sub.4, M.sub.5 is moved with the vehicle to increase its gap l.sub.4 or l.sub.5 above the equal gap setting In such case, the generated attractive force will setting. in proportion to the increase in gap and will oppose the acceleration force on the vehicle which caused the particular gap l.sub.4 or l.sub.5 to increase. In this case, one of the accelerometer sensors S.sub.A4 or S.sub.A5 will aid in the development of the attractive force required to overcome the lateral acceleration force. When the acceleration ceases, the other sensor will generate an opposing attractive force to control the deceleration of the vehicle upon return of the same to the equal gap condition.

When it is desired to use the force fields f.sub.4 and f.sub.5 for propulsion, in addition to guidance, some suitable strength of opposing attractive forces F.sub.M4 and F.sub.M5 is maintained at all times.

The feedback circuits of FIGS. 4 and 4A are taken from the parent application and are incorporated in this disclosure as embodiments of suitable circuitry for developing the magnetic attractive forces F.sub.M1 to F.sub.M5 of FIGS. 1 to 3, the feedback circuits for this purpose performing the multiplications and summations of equation (4). Other disclosures of the parent application are incorporated herein by reference to that application.

Referring first to FIG. 4, the accelerometer 20 represents any of the accelerometer sensors S.sub.A1 and S.sub.A2 of FIG. 2 and S.sub.A3 of FIG. 3 which have a mass of relatively appreciable magnitude disposed to be sensitive to vertical accelerations. It also represents either of accelerometer sensors S.sub.A4 and S.sub.A5 as the same are employed in the FIG. 2 and FIG. 3 arrangements to sense lateral acceleration and thereby provide inputs to the feedback circuits of motors M.sub.1 and M.sub.2 and motors M.sub.4 and M.sub.5 respectively, in the same manner as sensors S.sub.A1 and S.sub.A2 provide inputs to their respective feedback circuits.

Accelerometer 20 may be of a piezoelectric type, such as Endevco type 2200, or a servo type such as developed for space use which does not have the very low frequency "noise" and random variations characteristic of the piezoelectric types.

Signals from accelerometer 20 pass through a compensating network 21 which alters the frequency vs. amplitude response thereof to provide about 10 db of feedback within the range of frequencies of the order of 1/2 to 5 hertz to make the suspension system insensitive to second order variations such as variations in motor magnetic structure, variations in the a.c. resistance of windings, winding resistance variations with temperature, d.c. and a.c. gain variations in the feedback network, and instability at certain gap lengths. Network 21 also integrates the accelerometer signals to provide velocity feedback which is effective over a range of frequencies of the order of 4 to 10 hertz.

Position transducer 22 is a sensor element which provides length of gap information and represents any of the length of gap sensing position or placement sensors S.sub.P1 to S.sub.P5 of FIGS. 2 and 3. Sensor element 22 may employ mechanical contact, or optical, sonic or other suitable means to accomplish measurement of the gap which may range from substantially zero to one-half inches.

Position transducer 22, for example, may be a linear potentiometer having a mechanical roller which is carried by its slider and urged yieldably into contact with rail 2 whereby the potentiometer is adjusted as the roller and slider are moved in response to any changes in the motor-to-rail gap as the roller rides along the rail. Motor 1 and rail 2 represent the various motor and rail combinations disclosed in FIGS. 2 and 3, and the potentiometer may be suitable carried either by the vehicle or on the particular motor with which it is used.

An optical displacement sensor 22 may be arranged with a photocell on one side of the motor-rail gap and illumination means on the other so that more or less light is caused to enter the photocell to change its electrical response as a function of gap length.

An ultra-sonic sensor 22 may be arranged to produce ultra-sonic sound reflections from the rail so that detected changes in phase of the transmitted and reflected sound may provide a suitable measure of gap length and changes therein.

Signals from position transducer 22 are supplied to a compensating network 23 and also to a multiplier 25, subsequently to be described.

Compensating network 23 provides an adjustable reference for the gap measurement in electrical terms, that is to say, this reference may be adjusted to preset a selected gap which the position sensor will seek. The compensating network 23 also has provision for adjusting its position signal to zero for a selected gap, or to some strength other than its normal signal for that gap for purposes of the FIG. 3 vehicle guidance operation, aforedescribed. The compensating network 23, moreover, has provision for receiving signals from the accelerometer sensors S.sub.A4 and S.sub.A5 of FIG. 2 to provide banking adjustment of gaps l.sub.1 and l.sub.2, as aforedescribed. Network 23, in addition, provides velocity and integrated displacement feedback. Integration is performed over a range of frequencies from 0 to about 1.2 hertz, and differentiation is performed over a range of frequencies from 1.2 to about 5 hertz.

Signals from the compensating network 23 pass to compensating network 21 where they are combined, that is, are algebraically summed with the acceleration signals for common amplification to provide a force-proportional voltage representative of the function F.sub.M in equation (4). This force-proportional voltage operates in the whole feedback system to enable motor 1 to produce a magnetic force F.sub.M of 1 g, that is, an equal and opposite force in relation to gravity whereby the motor-vehicle mass is magnetically suspended.

As hereinbefore discussed, the magnetic force F.sub.M is proportional to the square of the motor current which is a non-linear relationship which must be linearized in order to provide feedback stability. Linearization is achieved by taking the square root of the force-proportional voltage output of network 21 in accordance with the mathematical requirement expressed by the function .sqroot.F.sub.M in equation (4).

This required square-rooting of the force-proportional voltage output of network 21 is performed by the square-root circuit 24 which is typically an operational amplifier entity employing non-linear transistor characteristics to give an electrical output that is the equivalent of the square-root of the electrical input.

The length of gap and square-root outputs of position transducer 22 and square-root circuit 24 are applied as first and second inputs to multiplier 25 and multiplied thereby to provide a product which corresponds to the product requirement .sqroot.F.sub.M .times. lR of equation (4). Multiplier 25 is an operational entity whose output is the product of two electrical inputs, and it thus provides an output voltage that increases with gap length. The electrical path through multiplier 25 is independent of frequency so that an output is produced thereby at zero frequency which is the condition when the gap length is constant between the motor 1 and rail 2.

The output of square-root circuit 24 is also applied to perfect differentiator 26 which is an amplifier having a resistance-capacitance circuit to perform electrical differentiation and thus provide the first derivative of its input over a frequency from substantially zero to 200 hertz. The capacitor is not shunted by any conductive path and so the output of the differentiator is zero for zero frequency, that is, for d.c., which is the condition when the motor-to-rail gap is constant. The amplifier-differentiator circuit of perfect differentiator thus produces and provides an a.c. path for the voltage which represents the reactive component j.sqroot. F.sub.M .times. K.sub.4 .omega. of equation (4). The output of differentiator 26 thus provides a voltage which increases with the feedback frequency, that is, the frequency of the sensed signals.

The outputs from multiplier 25 and differentiator 26 are summed algebraically to provide to the input of amplifier 95 a feedback control voltage which represents the sum of the resistance and reactance voltage components of equation (4), namely,

.sqroot.F.sub.M lR + j.sqroot.F.sub.M K.sub.4 .omega.

or

.sqroot.F.sub.M (lR + jK.sub.4 .omega.).

After amplification at level raising amplifier 95, and gain setting potentiometer 96, the feedback control voltage is applied to the controllable power supply 38 which is a power amplifier of the Class B type for low power output of about one kilowatt or of the Class D type or gated-silicon-controlled-rectifier type for higher power outputs. The basic source of power for these amplifiers, for example, is an external power supply 39 having 3rd rail connections 39' with the vehicle V.

Controllable power supply 38 provides the terminal voltage E applied to motor 1 to develop the magnetic attraction force F.sub.M. The combined gains of potentiometer 96 and the voltage gain of amplifier 38 determines the constant K.sub.3 in equation (4) such that the motor terminal voltages becomes:

E = K.sub.3 .sqroot.F.sub.M (lR + jK.sub.4 .omega.)

which is equation (4).

The motors may be built in a large range of sizes, but as an example, for a 30 inch long motor capable of supporting 2,000 pounds, the several aforementioned constants may have values expressed in inches as follows:

K.sub.1 = 0.48 K.sub.2 = 0.1 K.sub.3 = 2.1 K.sub.4 = 0.1.

Referring now to FIG. 4A, accelerometer 20 is a piezoelectric accelerometer of the Endevco type 2200 and is shown to have a mass 40 of appreciable magnitude which is so disposed on the vehicle V or on motor 1 of FIG. 4 so as to be sensitive to vertical acceleration to thus enable the accelerometer to perform its required feedback functions, as aforedescribed, as well as to provide the "soft" ride features which characterize this invention.

Amplifier entities 41, 42 and 43 comprise elements of compensating network 21.

Amplifier 41 is a known impedance-matching amplifier and is required to reduce the very high impedance of a piezoelectric accelerometer to an ordinary circuit value. The amplifier is a Motorola MC 1456G integrated circuit amplifier, or an equivalent operational amplifier. It is connected as a source-follower and has no gain, nor phase shift. The input circuit includes resistor 44, of 250 megohms resistance, connected from amplifier terminal 3 to ground to provide an input bias current path for the amplifier. This is shunted by capacitor 45, of 1,000 picofarads (pf) capacitance, which acts as a padding capacitor to the stray capacitance of the input lead from the accelerometer to terminal 3. The several terminals of the integrated circuits, operational amplifiers, etc. have been given small numerals, corresponding to those given by the manufacturer on the device itself. The internal circuits for these devices are known from the manufacturer's catalogs.

Amplifier 41 has a feedback circuit between its terminals 6 and 2 comprised of a 250 megohm resistor 46, shunted by capacitor 47, of 1,000 pf capacitance. Terminal 7 is connected to a direct current energizing power source having a voltage of the order of + 15 volts, while terminal 4 is connected to a similar source having the opposite polarity of - 15 volts. Each of these connections is filtered by a 0.1 microfarad (.mu.f) capacitor connected therefrom to ground.

Capacitor 48, of 200 .mu.f capacitance, is connected to the output terminal 6 of amplifier 41 to restrict the low frequency signal amplitude from the accelerometer with a roll-off starting at 0.13 hertz. This removes the "noise" from the accelerometer circuit at low frequencies. Resistor 49, of 6,800 ohms, connected in series with capacitor 48 and with resistor 50, of 0.2 megohms, sets the accelerometer channel gain. Amplifier 42 provides an accelerometer channel gain of 200/6.8 = 30. The second terminal of resistor 49 connects to input terminal 2 of amplifier 42, a Motorola MC 1741CG integrated circuit or equivalent.

There is also another connection to terminal 2; from the output of the gap-length sensor circuit, to be later described.

Amplifier 42 functions as a simple amplifier, having a feedback circuit connected between input terminal 2 and output terminal 6 comprised of resistor 50, of 20 K ohms, shunted by capacitor 51, of 1,500 pf. The voltage supply and grounding connections are standard and are known. The gain of amplifier 42 is approximately 30, up to an upper cut-off frequency of 8 hertz.

The algebraically summed signals from the accelerometer and gap-sensor now pass into terminal 2 of amplifier 43, of MC 1741G type, through resistor 53, of 30,000 ohms resistance, which is used for gain setting. The feedback circuit of amplifier 43 is the same as that of amplifier 42; i.e., resistor 50' of 0.2 megohm and capacitor 55 of 0.2 microfarad. Supply circuits are conventional. The gain of amplifier 43 is approximately 7, with an upper cut-off frequency of 4 hertz.

Capacitor 55 acts as a partial integrator upon the acceleration feedback signal. This provides a quasi-velocity feedback signal and prevents an oscillatory condition otherwise existing because of an 180.degree. phase shift between acceleration and displacement. This is effective from a frequency of the order of 10 hertz down to 4 hertz. Below 4 hertz differentiation of the position (displacement) feedback occurs to provide the velocity component. This is produced by capacitor 58 in the input circuit to amplifier 61, hereinafter to be described.

The combination of these two signals gives control of the phase of the feedback circuit so that displacement information can be fed into a system that has feedback from an accelerometer included in it. Actually, four aspects of feedback are present in the system to give a high degree of stability; the integral of displacement to bring the system back to a mean gap length after load changes in the vehicle, displacement feedback to stabilize the integral displacement feedback circuit, velocity feedback to stabilize and damp the displacement feedback, and acceleration feedback to stabilize and damp the velocity feedback. At the same time the acceleration feedback corrects second order non-linearities in the linearizing circuit comprised of square-root circuit 24, multiplier 25, and differentiator 26. This mode of operation is required for any system of the nature of a magnetically supported railroad, where the air-gap length is purposely allowed to vary to accommodate "rough track." The gap is brought back to a mean value gradually, to provide a "soft" ride.

Position transducer 22 is shown to be a potentiometer 56 connected to ground and shunted by a source of voltage such as battery 57. Its slider or wiper carries the aforedescribed rail-engaging-roller, not shown. Typically, battery 57 may have a voltage of 10 volts and the travel of the slider have a travel of one-half inch. This range of travel normally covers the operating change in the length of the air gap, the preferred length of which is one-quarter inch or perhaps slightly less. These constants give a voltage of 20 times l; i.e., 20 times the length of the air gap as measured in inches. Battery 57 may, alternately, be a regulated power supply of the same voltage.

The output from position transducer element 22 passes to compensating network 23. Capacitor 58, of 0.1 .mu.f, in series with resistor 59, of 4,700 ohms, all shunted by resistor 60, of 1.5 megohms, are the initial elements of compensating network 23. This network has a resistive impedance of 1.5 megohms from d.c. to 1.2 hertz, decreasing to about 4,700 ohms at 350 hertz. This provides a velocity signal (i.e., differentiated displacement) at frequencies above 1.2 hertz.

This output passes to input terminal 2 of operational amplifier 61, an MC 1741G type. Both input terminals 2 and 3 of this amplifier are individually returned to ground through resistors 62 and 63, of 22,000 ohms, to provide a path for the input bias currents of this amplifier.

The feedback circuit for amplifier 61 is comprised of resistor 64, 10,000 ohms, in series with capacitor 65, 100 .mu.f; with resistor 66, 100,000 ohms, shunted across the capacitor. This gives an impedance of 110,000 ohms for d.c. and of 10,100 ohms at 14 hertz, approximately. This results in the gain of amplifier 61 at frequencies below 1 hertz being considerably greater than at higher frequencies. This is to increase the loop gain at low frequencies and to provide an integral of displacement function as a feedback signal to gradually correct for changes in load.

Since the purpose of the feedback system is to correct for changes in loading of the vehicle, wind pressure and unevenness of the track, the frequency of the feedback signals is very low with respect to the frequencies handled by usual electrical networks. Feedback must be maintained at zero frequency (d.c.). The range of frequencies of maximum interest extends from 0 to 5 hertz for the displacement channel and from 0.3 to 30 hertz for the accelerometer channel.

Potentiometer 67, of 50,000 ohms total resistance, is connected between positive and negative voltage supply sources, each of which has a voltage of 15 volts with respect to ground. Bypass capacitors, of 50 .mu.f, are provided from each to ground to remove extraneous variations, as known. Potentiometer 67 provides a voltage adjustment for any initial offset voltage in amplifier 61. Its slider is connected to input terminal 3 thereof, through isolating resistor 67' of 1 megohm.

An additional input to terminal 3 of amplifier 61 is from potentiometer 68, of 2,000 ohms, and passes through attenuating resistor 68' of 1.5 megohms, to provide a reference displacement proportional voltage. Amplifier 61 generates an output voltage proportional to the difference between the voltage reference input to resistor 68' and the input to resistor 60, which is the voltage from displacement transducer 22. Voltage dropping resistor 69, connected in series with potentiometer 68 from the positive voltage connection to ground, typically has a resistance value half as great as the resistance value of potentiometer 68.

The output of amplifier 61, from terminal 6, passes to terminal 2 input of amplifier 42 through resistor 66', of 22,000 ohms, a summing resistor. It is at this point that compensating network 23 joins that of 21, for the inclusion of amplifiers 42 and 43 in common. The output from amplifier 43 is taken from terminal 6 and passes through diode 54 with the cathode thereof connected to the terminal so that only negative signal variations will be passed on. Additionally, diode 52 is connected as a feedback element on amplifier 43 to prevent positive voltage excursions.

Only negative voltages are allowable at the input of the square-root circuit which follows because inversion therein to positive signal polarity occurs before the square-root function takes place. This prevents taking the square-root of negative numbers, which are imaginary. Herein the square-root circuit becomes inoperative because feedback of positive polarity drives it to current saturation.

The force-proportional voltage output at amplifier 43 is made to be linearly proportional to a force between the load mass and the rail. Referring to equation (4), to develop the proper voltage E to be applied to the motor windings, the force-proportional voltage is to be square-rooted and multiplied by (lR + jK.sub.4 .omega.).

The first electrical device to significantly execute the mathematics of linearization is the square-root circuit 24. This may be an integrated circuit 24', of type MC 1494L (Motorola) normally known as a "multiplier" of electrical signals fed into it. This multiplier is placed in the feedback circuit of an operational amplifier 70 and the square-root of the signal input is provided therefrom. The theory and practice of this square-root performance is known, being set forth in the (Motorola) manufacturer's, "Specifications and Applications Information," October 1970 -- DS 9163. Operational amplifier 70 may be an MC1741G integrated circuit.

The output from the previously mentioned diode 54 is connected to gain-setting resistor 71, of 52,000 ohms, and also to ground through resistor 72, of 1,000 ohms. The latter resistor provides a path for any leakage current in diode 54. The input from resistor 71 is connected to terminal 14 of multiplier 24' and also to terminal 2 of amplifier 70. The output of this amplifier, at terminal 6, is connected to terminals 9 and 10 of the multiplier and also to ground by a small capacitor 73, of 10 pf capacitance, in series with resistor 74, of 510 ohms. Zener diode 75 is also connected between the output of amplifier 70 and ground to prevent accidental latch-up (malfunctioning) of the circuit. A type 1N5241 may be used.

The feedback path for amplifier 70 is the multiplier 24' connected between input terminal 2 and output terminal 6 of amplifier 70 and terminals 9 - 10 and 14 of the multiplier. Capacitor 76, of 10 pf capacitance, is connected between amplifier terminals 2 and 6 for the purpose of phase-compensating the amplifier. Input terminal 3 thereof is connected to the slider of potentiometer 77, which potentiometer has a resistance of 20,000 ohms. This provides a voltage reference for the amplifier. This potentiometer is connected in parallel with a duplicate potentiometer 78, which is connected between terminals 2 and 4 of multiplier 24'. A resistor 79, of 62,000 ohms, and a resistor 80, of 30,000 ohms, are respectively connected between terminals 7 and 8 and 11 and 12 of multiplier 24'; and a resistor 81, of 16,000 ohms, is connected between terminal 1 and ground. A voltage source, typically of 15 volts of positive polarity, is connected respectively to terminals 7 and 15 of the amplifier and multiplier, whereas a voltage source typically of 15 volts of negative polarity, is respectively connected to terminals 4 and 5 of the amplifier and multiplier.

At the input to the square-root circuit 24, a negative signal voltage of 4 volts produces in the whole system a force of 1 g; that is, there is produced an equal an opposite force in relation to that of gravity, whereby the motor-vehicle mass is magnetically suspended. With the connections and voltages given, the output of the square-rooter circuit 24 at terminal 6 of amplifier 70 is the square-root of 10 times the input. This is the square-root of 10 in effective amount and is taken into consideration in establishing the whole feedback gain. Mathematically, such functioning of the electrical circuits is accounted for in the values of the several K constants.

The output from the square-root circuit is connected to the input of multiplier 25 to perform the lR portion of equation (4), and also to the input of perfect differentiator 26 to perform the jK.sub.4 .omega. term. The input to multiplier 25 is terminal 10 of multiplier 25' and to the perfect differentiator is capacitor 83 through resistor 90.

The above input to the multiplier may be termined the x input. The y input is connected to input terminal 9 and comes directly from potentiometer 56 of position sensor 22 through resistor 84 for isolation. The resistance value of resistor 84 may be 0.1 megohm. Both input terminals 10 and 09 are also connected to ground through capacitors 85 and 85', of 10 pf capacitance, in series with resistors 86 and 86', of 510 ohms resistance, respectively. These prevent high frequency parasitic oscillations.

Resistors 79', 80' and 81' are identical in resistance value and connection to multiplier unit 25' as these were with respect to unit 24' of square-root circuit 24. So also are potentiometers 77' and 78', except that the resistance value of potentiometer 77' is 50,000 ohms. An additional potentiometer 87, of 20,000 ohms, is connected across terminals 2 and 4 of units 25', with the slider connected to terminal 6. These three potentiometers are adjusted to give proper x, y and output offset bias, as outlined in the manufacturer's "Specification and Application Information" previously referred to.

An MC 1741G operational amplifier 89 coacts with multiplier unit 25' to give the complete multiplier 25. Feedback capacitor 76', of 10 pf, is connected to the amplifier at terminals 2 and 6, and is shunted by resistor 88, of 52,000 ohms. Positive and negative voltage supply sources are as previously described.

Perfect differentiator capacitor 83 has a capacitance of 0.2 .mu.f. It is in series with resistor 90, of 1,000 ohms resistance. The capacitor connects to input terminal 2 of operational amplifier 91, which may be a MC 1741G type. The feedback circuit of this amplifier is comprised of capacitor 92, of 0.0068 .mu.f, and resistor 93, of 0.1 megohm, in parallel and connected between amplifier terminals 2 and 6. Second input terminal 3 is grounded. Positive power supply voltage is connected to terminal 7, while the same in negative polarity is connected to terminal 4. This amplifier-differentiator provides the first derivative of the input over a frequency range of from essentially zero to 200 hertz.

The output from amplifier 91 is taken through summing resistor 94, of 62,000 ohms, to input terminal 2 of amplifier 95. The latter mainly raises the signal level, after providing for the summing, for parallel feeding all of the three-phase multipliers that follow. Similarly, the output from multiplier operational amplifier 89 is taken through summing resistor 94', of 62,000 ohms, and connects to input terminal 2 of amplifier 95. This provides the total electrical representation of .sqroot.F (lR + jK.sub.4 .omega.) of equation (4).

The feedback circuit 92', 93' of amplifier 95 is the same as the feedback circuit 92, 93 of amplifier 91; also, input terminal 3 is connected to ground and the power supply connections are the same as for amplifier 91.

The output at terminal 6 of amplifier 95 passes to potentiometer 96, which is grounded, as shown. The slider of the potentiometer is connected to the controllable power amplifier 38 of FIG. 4 which provides a motor terminal voltage and motor current which, in turn, produces a magnetic force F.sub.M equal to 1 g when a negative voltage input to the square root circuit is 4 volts.

Considering operative details of the feedback circuits of FIGS. 4 and 4A which are designed to provide a "smooth" ride in the transportation of people, adjustment of the suspension gap length l is accomplished by varying the voltage at input 3 of amplifier 61, as determined by the setting of potentiometer 68. The gain of amplifier 41, of course, is unity. The gain of amplifier 42 is approximately 30, up to an upper cut-off frequency of 8 hertz. The gain of amplifier 43 is approximately 7, with an upper cut-off frequency of 4 hertz. When the output of this amplifier is -4 volts, the force exerted by motor 1 is 1 g; i.e., the vehicle is suspended.

In forming the feedback circuits according to this invention use is made of the fact that the a.c. flux density in the motor to rail air-gap does not vary if the length of the gap changes. This flux density is affected only by the value of the volts-per-turn in the magnetic structure, and so the voltage only in any given magnetic structure. Multiplier 25 provides compensation for d.c. flux density changes with change in the length of the air-gap. Position transducer element 22 senses the d.c. gap length and the gain of the feedback circuit is modulated to increase with gap length, maintaining the overall system gain, including the characteristics of motor 1, constant.

In a typical motor the inductive reactance of the coils is equal to the resistance of the coils at a frequency of the order of 2 hertz. The inductance varies inversely with the length of the air-gap. Proper feedback performance is maintained, however, by provision of the d.c. path through multiplier 25 and the a.c. path through perfect differentiator 26. The exciting current through the motor coils increases with gap length, thus the d.c. flux remains constant.

In practical operation, this necessary mode of operation requires that extended periods of suspension at long air-gaps cannot be allowed. It is good practice to rate the amplifiers comprising controlled power supply 38 for the average length of gap encountered and to return the vehicle to that length within a few seconds without causing an artificial jolt after a gap-lengthening perturbation.

The force exerted magnetically by the motor in providing suspension varies as the square of the current in the windings of the motor. This is a non-linear relation. Non-linear elements in the feedback circuit, such as the square-root circuit 24 of FIGS. 4 and 4A make the output of the feedback circuit linear, from a voltage input to a force output. This results in a constant feedback loop gain at all values of alternating current frequency and at all gap lengths of the motor to the rail. Moreover, this results in a uniform easiness of ride. A typical variation of gap may extend from + 100 percent to nearly - 100 percent of a normal value of 1.0 inch. To prevent the motor from actually contacting the rail, a flat automotive type brake shoe may be arranged to bear upon the rail instead, as a safety measure.

Because an inertial reference, accelerometer 20, is used in the vertical plane, the feedback circuit ignores small track irregularities and does not pass them on to the passengers in the form of vibration or quick jolts. Only a mean gap is maintained by the displacement (position) transducer 22.

Referring again to the FIG. 4A showing of compensating network 23, a selected gap l for suspension would normally be set by adjustment of potentiometer 68. If the same magnetic forces involved in suspension are applied laterally as in FIG. 3, and the motors M.sub.4, M.sub.5 therein have selected gaps which are equal, the magnetic forces F.sub.M4 and F.sub.M5 will be equal and opposite and each have a magnitude corresponding to their equal gaps determined by adjustment of their respective potentiometers 68. When it is desired that the forces F.sub.M4 and F.sub.M5 be generated only upon deviations from the equal gaps, offset voltage adjusting potentiometer 67 is set to reduce the voltage applied to input terminal of amplifier 61 to zero.

When it is desired that some magnetic coupling between the rails R.sub.4 and R.sub.5 and motors M.sub.4 and M.sub.5 be maintained at all times, as for increased stability in guidance control notwithstanding the accompanying magneti drag, or to provide propulsion, the potentiometers 67 for the respective motors may be set at some suitable value to provide strengths F.sub.M4 and F.sub.M5 which are greater than zero at equal gap settings.

For purposes of achieving banking of the vehicle V shown in FIG. 2, banking control channels for accelerometer sensors S.sub.A4 and S.sub.A5 respectively comprise its accelerometer and an amplifier such as amplifier 41 together with its associated input and output circuit elements. In such case, the output resistor 49 of each banking control channel is connected as shown in FIG. 4A to the slider of potentiometer 67. Any input from the banking channel will thus alter the gap as long as the lateral turning force sensed by its accelerometer persists.

Reference is now directed to FIGS. 5 and 6 which disclose the preferred embodiment of a complete feedback circuit for controlling both the suspension and propulsion of a tracked vehicle-linear electric motor system such as disclosed in FIG. 2.

Referring first to FIGS. 5 and 2, the accelerometer 20, as before, provides a signal proportional to an upward or downward inertial force acting on the vehicle V. The position transducer 22, as before, provides a signal proportional to the length of the motor-to-rail gap l.

The frequency compensating networks 21' and 23' have generally the same composition as their counterpart circuit networks 21 and 23, of FIG. 4, and function, moreover, generally in the same manner to produce at the output of network 21' a force-proportional voltage which represents the quantity F.sub.M in equation (4). When this voltage is a negative 4 volts, the terminal voltage at the motor windings is just sufficient so that the motor produces a suspension force F.sub.M of 1g.

Square root circuit 24" also has generally the same composition and functions generally in the same manner as its counterpart element 24 in FIG. 4 whereby the square root of the force-proportional voltage represented by .sqroot.F.sub.M in equation (4) is provided in its output.

For the purposes of explaining the feedback circuit arrangement of FIG. 5 and its manner of functioning to perform the summations and multiplications required by equation (4), this equation preferably is expressed in the form:

E = K.sub.1 .sqroot. F.sub.M (lR + jK.sub.2 f) (9) =K.sub.1 .sqroot. F.sub.M lR + jK.sub.1 .sqroot. F.sub.M (9A) b.2 f

where:

j represents the reaction symbol

f is the propulsion frequency

K.sub.1 and K.sub.2 have constant values hereinafter to be described.

The multiplications and product summations involving the square-root quantity .sqroot.F.sub.M as set forth in equation (9) are performed in a frequency control channel presently to be described. This channel comprises speed control 30, three phase variable frequency oscillator 31, multipliers 120 to 122 and 135 to 137, and differentiators 143 to 145.

Speed control 30 controls the frequency of oscillator 31 which preferably provides the three phase voltages .phi.A, .phi.B and .phi.C, although any number of phases from two upward may be used. The three phases typically are separated by 120 electrical degrees in time, and the circuits and windings 111, 112 and 113, FIG. 6B, are typically "star" (i.e., "Y") connected. Oscillator 31 supplies alternating current at constant amplitude and essentially of sinusoidal shape over a frequency range from zero frequency at standstill to a low audio frequency of the order of 80 hertz at high speed.

When the system is in operation at standstill and zero frequency, each phase of the oscillator is required to produce an output to enable the feedback circuit to provide the suspension magnetic flux in the motor-to-rail gap. It will be understood, however, that the system may be operated at standstill at any frequency providing at least one of the three phase windings is disconnected so that the moving field required for propulsion is not established, and at least one of the phased circuits is in operation to enable the feedback circuit to develop the suspension flux.

Oscillator 31 may be comprised of three mechanically driven sine-wave-generating potentiometers to provide relatively low frequencies, the potentiometers being rotated by hand for testing or by a geared-down variable speed motor for relatively low speed transport use. In such case, speed control 30 is a rotatable shaft, hand or motor driven, having three potentiometer sliders attached thereto and angularly spaced apart from each other thereon by 120 electrical degrees. The potentiometers are of circular configuration and suitable for full and repeated rotation of the sliders thereon. The potentiometers preferably are wound to provide sinusoidal voltage variations with rotation of the sliders, the three phase output being provided therefrom when a d.c. source is applied across the potentiometers connected electrically in parallel.

Oscillator 31, alternatively, may be a function generator such as type 120- 020-3, manufactured by the Wavetek company of San Diego, Calif. Such oscillators are voltage responsive, the frequency output increasing with the input voltage. In such case the speed control device 30 may be a potentiometer.

The three phase output from oscillator 31, namely, phased voltages .phi.A, .phi.B & .phi.C, are applied as the X inputs to multipliers 120, 121 and 122, respectively, the aforementioned square root voltage from the square-root circuit 24" being applied to the Y inputs thereof. The resulting product output of each of these multipliers is a sinusoidal voltage having a magnitude represented by the equation product K.sub.1 .sqroot. F.sub.M.

The outputs from multipliers 120, 121 and 122 are applied, respectively, as the X inputs to multipliers 135, 136 and 137, the aforementioned air gap length proportional signal from transducer 22 being applied to the Y inputs thereof. The resulting product output of these multipliers is a sinusoidal voltage having a magnitude represented by the equation product K.sub.1 .sqroot. F.sub.M lR. This voltage is the resistive or non-reactive component of the feedback control voltage E of equation (9A).

It will be understood that each of multipliers 120, 121 and 122 and 135, 136 and 137 gives the product of its X and Y inputs whether or not there is propulsion, that is, whether or not, the .phi.A, .phi.B and .phi.C voltages are varying sinusoidally or are "frozen" to instantaneous values at standstill. A common control is thus exercised over the control signals and suspension is maintained both at standstill and during propulsion.

It will also be understood that multipliers 120 to 122 and 135 to 137 have substantially the same composition and function as the aforedescribed multiplier 25 of FIGS. 4 and 4A and thus, like multiplier 25, are not influenced by the frequency of the signal inputs thereto since the paths therethrough are essentially d.c. The varying frequency of the X inputs to the multipliers will thus have no effect on the magnitude of their outputs, and the frequency can be varied as required for vehicle speed control without affecting the feedback voltage control required to maintain suspension.

The impedance of the motor windings, however, increases with frequency, as before discussed, and it is necessary therefore to increase the feedback voltage E accordingly so that the motor current will be of the proper strength to keep the suspension flux constant at all motor speeds. This increase in control voltage E as a function of propulsion frequence and speed, is provided by differentiators 143 to 145 which are connected in parallel across their associated multipliers 135 to 137, that is, the differentiators also receive the X input signals to their respective multipliers and supply their outputs to the inputs of the multiplier amplifiers, as will more fully appear in the description of the circuit details of FIG. 6B.

Differentiators 143 to 145 have generally the same composition and function generally in the same manner as perfect differentiator 26 of FIGS. 4 and 4A. Thus, each of these differentiators provides only an a.c. path therethrough and an output which is a first derivative of the input over a range of frequencies determined by the values of its resistance-capacitance. In the case of differentiators 143 to 145, the voltage output thereof, represented by the reactive voltage component K.sub.1 .sqroot. F.sub.M K.sub.2 f of equation (9A), will increase with frequency from zero to about 700 hertz, being zero to zero frequency.

A significant feature and arrangement of the feedback circuit of the present invention is that the increased voltage function provided by the differentiators to compensate for the increase in motor impedance with propulsion frequency does not affect the operations of the multipliers which are performed at voltage levels which vary only as required to support suspension, such variations being well within the dynamic response range of the multipliers. The dynamic response range of the differentiators, on the other hand, may be provided fully adequate to accommodate the large voltage increases imposed by the vehicle speed requirements.

The respective multiplier and differentiator outputs K.sub.l .sqroot. F.sub.M lR and K.sub.1 .sqroot.F.sub.M K.sub.2 f for each of phases .phi.A, .phi.B and .phi.C are summed in accordance with the requirement of equation (9A) and presented to the controllable power supply 38' which comprises three high power amplifiers 108, 109 and 110 which respectively receive the inputs for phases .phi.A, .phi.B and .phi.C. These amplifiers preferably are of the Class D type such as type MCB1002 available commercially from TRW Semiconductors, Inc. of Lawndale, Calif., or a pulse-width switching type which uses silicon-controlled-rectifiers instead of power transistors, such as Model Y-400642 available commercially from the Gates Learjet Corporation of Irvine, Calif.

Amplifiers 108 to 110 respectively supply their outputs to the phased windings 111 to 113, FIG. 6B. Wayside power for these amplifiers comprises a 3.phi. source 39' having 3rd rail connections 39" with controllable power supply 38'.

Referring now to FIGS. 6A and 6B for circuit details of the suspension and propulsion control circuit of FIG. 5, and first more particularly to FIG. 6A, the accelerometer 20, as before, has the massive weight 40 and connects to the impedance matching network 44, 45 and amplifier 41 of compensating network 21' generally in the same manner and for the same purpose as in the compensating network 21 of FIG. 4 except that a pre-amplifier or first stage amplifier 150 is interposed between the input network 44, 45 and amplifier 41 with an additional resistor 151 providing an input bias current path for amplifier 41.

Capacitor 48, as before, restricts the low frequency signal amplitude from the accelerometer with a roll-off starting at 0.13 hertz. This removes the accelerometer "noise" at low frequencies. Resistor 49, connected in series with capacitor 48 and resistor 50, together set the accelerometer channel gain, as provided by amplifier 42, to about 12, with a lower cut off frequency of about 0.3 hertz.

Resistors 152, 153, 53 and 50' set the accelerometer channel gain, as provided by amplifier 43 to about 7 with an upper cutoff frequency of about 1.7 hertz, this gain being principally set by resistors 50' and 53 as in the FIG. 4 arrangement. The resistance-capacitance network comprises of resistors 152 and 153 and capacitors 155, 156 and 157 provide a constant accelerometer gain of about 7.4 (17.4 db) over the frequency range from 0.3 to 3.0 hertz. This value of inertial acceleration feedback gives the vehicle an apparent mass of 7.4 times it actual mass over this frequency range.

Capacitor 55 acts, as in the FIG. 4A circuit arrangement, as a partial integrator upon the acceleration feedback signal to provide the quasi-velocity feedback effective over the range of frequencies from about 10 hertz down to 4 hertz. The frequency compensating network 21' makes a second order gain correction of about 10db of feedback to the overall feedback network over the frequency range from about (0.13) to about 5 hertz, the feedback provided by the frequency compensating network 23' otherwise dominating in the frequency range from zero to about 4 hertz.

The accelerometer channel loop gain vs. frequency will become more fully apparent from the graphical showing of FIG. 8, subsequently to be described. The specific component values for the circuit elements of the accelerometer and frequency compensating network 21' to provide the response represented by the graphs of FIGS. 8 to 10 are set forth in the following table:

Accelerometer Channel

20 Accelerometer Endevco Type 2200 44 Resistor 500 megohms 45 Capacitor 800 pf 150 Amplifier Philbrick/Nexu no. 1009 151 Resistor 10,000 ohms 41 Amplifier Motorola MC 1456 46 Resistor 0.1 Megohm 47 Capacitor 0.001 uf 48 Capacitor 200 uf 49 Resistor 1800 ohms 66' Resistor 22,000 ohms 42 Amplifier Motorola MC 1741 50 Resistor 20,000 ohms 152 Resistor 475 ohms 153 Resistor 475 ohms 154 Capacitor 6.8 uf 155 Capacitor 3.3 uf 156 Capacitor 3.3 uf 53 Resistor 30,000 ohms 43 Amplifier MC 1741 Motorola 50' Resistor 0.2 megohms 52 Diode 1N411 (Sylvania) 55 Capacitor 0.47 uf

Square root circuit 24" has generally the same composition and circuit arrangement as its counterpart circuit 24 disclosed in FIG. 4A except that the elements 73, 74 and 75 of FIG. 4A are not employed in the circuit arrangement of FIG. 6A.

The specific component values for the circuit elements of square-root circuit 24" are set forth in the following table:

Square-Root Circuit

24' Integrated Circuit MC1794L Motorola 54 Diode IN4148 (Sylvania) 70 Amplifier MC1456 (Motorola) 71 Resistor 51,000 ohms 72 Resistor 1,000 ohms 76 Capacitor 19 pf 77 Potentiometer 20,000 ohms 78 Potentiometer 20,000 ohms 79 Resistor 61,900 ohms 80 Resistor 30,100 ohms 81 Resistor 16,200 ohms

A position sensor 22' which may be of an eddy current type such, for example, as that available commercially from Kaman-Science Corp. No. KD-2300-10C is employed to provide positive potential with respect to ground. This eddy current sensor may be used in the circuit arrangement of FIGS. 4 and 4A in lieu of position transducer 22 employed therein. In the use of sensor 22', the length of air gap may be of the order of 2 inches, the normal value of the gap in such case being 1.0 inch.

Frequency compensating network 23' has generally the same composition and circuit arrangement as its counterpart network 23 disclosed in FIG. 4A except that terminal 3 of amplifier 61 is grounded and terminal 2 has the position voltage output of transducer 22' applied thereto and is returned to ground through resistor 62 connected in series with gap setting potentiometer 161 with appropriate polarity to provide negative voltage from its wiper W.sub.S to ground. Resistor 62 and potentiometer 161 provide the path for the input bias currents of amplifier 61, and wiper W.sub.S is preset in accordance with the desired operating gap. In response to the setting of wiper W.sub.S in the selected position, vehicle V seeks a motor-to-rail gap position in which the difference in the voltages on terminal 2 of amplifier 61 provides the required feedback to suspend vehicle V at the selected gap, this operation being substantially the same as described in connection with FIG. 4A.

The specific component values for the circuit elements of the displacement channel are set forth in the following table:

Displacement Channel

22' Position Transducer Kaman-Science KD-2300-10C 58 Capacitor 0.1 uf 59 Resistor 4700 ohms 60 Resistor 1.5 megohms 61 Amplifier MC1456 Motorola 62 Resistor 1.5 megohms 64 Resistor 0.36 megohms 65 Capacitor 8.4 uf 66 Resistor 3.6 megohms 160 Power Supply 10.4 volts d.c. 161 Potentiometer 1000 ohms

With reference to frequency compensating network 23', the integral of displacement provided thereby is performed by the action of its integrating capacitor 65, FIG. 6A. Any displacement signal from transducer 22' differing from the reference signal on wiper W.sub.S results in a slow voltage change across capacitor 65.

Assume, for example, that the load on vehicle V increases by 50 percent. This requires the output of amplifier 43 to change from the aforementioned -4 volts (equivalent to 1g) to -6 volts. The d.c. gain from the displacement transducer 22' to the amplifier 43 output is approximately equal to 155, derived as follows:

Amplifier Amplifier Amplifier 61 43 42 (Circuit elements) 50' .times. 50 .times. 64+66 , or, 152+153+53 66' 62 (Resistance Values) 2 .times. 10.sup.5 .times. 2.times.. 1 3.96 .times. 10.sup.6 3.095 .times. 10.sup.3 2.2 .times. 10.sup.4 = 155 approximately. 1.5 .times. 10.sup.6

After current has stopped flowing in integrating capacitor 65, there is a resultant displacement error of:

[-4 - (-6)]/155 = 0.0129 volts

at terminal 2 of amplifier 61. Since it is assumed that 20 volts at transducer 22' corresponds to 1 inch, as it does in the case of transducer 22 of FIGS. 4 and 4A, then:

(1" .times. 0.0129 volts)/(20 volts) = 0.0006" = 0.6 mil error

for a 50 percent load change.

The 0.6 mil error does not integrate to zero because resistor 66 is shunted across the integrating capacitor 65. This error is considered to have negligible effect on the operation of the feedback system, however, and as a practical matter, may be ignored.

As an alternative arrangement, the gap may be maintained constant not withstanding changes in loading by applying to the output of amplifier 43, a load compensating voltage which is proportional to changes in the vehicle payload. This load compensating voltage may be produced by a transducer of a well known type such, for example, as the type known and used in the electronic scale art. Such a transducer would be interposed, for example, between the loaded vehicle mass and its support motors, to thus measure the changing load, and with its output paralleled with the output of amplifier 43, to thus compensate for any gap spacing errors due to load variations such as resulted in the aforementioned 0.6 mil error. Such load compensation would maintain a substantially constant gap not withstanding loading changes, accumulations, etc.

As described in connection with the circuit arrangement of FIG. 4A, the RC input network 58 to 60 effectively provides velocity feedback (differentiated displacement) over the frequency range from 1.3 to about 4 to 5 hertz, as may be seen in FIG. 8, noting curve 180 between points 181 and 182 thereon. Curve 180 represents the system response when the circuit elements of the acceleration and displacement channels of FIG. 6A have the specific aforementioned component values. It will be noted, moreover, that the DB level of displacement feedback increases rapidly as the frequency decreases below 1.3 hertz toward zero, that is, to the d.c. state, this being controlled by the RC network 64 to 66 in the feedback circuit for amplifier 61 which increases the amplifier gain with decreasing frequency.

The relative frequency responses of the acceleration and displacement channels may be adjusted by adjustment of the frequency compensating networks 21' and 23' to give any desired vertical dynamic characteristic. Thus, by changing the gain settings provided by adjustment of the values of circuit elements 58, 59, 64, 65, and 66, various ratios of acceleration and displacement feedback may be used, depending upon the desired "stiffness" of the ride with respect to the rails.

In addition to the aforementioned curve 180 of FIG. 8 which represents use of a nominal amount of position feedback, curve 183 represents a relatively large value of position feedback, and curve 184 is for a low value of position feedback as would be used for a large high speed vehicle operating with an air gap of about 1 inch over a relatively uneven track.

Curve 185 - 186 - 187 of FIG. 8 depicts the open loop response through the acceleration channel, this being constant for the three disclosed examples 180, 183 and 184 of position feedback. It may be noted that the acceleration loop gain of 7.4 (17.4 db) is constant over the flat curve portion 186 which covers the frequency range from 0.3 to 3.0 hertz. This value of inertial acceleration feedback gives the vehicle V an apparent mass of 7.4 times its actual mass over this specified frequency range. Note also, as aforementioned, that the acceleration channel "roll-off" in the curve portion 185 begins approximately at 0.13 hertz. Attention is further directed to the portion 187 of the acceleration channel response which discloses that the velocity feedback provided by this channel extends over the frequency range of about 5 to 12 hertz.

The curves of FIG. 9 show the deviation from a preset mean gap vs. time when the change in loading is due to an external vertical force equal to 0.1 the vehicle weight, such loading being continuous as by a wind gust or by a change in the number of onboard passengers, as aforementioned. The curves 190, 193 and 194 respectively correspond to the curves 180, 183 and 184 of FIG. 8 in that they represent responses obtainable from the same values of relative displacement feed back. As is apparent from the showing of FIG. 9, the displacement is the least when the value of position feedback is the greatest, this being exemplified by curves 193 and 194 which respectively exhibit greater and lesser "stiffness" than normal feedback curve 190. The recovery time for the normal feedback is the least of the three examples depicted. However, curve 193 exhibits the desired gradual return to mean gap whereas curves 190 and 194 which permit greater deviations before correction, show greater rates of return movement to mean gap, i.e., the return slopes are steeper.

FIG. 10 shows the ability of vehicle V to follow a track which has sudden change of radius of upward curvature which corresponds to a step change of upward acceleration for the three examples of position feedback gain. The curves 200, 203 and 204 respectively correspond to the three values of relative displacement depicted in FIGS. 8 and 9. The minimum gain curve 204 shows that the gap is allowed to increase 0.6 inches greater than the nominal value of 0.4 second after the deviation occurred. The deviation rate is zero so that the car acceleration is the same as the upward track acceleration. This large "jerk" of the track is reduced by the magnetic suspension to: 0.1/0.4 = 0.25 g/sec. At 0.8 second the car is accelerating upward at 0.09 g and remains at 0.1 g 0.01 g. Curve 200 shows that the vehicle vertical acceleration is the same as the track vertical acceleration after 0.1 second, and the high gain curve 203 results in vehicle vertical acceleration corresponding to track vehicle acceleration after only 0.05 second.

Referring now to FIG. 6B, it will be seen that speed control 30 comprises a potentiometer 210 to provide a variable voltage input to the voltage controlled variable frequency three phase oscillator 31. A single pole, triple throw switch 212 connects potentiometer 210 selectively across a d.c. power supply 211 having a grounded center tap so that the oscillator is grounded when the switch is in the ground position, as shown, and provides positive or negative potential to ground selectively in accordance with the setting of the switch in the positive or negative polarity positions thereof.

Multipliers 120 - 122 are identical and each, as may be seen by reference to the circuit details of multiplier 120, comprises an integrated circuit 25" and amplifier 89'. Multipliers 135 - 137 are also identical and each, as may be seen by reference to the circuit details of multiplier 135, comprises an integrated circuit 25'" and an amplifier 89".

Multipliers 120 - 122 and 135 - 137 have generally the same composition and circuit arrangement as multiplier 25 of FIG. 4A except that the RC networks 85, 86 and 85', 86' and amplifier feedback capacitor 76' of multiplier 25 are not used in multipliers 120 - 122 and 135 - 137.

Differentiators 143 - 145 have generally the same composition and circuit arrangement as perfect differentiator 26 of FIG. 4A except that differentiators 143 - 145 pass their signal outputs to the amplifiers of the associated multipliers 135 - 137, respectively.

Power amplifiers 108 to 110 are of any type suitable for the purpose such as Class D amplifiers and preferably are of the Class D type disclosed and claimed in U.S. Pat. No. 3,579,132, issued to James A. Ross on May 18, 1971.

Power connection 39" is shown to constitute a pantograph 215 in sliding engagement with a 3rd rail 216, it being understood that there are three such pantograph-rail systems required, one for each of the three phases .phi.A, .phi.B and .phi.C respectively supplied by amplifiers 108 to 110.

The specific component values for the circuit elements of the frequency control channel are set forth in the following table:

Frequency Control Channel

30 Speed Control Elements 210 and 211 and 212 31 Oscillator Wavetek type 120-020-3 210 Potentiometer 1000 ohms 211 Power Supply 10 volts 212 Switch Single Pole, tripple throw 120 Multiplier Elements 25" and 89' 121 " " 122 " " 135 " Elements 25'" and 89" 136 " " 137 " " 25" Integrated Circuit MC1794L Motorola 25'" Integrated Circuit " 81" Resistor 16,200 ohms 79" resistor 61,900 ohms 80" Resistor 10,000 ohms 87' Potentiometer 20,000 ohms 78" Potentiometer 20,000 ohms 77' Potentiometer 50,000 ohms 89' Amplifier MC 1456C Motorola 89" Amplifier MC 1456C Motorola 88" Resistor 51,000 ohms 79"' Resistor 61,900 ohms 80'" Resistor 30,100 ohms 81'" Resistor 16,200 ohms 87" Potentiometer 20,000 ohms 78'" Potentiometer 20,000 ohms 77" Potentiometer 50,000 ohms 88" Resistor 2,400 ohms 143 Differentiator Elements 83' and 90' 144 Differentiator " 145 Differentiator " 83' Capacitor 1 uf 90' Resistor 220 ohms

The motors for vehicle V may be built in a wide range of sizes, the length of from 10 to 50 feet and a width of motor and rail of the order of three inches being typical. Four such motors typically weigh 5,000 pounds and, when energized, can suspend a vehicle mass of about 80,000 pounds. When the motors are suspending only, the vehicle being at rest with a 1 inch air gap, 40 kilowatts of power is consumed and the kilovolt-ampere power has the same value. As the motor speed increases with frequency and provides propulsive force, the kilovolt-amperes increases at a faster rate than does the wattage loss.

Motors of high efficiency will have low winding resistance and high inductance. The motors on the other hand will require high frequencies for high speeds which necessitates a proportionate increase in motor terminal voltage to compensate for the increase in motor impedance with frequency.

The RC network of each of differentiators 143 to 145, namely, capacitor 83' of 1 .mu.f and resistor 90' of 220 ohms provides a voltage increase with frequency in which the voltage across the capacitor will equal the voltage across the resistance when the frequency reaches about 700 hertz. A reluctance motor, such as disclosed in the aforesaid parent application, has a land and slot distance (pole pitch) of 36 inches and will move 72 inches per cycle, or about 300 miles per hour when the frequency is about 80 hertz. (See FIG. 7A ).

It should now be apparent that there has been provided a feedback control system in which the terminal voltage of an electroresponsive force generator such as an electromagnet or linear electric motor under control of position and inertial sensors carried thereby is caused to produce an attractive force with respect to a coacting member sufficient to maintain the same in controlled spacial relationship against an opposing force acting on the force generator by itself, or with its load, such as a vehicle.

It should also be apparent that the generated attractive force may be produced by a magnetic force field, as shown, or by an electrostatic, or other force field in which the force varies as the square of the generator current and inversely as the length of gap physically separating the force generator and the member to which it is attracted by the force field set up between them. It should further be apparent that whereas such force-current-space relationship is non-linear, a non-linear feedback control circuit has been provided in which circuit elements are employed to perform square-rooting, multiplying, and summing functions which linearize the voltage vs. force function to stabilize the response over a wide range of gap lengths and feedback frequencies.

It should now be fully apparent, moreover, that such a feedback control system, as aforedescribed, is well adapted to control the magnetic flux of a linear electric motor to maintain the suspension of the motor and its vehicle load in controlled spacial relationship with respect to its support rail while also producing alternations of the suspension flux at controlled frequencies related to desired linear propulsive speeds of the vehicle along the rail, including zero frequency at standstill, without exceeding the dynamic response characteristics of the feedback circuit elements.

With particular reference to FIG. 7A it will be noted that the linear speed vs. frequency relationship of a synchronous reluctance motor operated in accordance with the feedback principles of the present invention for accelerating, coasting, and decelerating is a single straight line passing through zero. On the other hand, in the case of an induction motor, as depicted in FIG. 7B, the accelerating, coasting, and decelerating functions are represented by separate parallel straight lines of which only the coasting line representing near zero slip passes approximately through zero frequency and speed. Some frequency other than zero is required for accelerating and decelerating operations at standstill and low speeds.

Claims

What is claimed as new and useful and desired to be secured by U. S. Letters Patent is:

1. The non-linear feedback method of linearizing the voltage vs. force function of an electroresponsive force field generator whose generated attractive force with respect to a nonmovable co-acting member separated therefrom varies directly as the square of the generator current and inversely as the square of the separation distance, said method comprising the steps of:

sensing the gap defining the separation distance and any acceleration of the generator associated with any change in the gap to produce signals indicative of the length of the gap and the rate of change of the gap;

deriving from said signals a force proportional feedback voltage corresponding to a gap stabilizing attractive force to be generated by the generator which is sufficient against an opposing force thereon to restore and maintain the generator in a position of stable equilibrium at a predetermined gap;

deriving from said feedback voltage and said signals non-reactive and reactive feedback voltage components respectively proportional to the length of the gap and the frequency of the signals; and

applying to the generator a terminal voltage proportional to the sum of said non-reactive and reactive voltage components, whereby said stabilizing attractive force is produced by the generator.

2. The feedback method as in claim 1 wherein the generator is suspended below its co-acting member and the opposing force is the weight of the generator due to the acceleration of gravity.

3. The feedback method as in claim 1 wherein the opposing force is an inertial force acting on the generator.

4. The feedback method as in claim 2 wherein the opposing force has both gravitational and inertial components.

5. The feedback method as in claim 1 wherein the opposing force is zero in the absence of an inertial force acting on the generator.

6. The feedback method as in claim 1 wherein the opposing force is produced by an equivalent force field generator.

7. The feedback method as in claim 6 wherein the equivalent generators are physically connected together.

8. The feedback method as in claim 7 wherein the opposing forces of the equivalent generators are equal at a predetermined value in which the gaps between the generators and their respective co-acting members are equal.

9. The feedback method as in claim 7 wherein the opposing forces of the equivalent generators are zero when the gaps between the generators and their respective co-acting members are equal.

10. The feedback method as in claim 4 and comprising the further steps of:

sensing any lateral inertial force acting on the generator in a direction transversely to the direction of gravity acting thereon and indicative of a condition creating a need for adjustment of said predetermined gap, thereby to produce signals indicative of said lateral inertial force; and

adding said last named signals to said length of gap and rate of gap change signals to adjust the strength of said force proportional feedback voltage whereby said predetermined gap is adjusted sufficiently to satisfy said need.

11. The feedback method as in claim 1 wherein said step of deriving said non-reactive and reactive voltage components includes the step of electrically extracting the square root of said force proportional voltage.

12. The feedback method as in claim 1 wherein said step of deriving said non-reactive and reactive voltage components includes the steps of electrically extracting the square root of said force proportional voltage, electrically multiplying the square root voltage by the length of gap signal voltage, and differentiating the square root voltage.

13. The feedback method as in claim 1 wherein said step of deriving said terminal voltage includes the step of summing said non-reactive and reactive voltage components.

14. The feedback method as in claim 1 wherein the derivation of the force proportional and terminal voltages involves multiplications and summations expressed by the voltage vs. force function equation:

E = K.sub.3 (.sqroot. F lR = j .sqroot.F K.sub.4 .omega.)

where:

E is the terminal voltage

.sqroot.F lR is the non-reactive voltage component

j .sqroot.F K.sub.4 .omega. is the reactive voltage component

K.sub.3, K.sub.4 are constants

j is the reaction symbol

F is the attractive force; the force proportional voltage

l is the gap length

R is the generator resistance

.omega. is 2.pi.f

f is the sensed signal frequency.

15. The feedback method as in claim 1 wherein the generator is an electromagnetic device and its generated force field is a magnetic field.

16. The non-linear feedback method of linearizing the voltage vs. force function of a polyphase linear electric motor whose generated magnetic attractive force with respect to a ferromagnetic reaction rail from which it is suspended and physically separated varies directly as the square of the motor current and inversely as the square of the separation distance, said method comprising the steps of:

sensing the gap defining the separation distance and any acceleration of the motor associated with any change in the gap to produce signals indicative of the length of the gap and the rate of change of the gap;

deriving from said signals a force proportional feedback voltage corresponding to a gap stabilizing attractive force to be produced by the motor which is sufficient against an opposing force acting on the motor to restore and maintain the same in a position of stable equilibrium at a predetermined gap;

operating a constant amplitude variable frequency polyphase control voltage;

deriving from said force proportional voltage, from said signals and from said polyphase voltage per phase thereof non-reactive and reactive feedback voltage components respectively proportional to the length of the gap and the frequency of the polyphase voltage; and

applying to the motor a polyphase terminal voltage which is proportional for each phase thereof to the sum of said non-reactive and reactive voltage components, thereby to produce said stabilizing attractive force at any frequency upwards from zero of said polyphase control voltage.

17. The feedback method as in claim 16 wherein the magnetic field of the motor suspends and propels the same along the rail and wherein the motor linear speed along the rail is a function of the frequency of the magnetic field alternations.

18. The feedback method as in claim 17 wherein the reactive voltage component for each phase is proportional to the first derivative of the product of said constant amplitude variable frequency, polyphase control voltage and the square root of said force proportional voltage, and the nonreactive voltage component for each phase is proportional to the product of the gap length times the square root of the force proportional voltage times said polyphase control voltage.

19. The feedback method as in claim 18 wherein the products and summations are expressed by the voltage vs. force function equation:

E = K.sub.1 (.sqroot.F.sub.M lR + j .sqroot.F.sub.M K.sub.2 f)

where:

E is the polyphase alternating current terminal voltage

.sqroot.F.sub.M lR is the nonreactive voltage component

j.sqroot.F.sub.M K.sub.2 f is the reactive voltage component

F.sub.M is the attractive force between the motor and the rail; the force proportion voltage

l is the gap length

R is the motor winding resistance

f is the frequency of the terminal voltage

K.sub.1, K.sub.2 are constants.

20. The method of combined suspension and propulsion of an electric linear motor support for a high speed tracked transport vehicle which comprises the steps of

disposing an electric linear motor below a magnetic rail support therefor,

controlling the voltage and current relationship of the motor to establish an attractive magnetic field between the motor and rail sufficient to suspend the mass including the motor and its load against the force of gravity and at a selected gap defining the displacement of the motor from the rail,

sensing the gap displacement and any acceleration of said mass associated with any change in the gap displacement,

adjusting said voltage and current relationship of the motor in response to signals sensed by the displacement and acceleration sensors to maintain said selected gap displacement,

adjusting said voltage and current relationship to produce alternations of the suspension field and to move the same along the motor and in linear thrust producing relation to the rail to move the mass along the rail at a speed determined by the frequency of said field alternations,

varying the frequency of said field alternations to adjust the linear speed of the mass, and

adjusting said voltage and current relationship as a function of frequency to compensate for increasing motor impedance with frequency thereby to maintain the strength of the suspension field constant at all propulsion speeds.

21. A feedback control system comprising:

a fixed member;

an electroresponsive force field generator separated in free space at a predetermined separation distance from said fixed member for generating a force field therewith and resultant attractive force therebetween wherein the attractive force varies as the square of the generator current and inversely as the square of the separation distance;

means carried by the generator for producing a force proportional voltage proportional to the attractive force which is required to be generated by the generator to restore and maintain the same in stable equilibrium at said predetermined separation distance against an opposing force acting on the generator; and

means responsive to said force proportional voltage for producing and applying to said generator a terminal voltage sufficient to enable the same to generate said required attractive force.

22. A feedback system as in claim 21 wherein said terminal voltage producing means includes:

square rooter means for electrically producing a square root voltage which is the square root of said force proportional voltage.

23. A feedback control system as in claim 21 wherein:

said force proportional voltage means includes sensing means for producing a signal proportional to the separation distance; and

said terminal voltage producing means includes:

square rooter means for electrically producing a square root voltage which is the square root of said force proportional voltage; and

multiplier means for electrically producing a voltage which is the product of said square root voltage and said distance proportional signal.

24. A feedback control system as in claim 23 wherein:

said square root voltage has a frequency proportional to any variations in said distance proportional signal; and

said terminal voltage producing means also includes:

means for differentiating said square root voltage to produce a voltage proportional to its frequency; and

means for electrically summing said product voltage and said frequency proportional voltage.

25. A feedback control system as in claim 24 wherein said terminal voltage is produced in accordance with the equation:

E = K.sub.1 F (Rl = jK.sub.2 f)

where:

E is the terminal voltage

F is the required attractive force

R is the generator resistance

l is the separation distance

f is the frequency of the square root voltage

K.sub.1 and K.sub.2 are constants.

26. A suspension apparatus having a force generator, a co-acting support therefor, a feedback circuit for controlling a suspension force produced by said force generator to suspend the same in free space from said support therefor without contact therewith and against the force of gravity acting thereon to thereby maintain the generator in a state of stable equilibrium at a selected gap length within a range of selectable gap lengths between said generator and support, said feedback circuit having at least one input selected from a group of inputs which respectively represent the position, velocity and acceleration of the generator associated with any change in the gap, an output signal applicable to said force generator to control said suspension force, and circuit means responsive to said inputs to produce said output signal.

27. An apparatus according to claim 26, wherein said feedback circuit includes means for setting the magnitude of the suspension force sufficient to counterbalance the force of gravity at a preselected nominal gap within said range of gaps.

28. An apparatus according to claim 26 wherein the magnitude of the suspension force is regulated by sensing the vertical position of the generator and the acceleration of change of that position.

29. An apparatus according to claim 26, wherein said circuit means includes an element having an output proportional to a mathematical root of the input thereto.

30. An apparatus according to claim 26, wherein said circuit means includes an element having an output proportional to a mathematical differential of the input thereto.

31. A feedback circuit for controlling the voltage of an electroresponsive force field generator which is attracted by its force field toward a co-acting member and held physically separated therefrom by an opposing force thereon wherein the generator is maintained at a preselected separation distance when the attractive and opposing forces are equal and wherein the attractive force varies inversely as the square of the separation distance and directly as the square of the generator current, said feedback circuit comprising a first input having X signals which vary with the displacement distance and a second input having signals which vary with any acceleration of the generator associated with any change in the separation distance, and output having a feedback voltage for controlling the generator voltage to maintain the attractive force equal to the opposing force, and means responsive to the signals of said first and second inputs for producing said feedback voltage.

32. A suspension-propulsion feedback system comprising:

a ferromagnetic support rail having linear thrust producing reaction means;

an electric linear motor disposed beneath said rail in spaced relation therewith defining an air gap therebetween, said motor having plural phase windings for producing a combined motor suspension and propulsion magnetic field with respect to said rail and its reaction means;

a controllable plural phase power amplifier source of variable amplitude and variable frequency voltage for respectively energizing said plural phase windings; and

gap length and frequency control means carried by said motor for simultaneously regulating the amplitude of each phase of said energizing voltage to restore and maintain the motor in stable equilibrium at a predetermined gap and for simultaneously regulating the frequency of each phase of said energizing voltage to set the linear speed of the motor along the rail.

33. A feedback system as in claim 32 wherein said gap length control means includes:

means for sensing the gap length and any acceleration of the motor associated with any change in the gap length.

34. A feedback system as in claim 33 wherein said gap length control means also includes:

means responsive to signals produced by said sensing means for producing a feedback voltage input to said power amplifier source to regulate the amplitude of its output voltage.

35. A feedback system as in claim 34 wherein said signal responsive means includes:

operational amplifier means responsive to said signals for producing a force proportional voltage which is proportional to the magnetic motor-to-rail attractive force required to maintain the motor at said predetermined gap against the force of gravity acting thereon; and

means for electrically extracting the square root of said force proportional voltage to produce a square root voltage.

36. A feedback system as in claim 35 wherein:

said frequency control means comprises a plural phase source of constant amplitude and variable frequency control;

first multiplier means for electrically producing per phase of said control voltage an output which is the product of the control voltage amplitude times said square root voltage;

second multiplier means for electrically producing per phase of said control voltage the product of said first multiplier means output times the length of gap signal to produce a gap compensated control voltage component;

means for differentiating per phase of said control voltage the product output of said first multiplier means to produce a frequency compensated control voltage component; and

means per phase of said control voltage for electrically summing said gap and frequency compensated voltage components.

37. A feedback system as in claim 36 including means for simultaneously varying the frequency per phase of said control voltage.