U.S. patent number RE33,866 [Application Number 07/639,557] was granted by the patent office on 1992-03-31 for resonant inverter employing frequency and phase modulation using optimal trajectory control.
This patent grant is currently assigned to General Electric Company. Invention is credited to Ming H. Kuo, John N. Park, Michael J. Schutten.
United States Patent |
RE33,866 |
Schutten , et al. |
March 31, 1992 |
Resonant inverter employing frequency and phase modulation using
optimal trajectory control
Abstract
A series resonant inverter is controlled to provide a
substantially constant output voltage to a load. The control
utilizes a combination of optimal control methods and phase
modulation to enable time optimal responses to changes in state of
the system. State determinants (including resonant capacitor
voltage, resonant inductor current, source voltage, and output load
voltage) are continuously monitored, and an optimal control signal
is generated therefrom. When operating within the operable
frequency range of the inverter's controllable switch means,
frequency is varied to maintain proper operation. When operating at
an extremity of the operable frequency range, phase modulation is
employed.
Inventors: |
Schutten; Michael J.
(Schenectady, NY), Park; John N. (Rexford, NY), Kuo; Ming
H. (Caledonia, IL) |
Assignee: |
General Electric Company
(Schenectady, NY)
|
Family
ID: |
27008629 |
Appl.
No.: |
07/639,557 |
Filed: |
December 20, 1990 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
Reissue of: |
379461 |
Jul 13, 1989 |
04951185 |
Aug 21, 1990 |
|
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Current U.S.
Class: |
363/17;
363/98 |
Current CPC
Class: |
H02M
3/3376 (20130101); H02M 7/53878 (20210501); Y02B
70/10 (20130101) |
Current International
Class: |
H02M
3/337 (20060101); H02M 3/24 (20060101); H02M
003/337 () |
Field of
Search: |
;378/110,112
;363/17,28,98 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Oruganti, Ramesh and Lee, Fred C., "Resonant Power Processors: Part
I--State Plane Analysis", 1984 Industry Applications Society
Proceedings, pp. 860-867. .
Oruganti, Ramesh and Lee, Fred C., "Resonant Power Processors: Part
II--Methods of Control", 1984 Industry Applications Society
Proceedings, pp. 868-878. .
Oruganti et al., "Implementation of Optimal Trajectory Control of
Series Resonant Converter", 1987 Power Electronics Specialty
Conference Proceedings, pp. 451-459..
|
Primary Examiner: Beha, Jr.; William H.
Attorney, Agent or Firm: Breedlove; Jill M. Davis, Jr.;
James C. Snyder; Marvin
Claims
What is claimed is:
1. An improved dc-to-dc converter, comprising:
a resonant inverter having two pairs of controllable switch means,
the switch means of each pair being connected in series and each
pair of the series-connected switch means being adapted to be
connected in parallel across an external dc supply;
a series resonant circuit connected between the junctions of said
controllable switch means and comprising a capacitor and an
inductor, said inverter being adapted to apply a rectangular wave
voltage to said series resonant circuit;
a full wave rectifier inductively coupled to said series resonant
circuit, the output of said rectifier being adapted to supply a
substantially constant preselected output voltage to a load;
state determinant sensing means for continuously monitoring
converter state determinants comprising voltage across said
capacitor, current through said inductor, the .[.rectangular wave
voltage applied to said series resonant circuit.]. .Iadd.dc supply
voltage.Iaddend., and the output voltage;
optimal control means responsive to said state determinant sensing
means for generating an optimal control signal corresponding to the
instantaneous values of said state determinants;
first control means responsive to said optimal control signal for
controlling the output voltage by frequency modulating the
rectangular wave voltage applied to said series resonant circuit so
as to maintain stable operation of said series resonant circuit
when the operating frequency of said controllable switch means is
within the operable frequency range thereof; and
second control means responsive to said optimal control signal for
controlling the output voltage by providing a phase modulation
angle signal for phase modulating the rectangular wave voltage
applied to said series resonant circuit and modifying said optimal
control signal .Iadd.in .Iaddend.accordance therewith so as to
maintain stable operation .Iadd.of .Iaddend.said series resonant
circuit when the operating frequency of said controllable switch
means is at an extremity of the operable frequency range
thereof.
2. The improved converter of claim 1, further comprising:
frequency measuring means coupled to the output of said inverter
for determining when the operating frequency of said controllable
switch means is at an extremity of the operable range thereof.
3. The improved converter of claim 1 wherein said first control
means comprises:
frequency modulation means for generating a frequency modulation
signal;
comparison means for comparing said frequency modulation signal
with said optimal control signal and for generating a difference
signal resulting therefrom; and
frequency control means responsive to said difference signal for
generating a frequency control signal for varying the operating
frequency of said controllable switch means.
4. The improved converter of claim 3, further comprising:
sawtooth generator means responsive to said frequency control
signal for generating a ramp voltage;
second comparison means for comparing said ramp voltage with said
phase modulation angle signal; and
flip-flop means responsive to said frequency control signal and to
the output signal of said second comparison means, said flip-flop
means being coupled to said controllable switch means for providing
control signals to vary the operating frequency of said
controllable switch means when operating within the operable
frequency range thereof and to phase modulate the rectangular wave
voltage when operating at an extremity of the operable frequency
range.
5. .[.At.]. .Iadd.An .Iaddend.improved control for a resonant
inverter, said inverter including a series resonant circuit which
comprises a capacitor and an inductor, said inverter further
including controllable switch means for producing a rectangular
.[.are.]. .Iadd.wave .Iaddend.voltage .Iadd.when coupled to an
external dc supply .Iaddend.and applying said voltage to said
series resonant circuit, the output of said resonant inverter
providing a substantially constant output voltage to a load, said
improved control comprising:
state determinant sensing means for continuously monitoring
converter state determinants comprising voltage across said
capacitor, current through said inductor, the .[.rectangular wave
voltage and applying said voltage applied to said series resonant
circuit.]. .Iadd.dc supply voltage.Iaddend., and the output
voltage;
optimal control means responsive to said state determinant sensing
means for generating an optimal control signal corresponding to the
instantaneous values of said state determinants;
first control means responsive to said optimal control signal for
controlling the output voltage by frequency modulating the
rectangular wave voltage applied to said series resonant circuit so
as to maintain stable operation of said series resonant circuit
when the operating frequency of said controllable switch means is
within the operable frequency range thereof; and second
.[.controls.]. .Iadd.control .Iaddend.means responsive to said
optimal control signal for controlling the output voltage by
providing a phase modulation angle signal for phase modulating the
rectangular wave voltage applied to said series resonant circuit
and modifying said optimal control signal in accordance therewith
so as to maintain stable operation of said series resonant circuit
when the operating frequency of said controllable switch means is
at an extremity of the operable frequency range thereof.
6. The improved control of claim 5, further comprising:
frequency measuring means coupled to the output of said inverter
for determining when the operating frequency of said controllable
switch means is at an extremity of the operable range thereof.
7. The improved control of claim 5 wherein said first control means
comprises:
frequency modulation means for generating a frequency modulation
signal;
comparison means for comparing said frequency modulation signal
with said optimal control signal and for generating a difference
signal resulting therefrom; and
frequency control means responsive to said .[.differences.].
.Iadd.difference .Iaddend.signal for generating a frequency control
signal for varying the operating frequency of said controllable
switch means.
8. The improved control of claim 7, further comprising:
sawtooth generator means responsive to said frequency control
signal for generating a ramp voltage;
second comparison means for comparing said ramp voltage with said
phase modulation angle signal; and
flip-flop means responsive to said frequency control signal and to
the output signal of said second comparison means, said flip-flop
means being coupled to said controllable switch means for providing
control signals to vary the operating frequency of said
controllable switch means when operating within the operable
frequency range thereof and to phase modulate the rectangular wave
voltage when operating at an extremity of the operable frequency
range.
9. A method for controlling a resonant inverter, said inverter
having controllable switch means for producing a rectangular wave
signal .Iadd.when coupled to an external dc supply .Iaddend.and
applying said signal to a series resonant circuit which comprises a
capacitor and an inductor, the output of said resonant inverter
providing a substantially constant output voltage to a load, said
control method comprising the steps of:
continuously monitoring state determinants comprising voltage
across said capacitor, current through said inductor, .[.said
rectangular wave signal.]. .Iadd.the dc supply voltage.Iaddend.,
and said output voltage;
generating an optimal control signal corresponding to a
predetermined combination of the instantaneous values of said state
determinants;
frequency modulating said rectangular wave signal applied to said
series resonant circuit so as to maintain stable operation of said
series resonant circuit when the operating frequency of said
controllable switch means is within the operable frequency range
thereof; and
generating a phase modulation angle signal for phase modulating
said rectangular wave signal and modifying said optimal control
signal in accordance therewith so as to maintain stable operation
of said series resonant circuit when the operating frequency of
said controllable switch means is at an extremity of the operable
frequency range thereof.
Description
FIELD OF THE INVENTION
The present invention relates generally to resonant inverters. More
particularly, this invention relates to a series resonant inverter
with improved control which utilizes a method of optimal control in
combination with phase modulation to maintain substantially
constant output voltage over a wide range of operating
conditions.
BACKGROUND OF THE INVENTION
Resonant inverters advantageously have low switching losses and low
switching stresses. However, resonant operation is complex due to
the fast dynamics of the high-frequency resonant tank circuit; and,
hence, control is difficult. Disadvantageously, when input power or
output load conditions vary, output voltage or current control
cannot be achieved through the use of usual control techniques. For
example, one known resonant inverter output load voltage or current
control method is to vary the frequency of the rectangular wave
signal supplied to the resonant circuit by the inverter via closed
loop control. Commonly assigned U.S. Pat. No. 4,541,041, issued on
Sept. 10, 1985 to J. N. Park and R. L. Steigerwald, which is hereby
incorporated by reference, discloses in part such a frequency
control technique. Briefly explained, the resonant nature of the
circuit allows for control of output voltage or current through
variation of the frequency at which the inverter's controllable
switch means operate. Such a frequency control method has been
formed satisfactory under normal output load conditions for
particular types of resonant inverters (i.e., heavy or medium load
conditions for a series resonant inverter and light load conditions
for a parallel resonant inverter). The drawback to frequency
control, however, is that it may be inadequate to maintain a
desired output voltage or current under extended output load
conditions (i.e., light or no load conditions for a series resonant
inverter and heavy load conditions for a parallel resonant
inverter).
In particular, frequency control of a series resonant inverter will
normally be adequate to maintain a desired output voltage during
heavy or medium load conditions (i.e., low load resistance); that
is, for heavy or medium load conditions, a series resonant circuit
has a high quality factor Q and thus a good dynamic range of
voltage or current change as frequency is varied. However, under
extended or light output load conditions (i.e., high load
resistance) the series resonant circuit exhibits a low quality
factor Q and thus only a small dynamic range of output voltage or
current change can be achieved as a function of frequency. As a
result, for a series resonant inverter, it may be impossible to
maintain a desired output voltage or current under light load and
no load conditions solely with frequency control.
A resonant inverter control which provides an improved dynamic
range of output voltage or current control is disclosed in U.S.
Pat. No. 4,672,528, issued June 9, 1987 to J. N. Park and R. L.
Steigerwald and assigned to the assignee of the present invention.
This patent, which is hereby incorporated by reference, describes a
resonant inverter which is controlled using either a frequency
control mode or a phase shift control mode. In the frequency
control mode, output voltage is controlled by varying the frequency
of the rectangular wave signal supplied to the resonant circuit
within an operable range of the controllable switch means.
Selecting means allows the control to operate in the phase shift
control mode when the frequency of the rectangular wave signal is
at an extremity of the operable range of the controllable switch
means.
Another method of resonant inverter control, which is derived from
optimal control theory and state plane analysis, is presented in
"Resonant Power Processors: Part II-Methods of Control" by Ramesh
Oruganti and Fred C. Lee, 1984 Industry Applications Society
Proceedings, pp. 868-878, and is hereby incorporated by reference.
According to this method, hereinafter designated "optimal
trajectory control" to be described in detail below, each state
trajectory corresponds to particular values of instantaneous
resonant tank energy, output voltage, output current and switching
frequency. These state trajectories are utilized to define a
control law for the inverter control system which enables a series
resonant inverter to respond quickly to load and control
requirements. Disadvantageously, however, in the method of "optimal
trajectory control", as it presently exists, the controlled range
of output voltages is limited in the same manner as the hereinabove
described conventional frequency control method.
Accordingly, it is an object of the present invention to provide a
new and improved resonant inverter exhibiting an improved dynamic
range of output load voltage control.
Another object of this invention is to provide a new and improved
resonant inverter control which utilizes a combination of optimal
control methods and phase modulation to maintain output load
voltage substantially constant during all loading conditions.
Still another object of this invention is to provide a new and
improved resonant inverter control which switches automatically
between different control means to maintain a substantially
constant output load voltage.
Yet another object of the present invention is to provide an
improved method of controlling a resonant inverter in order to
maintain a desired output load voltage.
SUMMARY OF THE INVENTION
In accordance with the present invention, a new and improved
resonant inverter is controlled using a combination of optimal
trajectory control and phase modulation. In particular, optimal
control means are employed to continuously monitor resonant
capacitor voltage, resonant inductor current, .[.rectangular wave
voltage applied to the resonant tank circuit.]. .Iadd.source
voltage .Iaddend.and output load voltage, thereby determining the
instantaneous "states" of the resonant inverter. A control law,
defined in terms of state plane analysis, enables maintenance of
stable operation on state trajectories corresponding to particular
values of the aforementioned state determinants. In this way, the
improved control enables a time optimal response corresponding to a
change in load conditions and, hence, a fast and efficient
transition between state trajectories.
For a series resonant inverter operating above resonance, there is
a maximum frequency at which the controllable switch means can
adequately function. When operating within the operable frequency
range of the controllable switch means (i.e. below this maximum
frequency and above the resonant frequency), a first control means
provides frequency control signals which frequency modulate the
rectangular wave voltage applied to the series resonant circuit so
as to provide a constant output voltage and maintain stable
operation. At an extremity of the operable frequency range of the
controllable switch means, inverter control automatically switches
to a second control means. The second control means calculates a
phase modulation angle corresponding to the desired output voltage
and generates a phase shift control signal representative thereof.
By thus combining a method of optimal control with phase
modulation, a broader dynamic range of output load voltage can be
achieved under all operating conditions.
In another aspect of the present invention, a method is provided
for controlling output load voltage through a combination of
optimal control methods and phase modulation.
BRIEF DESCRIPTION OF THE DRAWINGS
The features and advantages of the present invention will become
apparent from the following detailed description of the invention
when read with the accompanying drawings in which:
FIG. 1 is a schematic representation of a dc-to-dc converter
including a series resonant inverter;
FIG. 2 is a graphical illustration showing the magnitude of the
output voltage plotted against the log of the frequency of the
rectangular wave signal supplied to the series resonant circuit
employed in the inverter of FIG. 1 for heavy load, medium load,
light load and no load conditions;
FIG. 3 is a single state trajectory, state plane diagram for the
resonant inverter of FIG. 1 operating above the resonant
frequency;
FIG. 4a is a graphical representation of the rectangular wave
voltage applied to the series resonant inverter of FIG. 1;
FIG. 4b is a graphical representation of the phase modulated signal
of FIG. 4;
FIG. 5 is a graphical illustration showing the amplitude of the
first harmonic of the signal of FIG. 5 plotted against the phase
modulation angle;
FIG. 6 is a functional block diagram of a resonant inverter control
system employing the series resonant inverter control of the
present invention;
FIGS. 7a and 7b together comprise a functional block diagram of the
preferred embodiment of the resonant inverter control according to
the present invention; and
FIGS. 8a-8i are graphical representations of output signals from
certain elements comprising the block diagram of FIGS. 7a-7b in
order to illustrate operation of the resonant inverter control 12
of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
The improved resonant inverter control of the present invention
will be described with reference to the dc-to-dc converter shown in
FIG. 1. An external source (not shown) provides input dc voltage
V.sub.s to the converter at terminals 10 and 11. Connected across
terminals 10 and 11 is a full bridge inverter 12 having four
switching devices that are capable of carrying reverse current and
capable of being turned off by a switching signal. The switching
devices are illustrated as bipolar junction transistors (BJTs) S1,
S2, S3 and S4. Each respective switching device has a diode D1, D2,
D3 and D4 connected in inverse parallel therewith, respectively. In
operation above the resonant frequency, the switching devices are
turned on at zero current, and the inverse parallel diodes are
commutated naturally. Hence, fast recovery diodes are not required.
Moreover, other switching devices with gate turn-off capability
could be used instead of the BJTs, such as FETs each having an
integral parasitic diode for carrying reverse current or monolithic
Darlington power transistors. It is further to be understood that
the full bridge inverter is illustrated for purposes of description
only and that the control technique of the present invention is not
limited to such an inverter.
A series resonant tank circuit, comprising an inductor 14, a
capacitor 16, and the primary winding of an isolation transformer
18, is connected between junctions a and b. The secondary winding
of transformer 18 is connected to the input of a full wave
rectifier 20. The output of the rectifier is connected in parallel
with a filter capacitor 22 and an output load (not shown) across
which the converter output voltage V.sub.o is produced.
The resonant nature of the output load voltage of the inverter of
FIG. 1 is shown graphically in FIG. 2, where the magnitude of the
output load voltage is plotted against the log of the frequency of
the rectangular alternating voltage V.sub.ab which is produced by
inverter 12 and applied across the series resonant circuit. For
proper power switch self-commutation, operation above the natural
resonant frequency f.sub.r is necessary. However, there is a
maximum frequency f.sub.max beyond which these switching devices
will fail to operate satisfactorily. Thus, an operable range OF of
the switching devices is defined as that frequency range between
f.sub.r and f.sub.max. During medium or high output load
conditions, variation of frequency within this operable range OF is
sufficient to provide the desired output voltage or current
control. As illustrated graphically in FIG. 2, a desired converter
output load voltage V.sub.d may be maintained during heavy load and
medium load conditions by frequency control of the rectangular wave
voltage V.sub.ab. However, during light load and theoretical no
load conditions, variation of frequency within the operable range
OF would be insufficient to attain the desired output load voltage
V.sub.d. The present invention, therefore, employs a control
technique for enhancing the dynamic range of converter output
voltage control primarily needed under light load or no load
conditions.
Within the operable frequency range OF of the controllable
switching devices, the switches are controlled by a method of
optimal trajectory control. This method is derived from optimal
control theory and state plane analysis. In accordance therewith,
the "control law" of the system is determined by the desired state
of the system. An instantaneous state of the system is a function
of resonant capacitor voltage, resonant inductor current.
.[.voltage applied to the resonant tank circuit.]. .Iadd.source
voltage .Iaddend.and output load voltage. An instantaneous state
corresponds to a specific state trajectory. The desired state
trajectory, therefore, determines the control law of the
system.
For operation above the resonant frequency f.sub.r, FIG. 3
illustrates a state plane diagram for the resonant inverter of FIG.
1. At the outset of the ensuing state plane analysis, it is assumed
that filter capacitor 22 is sufficiently large such that the output
voltage V.sub.o remains constant during any single switching cycle
interval As used herein, the term "switching cycle interval" is
defined as the time necessary to traverse a state trajectory. In
FIG. 3, state trajectory 23 represents the desired resonant
inverter operation and corresponds to a particular operating
frequency and to specific values of the above-listed state
determinants (i.e., resonant capacitor voltage, resonant inductor
current, .[.voltage applied to the resonant tank circuit.].
.Iadd.source voltage.Iaddend., and output load voltage).
Specifically, as a two-dimensional state representation, the state
trajectory is a plot of Z.sub.o i.sub.L versus v.sub.C, where:
Z.sub.o =.sqroot.L/C is the characteristic impedance of the series
resonant circuit; i.sub.L represents resonant inductor
.[.Current;.]. .Iadd.current .Iaddend.and v.sub.C represents
resonant capacitor voltage. Trajectory 23 comprises trajectory
segments AB, BC, CD and DA corresponding to the conduction
intervals of switching devices S1-S4 and diodes D1-D4. Each
trajectory segment is a circular arc with a center and a radius
determined by the state of the switching devices. For example, when
switching devices S1 and S4 are conducting, current flows from node
a through the series resonant circuit to node b, and the effective
voltage applied to the series resonant circuit is V.sub.S -
V.sub.O. As a result, trajectory segment AB having center (V.sub.s
-V.sub.o, 0) represents the conduction interval of switching
devices S1 and S4. The remaining trajectory segment centers are
similarly determined as follows.Iadd.:.Iaddend.trajectory segment
BC having center (-V.sub.s -V.sub.o, 0) represents the conduction
interval for diodes D2 and D3; trajectory segment CD having center
(-V.sub.s +V.sub.o, 0) represents the conduction interval for
switching devices S2 and S3; and trajectory segment DA having
center (V.sub.s +V.sub.o, 0) represents the conduction interval for
diodes D1 and D4.
As hereinabove discussed, the desired or optimal trajectory
determines the control law of the system and, hence, the
construction thereof. Besides the trajectory center, described
hereinabove, another parameter characterizing each trajectory
segment is the trajectory radius R.sub.d measured either from
center (V.sub.s +V.sub.o, O) or center (-V.sub.s -V.sub.o, O). In
operation, a control circuit computes radius R.sub.d from
continuous measurements of the state determinants (i.e., resonant
capacitor voltage, resonant inductor current, .[.voltage applied to
the resonant tank circuit.]. .Iadd.source voltage.Iaddend., and
output load voltage). In this way, the control circuit maintains
system operation corresponding to the desired state trajectory by
alternately switching the pairs of diagonally opposed switching
devices. Moreover, when any of the state determinants changes, a
control signal V.sub.CONTROL generated by an outer control loop, to
be described hereinafter, enables the system to respond by making a
time optimal transition to another steady state trajectory.
In the article entitled "Implementation of Optimal Trajectory
Control of Series Resonant Converters", by Ramesh Oruganti et al.,
1987 Power Electronics Specialty Conference Proceedings, pp.
451-459, which is hereby incorporated by reference, the control law
for a resonant inverter operating below resonance is derived on
pages 453-454 as:
where F is either +1 or -1, depending upon the sign of the inductor
current i.sub.L.
The control law of an inverter operating above resonance, such as
that of the present invention, may be similarly derived and may be
expressed as:
A resonant inverter control system constructed in accordance with
the control law of equation (2) advantageously enables time optimal
control of the switching devices when operating above resonance
within the operable frequency range thereof Disadvantageously,
however, optimal trajectory control according to .[.oruganti.].
.Iadd.Oruganti .Iaddend.et al. is limited to bi-level or frequency
modulation. That is, as shown in FIG. 4A, the voltage applied to
the resonant circuit is a rectangular wave signal having two
levels: +V.sub.S and -V.sub.S. Using optimal trajectory control,
frequency of the rectangular wave signal may be varied to control
output load voltage. Hence, like conventional frequency control
methods, the control range of output voltage is limited as the
frequency increases to the maximum operating frequency of the
switching devices. The present invention, therefore, modifies and
improves the above-described optimal trajectory control system to
provide a new resonant control which yields a significantly
increased range of controlled output load voltages under all
loading conditions. In accordance therewith, the present invention
combines optimal trajectory control with phase modulation.
Since a series resonant circuit acts like a second order filter to
the rectangular wave voltage applied to the resonant tank circuit,
as will be appreciated by those of ordinary skill in the art, a
useful approximation is that only the first harmonic of the
rectangular wave signal is applied to the resonant tank circuit.
Further, if the rectangular wave signal of FIG. 4A is phase
modulated, then the phase modulated signal takes the general
trilevel form illustrated in FIG. 4B, where pulse width pw varies
proportionately as the phase modulation angle .phi.. The
fundamental harmonic F1 of this phase modulated signal is
represented as:
where .phi.=.pi./2.times.(1-2.times.pw/period), as shown in FIG.
4B, and .phi. is defined in units of radians.
FIG. 5 is a graph of the magnitude of fundamental harmonic F1
versus phase modulation angle .phi.. As shown, for a 50% duty cycle
(i.e., .phi.=0), the fundamental harmonic F1 is at its maximum
value .[.4.pi.V.sub.s .].. ##EQU2## As .phi. increases, the
amplitude of the fundamental harmonic decreases.Iadd..
.Iaddend.Therefore, phase modulation can be used according to the
present invention to decrease the amplitude of the fundamental
harmonic of the voltage applied to the series resonant inverter. As
a result, and as is evident from FIG. 2, a broader range of
controlled output load voltage may be obtained under all loading
conditions by decreasing the effective voltage applied to the
series resonant circuit.
FIG. 6 is a block diagram illustrating a resonant inverter control
system employing the series resonant inverter control of the
present invention. A commanded output voltage V.sub.REF is compared
to output voltage V.sub.o by a summer 24. The resulting error
signal V.sub.ERR is inputted to a proportional plus integral (PI)
compensator 26 which generates control signal V.sub.CONTROL.
Control signal V.sub.CONTROL is provided to series resonant
inverter control 28 which drives inverter 12. Control signals
proportional to the aforementioned state determinants are also
inputted to series resonant inverter control 28. These signals are
represented as: k.sub.1 i.sub.L, k.sub.3 v.sub.c, k.sub.3 V.sub.o,
and k.sub.3 V.sub.5, where k.sub.1 and k.sub.3 are constant scale
factors to be described hereinafter.
FIGS. 7a and 7b, connected at points 27 and 29, respectively,
illustrate the preferred embodiment of the improved resonant
inverter control 28 of the present invention. The control law of
this improved system is a modification of the control law given by
equation (2) to employ phase modulation and is represented as:
The state trajectory of the present invention (not shown),
therefore, is a modification of that of FIG. 3 to account for the
differences in a switching cycle interval resulting from the
application of phase modulation to be described hereinafter.
Implementation of the control circuit according to the present
invention involves the use of sensing devices to detect
instantaneous values of state determinants v.sub.c, i.sub.L,
V.sub.s and V.sub.o. Since these sensing devices involve scaling to
produce signals proportional to the respective state determinants,
the following description, therefore, includes the aforementioned
exemplary scale factors represented as constants k.sub.1 and
k.sub.3. For example, control signal k.sub.1 i.sub.L, which is
proportional to resonant inductor current, is derived from a
suitable current sensor 19. Typical current sensors are well known
in the art and many comprise, as examples: Hall effect current
sensors, current sensing resistors, or current sensing
transformers.
As shown in FIG. 7a, control signal k.sub.1 i.sub.L is applied to a
comparator 30. The output signal F of comparator 30 is either +1 or
-1, depending upon the sign of inductor current i.sub.L. The signal
F is inputted to multipliers 32 and 34, the value of F being the
multiplicative factor thereof. The control signal k.sub.1 i.sub.L
is also applied to a multiplier 36 which performs a squaring
operation to produce the signal k.sub.2 (Z.sub.o i.sub.L).sup.2,
where Z.sub.o =.sqroot.L/C, a constant, is the characteristic
impedance of the series resonant circuit, and k.sub.2 is also a
constant.
Control signal k.sub.3 V.sub.s, which is proportional to the
applied source voltage, is supplied by a source voltage sensor 21
to a multiplier 31 which multiplies control signal k.sub.3 V.sub.s
by cos .phi., where .phi. is the aforementioned phase modulation
angle value. Suitable voltage sensors are well known in the art and
may comprise, for example, a voltage dividing network of resistors.
Signal k.sub.3 V.sub.s cos .phi. is applied to multiplier 32 and is
thereby multiplied by signal F.
Control signal k.sub.3 V.sub.o, which is proportional to the output
load voltage, is produced by a voltage sensor 23 and applied to
multiplier 34 to yield a signal Fk.sub.3 V.sub.o. A summer 40 adds
the signal Fk.sub.3 V.sub.o to still another sensed control signal
k.sub.3 v.sub.c, which is sensed by a voltage sensor 25 and is
proportional to the voltage across the resonant capacitor. The
resulting signal .[.k.sub.3 (v.sub.c -FV.sub.o).]. .Iadd.k.sub.3
(v.sub.c +FV.sub.o) .Iaddend.is added to the aforementioned signal
Fk.sub.3 V.sub.s cos .phi. by summer 42 to yield the signal
.[.k.sub.3 (v.sub.c -FV.sub.o -FV.sub.s cos .phi.)..].
.Iadd.k.sub.3 (v.sub.c +FV.sub.o +FV.sub.s cos.phi.). .Iaddend.The
latter signal is inputted to a multiplier 44 which performs a
squaring operation. The resulting squared signal .[.k.sub.2
(v.sub.c -FV.sub.o -FV.sub.s cos .phi.).sup.2 .]. .Iadd.k.sub.2
(v.sub.c +FV.sub.o +FV.sub.s cos .phi.).sup.2 .Iaddend. is added to
the hereinabove derived signal k.sub.2 (Z.sub.o i.sub.L).sup.2 by a
summer 46 and, as shown in FIG. 7b, is then inputted to gain
amplifier 48 having the transfer function -k.sub.4 /k.sub.2 where
k.sub.4 is a constant. The output of amplifier 48 is a signal
.[.-k.sub.4 [(v.sub.c -FV.sub.o -FV.sub.s cos .phi.).sup.2
+(Z.sub.o i.sub.L).sup.2 ].]. .Iadd.-k.sub.4 [(v.sub.c +FV.sub.o
+FV.sub.s cos .phi.).sup.2 +(Z.sub.o i.sub.L).sup.2 ].Iaddend.,
which is hereinafter referred to as the optimal control signal.
Control signal V.sub.CONTROL is provided to a frequency modulation
controller 50 and a phase modulation controller 52. The transfer
function of frequency modulation controller 50 is shown in FIG. 7b
and may be represented mathematically as: ##EQU3## where V.sub.F is
the output voltage of frequency modulation controller 50, V.sub.T
is a threshold voltage representing operation at an extremity of
the operable frequency range for the controllable switch means, and
C.sub.1 is a constant. Voltage V.sub.F is added in a summer 54 to
the output signal of gain amplifier 48, and the result is inputted
to the non-inverting input of a comparator 56. The output signal
from comparator 56 is supplied to a saw-tooth generator 58.
The transfer function of phase modulation controller 52 is also
shown in FIG. 7b and may be represented mathematically as: ##EQU4##
where V.sub..phi. is the output voltage from phase modulation
controller 52, V.sub..phi. being proportional to phase modulation
angle .phi., and C.sub.2 is a constant. Voltage V.sub..phi. is
inputted to the inverting input of a comparator 60. The output
signal V.sub.G of sawtooth generator 58 is supplied to the
noninverting input of comparator 60. Voltage V.sub..phi. is also
supplied to multiplier 31 for which cos .phi. is the multiplicative
factor.
The output signals CP1 and CP2 from comparators 56 and 60,
respectively, provide the clock pulses for D-type (delay)
flip-flops 62 and 64, respectively. As will be appreciated by those
of skill in the art, since the signal at output D flip-flop 62 is
supplied to the D1 input of D flip-flop 62, D flip-flop 62 is a
divide-by-two flip-flop; that is, the output frequency is one-half
that of the clock frequency. The output signals from the D
flip-flops control the base drive circuitry 65a-65d for the
respective switching devices S1-S4. Suitable base drive circuitry
is well-known in the art.
In operation, since the output signal from comparator 56 which
provides clock pulses to the divide-by-two D flip-flop 62 also
drives sawtooth generator 58, the sawtooth generator produces a
voltage ramp signal V.sub.G operating at twice the frequency of
gate drive circuitry 65a-65d. In particular, the voltage ramp
signal V.sub.G resets to zero each time the output signal at Q1 of
D flip-flop 62 transitions from logic level 0 to 1 or 1 to 0. The
output ramp voltage of sawtooth generator 58 is compared with
voltage V.sub..phi. by comparator 60 which provides clock pulses
for D flip-flop 64. For a positive edge triggered D flip-flop 64,
for example, when the output signal of comparator 60 transitions
from a low logic level to a high logic level, the signal at output
Q2 of D-flip-flop 64 latches to the same value as the signal at
output Q1 of D flip-flop 62.
For V.sub.CONTROL <V.sub.T, the output voltage V.sub.F of
frequency modulation controller 50 is C.sub.1 V.sub.CONTROL, and
the output voltage V.sub..phi. of phase modulation controller 52 is
zero, thus indicating that phase modulation angle .phi.=0.
Therefore, since the value of phase modulation angle .phi. is
provided to multiplier 31, and cos .phi.=1 for .phi.=0, there is no
phase modulation. On the other hand, there is frequency modulation.
That is, the output voltage C.sub.1 V.sub.CONTROL of frequency
modulation controller 50 is added to the output signal of summing
amplifier 48 and applied to the non-inverting input of comparator
56. The output signal CP1 of comparator 56 provides clock pulses to
D flip-flop 62 to toggle its state and, as stated above, also
drives sawtooth generator 58. The output voltage .[.V.sub.c .].
.Iadd.V.sub.G .Iaddend.of the sawtooth generator is compared with
voltage V.sub..phi. =0 by comparator 60 which provides clock pulses
CP2 to D flip-flop 64. As a result, D flip-flop 64 is toggled
almost simultaneously with D flip-flop 62. In this way, for
V.sub.CONTROL <V.sub.T, frequency modulation using optimal
control is achieved when operating within the operable frequency
range of the switching devices.
For V.sub.CONTROL .gtoreq.V.sub.T, the output voltage V.sub.F of
frequency modulation controller 50 is C.sub.1 V.sub.T, a constant,
so that the switching frequency of switching devices S1, S2, S3 and
S4 is fixed at an extremity of the operable frequency range
thereof. Under these conditions, the output voltage V.sub..phi. of
phase modulation controller 52 is C.sub.2 (V.sub.CONTROL -V.sub.T).
This voltage V.sub..phi. is compared with the output signal V.sub.G
of sawtooth generator 58 by comparator 60. As a result, the clock
pulses CP2 from comparator 60 to D flip-flop 64 are delayed by an
amount of time proportional to phase modulation angle .phi..
Voltage V.sub..phi. also enables multiplier 31 to multiple source
voltage V.sub.S by cos .phi.. In this way, phase modulation is
employed to produce the tri-level voltage waveform shown in FIG. 4B
for controlling the series resonant inverter. By thus combining a
method of optimal trajectory control with phase modulation, a
broader dynamic range of output load voltage can be achieved under
all operating conditions.
FIGS. 8a-8i are waveforms that illustrate in detail the operation
of the new resonant inverter control for a specific case of
V.sub.CONTROL >V.sub.T. For simplicity, assume the output signal
CP1 of comparator 56 has a constant pulse width and is represented
by the signal of FIG. 8a. For a positive edge-triggered D flip-flop
62, the output signals at Q1 and Q1 respectively, are illustrated
in FIGS. 8b and 8c, respectively. Voltage ramp signal V.sub.G from
sawtooth generator 58, which is reset each time the output signals
from D flip-flop 62 change state, is shown in FIG. 8d. Voltage
V.sub..phi., which determines the phase modulation angle .phi., is
illustrated as a voltage between 0 and 10 V in FIG. 8e. For this
example, voltage V.sub..phi. =5 V. The output signal CP2 of
comparator 60, determined by comparing voltage V.sub..phi. with the
output ramp voltage V.sub.G of sawtooth generator 58, is
represented in FIG. 8f and constitutes clock pulses for D flip-flop
64. For a positive edge-triggered D flip-flop 64, the output
signals at Q2 and .[.Q2.]. .Iadd.Q2 .Iaddend.respectively, are
illustrated in FIGS. 8g and 8h, respectively. The flip-flop output
signals at Q1, .[.Q1.]. .Iadd.Q1.Iaddend., Q2 and .[.Q2.].
.Iadd.Q2.Iaddend., respectively, control the base drive circuitry
65a-65 d, respectively, and produce as a result the tri-level phase
modulated signal shown in FIG. 8i. From FIG. 8i and the equation
for phase modulation angle .phi. given hereinabove, it can be seen
that phase modulation angle .phi.=.pi./4 radians for this
example.
While the preferred embodiments of the present invention have been
shown and described herein, it will be obvious that such
embodiments are provided by way of example only. Numerous
variations, changes and substitutions will occur to those of skill
in the art without departing from the invention herein.
Accordingly, it is intended that the invention be limited only by
the spirit and scope of the appended claims.
* * * * *