U.S. patent application number 11/566829 was filed with the patent office on 2007-05-31 for system and method for adjusting a pid controller in a limited rotation motor system.
This patent application is currently assigned to GSI GROUP CORPORATION. Invention is credited to Yuhong Huang.
Application Number | 20070121485 11/566829 |
Document ID | / |
Family ID | 34831198 |
Filed Date | 2007-05-31 |
United States Patent
Application |
20070121485 |
Kind Code |
A1 |
Huang; Yuhong |
May 31, 2007 |
SYSTEM AND METHOD FOR ADJUSTING A PID CONTROLLER IN A LIMITED
ROTATION MOTOR SYSTEM
Abstract
A method is disclosed for adjusting a proportional, integral,
derivative controller in a limited rotation motor system. The
method includes the step of providing a first frequency domain
sequence that is representative of a frequency domain
representation of a motor control signal responsive to a first
digital signal that is representative of the motor control signal.
The method also includes the step of providing a second frequency
domain sequence that is representative of a frequency domain
representation of a position detection signal responsive to a
second digital signal that is representative of the position
detection signal. The method further includes the steps of
identifying a representation of a ratio of the first and second
frequency domain sequences, and identifying appropriate values for
the coefficient k.sub.p of a proportional unit of the system, for
the coefficient k.sub.i of an integral unit for the system, and for
the coefficient k.sub.d of a derivative unit for the system
responsive to the ratio of the first and second frequency domain
signals.
Inventors: |
Huang; Yuhong; (Acton,
MA) |
Correspondence
Address: |
GAUTHIER & CONNORS, LLP
225 FRANKLIN STREET
SUITE 2300
BOSTON
MA
02110
US
|
Assignee: |
GSI GROUP CORPORATION
39 Manning Road
Billerica
MA
01821
|
Family ID: |
34831198 |
Appl. No.: |
11/566829 |
Filed: |
December 5, 2006 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
11040230 |
Jan 21, 2005 |
7190144 |
|
|
11566829 |
Dec 5, 2006 |
|
|
|
60538842 |
Jan 23, 2004 |
|
|
|
60575255 |
May 28, 2004 |
|
|
|
60613962 |
Sep 28, 2004 |
|
|
|
Current U.S.
Class: |
370/210 |
Current CPC
Class: |
G02B 26/0816 20130101;
G02B 26/101 20130101; G05B 11/42 20130101; B23K 26/04 20130101;
B41M 5/26 20130101; G05B 13/042 20130101; Y02P 70/10 20151101; B23K
26/043 20130101; G01R 31/343 20130101 |
Class at
Publication: |
370/210 |
International
Class: |
H04J 11/00 20060101
H04J011/00 |
Claims
1.-20. (canceled)
21. A method for adjusting a proportional, integral, derivative PID
controller in a limited rotation motor system, said method
comprising the steps of: providing a first frequency domain
sequence that is representative of a frequency domain
representation of a motor control signal responsive to a first
digital signal that is representative of the motor control signal;
providing a second frequency domain sequence that is representative
of a frequency domain representation of a position detection signal
responsive to a second digital signal that is representative of the
position detection signal; identifying a representation of a ratio
of the first and second frequency domain sequences; and identifying
appropriate values for the coefficient k.sub.p of a proportional
unit of the system, for the coefficient k.sub.i of an integral unit
for the system, and for the coefficient k.sub.d of a derivative
unit for the system responsive to the ratio of the first and second
frequency domain sequences.
22. The method as claimed in claim 21, wherein said steps of
providing a first frequency domain sequence that is representative
of a frequency domain representation of the motor control signal
and of providing a second frequency domain sequence that is
representative of a frequency domain representation of the position
detection signal each involve performing a Fast Fourier
Transform.
23. The method as claimed in claim 21, wherein said step of
identifying appropriate values for the coefficients k.sub.p,
k.sub.i, and k.sub.d involves communication between the
proportional, integral, derivative PID controller via a digital
network.
24. The method as claimed in claim 21, wherein said step of
identifying a representation of a ratio of the first and second
frequency domain sequences involves identifying a known frequency
response that most closely matches the ratio of the first and
second frequency domain sequences.
25. The method as claimed in claim 21, wherein the ratio of the
first and second frequency domain sequences is provided by the
second frequency domain sequence divided by the first frequency
domain sequence.
26. The method as claimed in claim 21, wherein the proportional,
integral, derivative controller is a PI plus D controller.
27. The method as claimed in claim 21, wherein the proportional,
integral, derivative controller is a P plus I plus D
controller.
28. The method as claimed in claim 21, wherein said proportional,
integral, derivative controller is employed in a limited rotation
motor system.
29. A method of operating a proportional, integral, derivative PID
controller including a proportional unit, an integral unit, and a
derivative unit, said method comprising the steps of: providing a
first frequency domain sequence that is representative of a
frequency domain representation of a motor control signal
responsive to a first digital signal that is representative of the
motor control signal; providing a second frequency domain sequence
that is representative of a frequency domain representation of a
position detection signal responsive to a second digital signal
that is representative of the position detection signal;
identifying a representation of a ratio of the first and second
frequency domain sequences; and identifying appropriate values for
the coefficient k.sub.p of the proportional unit of the system, for
the coefficient k.sub.i of the integral unit for the system, and
for the coefficient k.sub.d of the derivative unit for the system
responsive to the ratio of the first and second frequency domain
sequences.
30. The method as claimed in claim 29, wherein said step of
identifying appropriate values for the coefficients k.sub.p,
k.sub.i, and k.sub.d involves communication between the
proportional, integral, derivative PID controller via a digital
network.
31. The method as claimed in claim 29, wherein said step of
identifying a representation of a ratio of the first and second
frequency domain sequences involves identifying a known frequency
response that most closely matches the ratio of the first and
second frequency domain sequences.
32. The method as claimed in claim 29, wherein the ratio of the
first and second frequency domain sequences is provided by the
second frequency domain sequence divided by the first frequency
domain sequence.
33. The method as claimed in claim 29, wherein the proportional,
integral, derivative controller is a PI plus D controller.
34. The method as claimed in claim 29, wherein the proportional,
integral, derivative controller is a P plus I plus D
controller.
35. The method as claimed in claim 29, wherein said proportional,
integral, derivative controller is employed in a limited rotation
motor system.
36. A method of operating a proportional, integral, derivative PID
controller system including a first controller for controlling a
first axis limited rotation motor, and a second controller for
controlling a second axis limited rotation motor, said method
including the following steps for each of said first and second
controllers: providing a first frequency domain sequence that is
representative of a frequency domain representation of a motor
control signal responsive to a first digital signal that is
representative of the motor control signal; providing a second
frequency domain sequence that is representative of a frequency
domain representation of a position detection signal responsive to
a second digital signal that is representative of the position
detection signal; identifying a representation of a ratio of the
first and second frequency domain sequences; and identifying
appropriate values for the coefficient k.sub.p of a proportional
unit of the system, for the coefficient k.sub.i of the integral
unit for the system, and for the coefficient k.sub.d of a
derivative unit for the system responsive to the ratio of the first
and second frequency domain sequences.
37. The method as claimed in claim 36, wherein said step of
identifying appropriate values for the coefficients k.sub.p,
k.sub.i, and k.sub.d involves communication between the
proportional, integral, derivative PID controller via a digital
network.
38. The method as claimed in claim 36, wherein said step of
identifying a representation of a ratio of the first and second
frequency domain sequences involves identifying a known frequency
response that most closely matches the ratio of the first and
second frequency domain sequences.
39. The method as claimed in claim 36, wherein the ratio of the
first and second frequency domain sequences is provided by the
second frequency domain sequence divided by the first frequency
domain sequence.
40. The method as claimed in claim 36, wherein said proportional,
integral, derivative controller system is employed in a limited
rotation motor system.
Description
[0001] The present application is a continuation application of
U.S. patent application Ser. No. 11/040,230 which was filed on Jan.
21, 2005, which claims priority to U.S. Provisional Patent
Application Ser. No. 60/538,842 filed Jan. 23, 2004, and claims
priority to U.S. Provisional Patent Application Ser. No. 60/575,255
filed May 28, 2004, and claims priority to U.S. Provisional Patent
Application Ser. No. 60/613,962 filed Sep. 28, 2004.
BACKGROUND
[0002] The present invention generally relates to limited rotation
motor systems, and relates in particular to systems and methods for
designing and adjusting limited rotation motor systems.
[0003] Limited rotation motors generally include stepper motors and
constant velocity motors. Certain stepper motors are well suited
for applications requiring high speed and high duty cycle sawtooth
scanning at large scan angles. For example, U.S. Pat. No. 6,275,319
discloses an optical scanning device for raster scanning
applications.
[0004] Limited rotation motors for certain applications, however,
require the rotor to move between two positions with a precise and
constant velocity rather than by stepping and settling in a
sawtooth fashion. Such applications require that the time needed to
reach the constant velocity be as short as possible and that the
amount of error in the achieved velocity be as small as possible.
Constant velocity motors generally provide a higher torque constant
and typically include a rotor and drive circuitry for causing the
rotor to rotate about a central axis, as well as a position
transducer, e.g., a tachometer or a position sensor, and a feedback
circuit coupled to the transducer that permits the rotor to be
driven by the drive circuitry responsive to an input signal and a
feedback signal. For example, U.S. Pat. No. 5,424,632 discloses a
conventional two-pole limited rotation motor.
[0005] A requirement of a desired limited rotation motor for
certain applications is a system that is capable of changing the
angular position of a load such as a mirror from angle A to angle
B, with angles A and B both within the range of angular motion of
the scanner, and both defined arbitrarily precisely, in an
arbitrarily short time while maintaining a desired linearity of
velocity within an arbitrarily small error. Both the minimum time
of response of this system and the minimum velocity error are
dominated by the effective bandwidth of the system. The effective
bandwidth of the system, however, is governed by many factors,
including the open loop gain of the system.
[0006] A limited rotation torque motor may be modeled or
represented by a double-integrator model plus several flexible
modes and low frequency non-linear effects. A typical closed-loop
servo system for a galvanometer includes integral actions for low
frequency uncertainties and a notch filter for high frequency
resonant modes. System operation is chosen at the mid-frequency
range where the system is well modeled by the rigid body. For a
double integrator rigid body model, there is a direct relationship
between the open-loop gain and the cross-over frequency on the
frequency response plot. For example, an automatic tuning system
for a servowriter head positioning system is disclosed in
Autotuning of a servowriter head positioning system with minimum
position error, Y. H. Huang, S. Weerasooriya and T. S. Low, J.
Applied Physics, v. 79 pp. 5674-5676 (1996).
[0007] FIG. 1 shows a model of a limited rotation torque motor
system 10 of the prior art. The system 10 includes a controller12
(e.g., a position, integral, derivative or PID controller) that
receives an input command 14. The controller 12 provides a control
signal to a motor 16, which moves an optical element such as a
mirror to provide position changes 18 responsive to the input
command 14. The system also includes a position detector 20 that
provides a position detection signal 22 that is also provided to
the controller 12 with the input command 14. Open-loop gain (or 0
dB cross-over variations) of the system affects closed-loop system
performance if the controller is not adaptive to these
variations.
[0008] In the limited rotation motor actuator, the open-loop gain
is determined by the torque constant of the motor, the inertia of
the mirror and rotor structure, and the gain characteristics of the
power amplifier. The torque constant may change with the operation
temperature. For example, the magnetic material used in the motor
may have temperature coefficients of between about 0.1% C and 1% C.
With a temperature change of 20 C, the resulting change in torque
constant may be non-negligible. The torque constant also changes
with the angle of operations. There are other factors that may
affect the torque constant as well as the imperfect coil winding,
which causes changes in the field density (see for example, U.S.
Pat. No. 5,225,770).
[0009] The change of head from one size to another size may also
cause significant changes in total inertia, and consequently the
open-loop gain. Adaptive filter adjustment of open-loop gain
variations due to change in mirrors is more desirable when human
intervention is not required at initial set up. Other factors that
may contribute to open-loop gain variations are temperature
dependence of the power amplifier and changes in power amplifier
circuits due to aging.
[0010] Such limited rotation motors may be used, for example, in a
variety of laser scanning applications, such as high speed surface
metrology. Further laser processing applications include laser
welding (for example high speed spot welding), surface treatment,
cutting, drilling, marking, trimming, laser repair, rapid
prototyping, forming microstructures, or forming dense arrays of
nanostructures on various materials.
[0011] The processing speeds of such systems are typically limited
by one of more of mirror speed, X-Y stage speed, material
interaction and material thermal time constants, the layout of
target material and regions to be processed, and software
performance. Generally, in applications where one or more of mirror
speed, position accuracy, and settling time are factors that limit
performance, any significant improvement in scanning system open
loop gain may translate into immediate throughput improvements.
[0012] There is a need, therefore, for an improved limited rotation
motor system, and more particularly, there is a need for a rotor
for a limited rotation motor system that provides maximum
performance.
SUMMARY
[0013] In accordance with an embodiment, the invention provides a
method for adjusting a proportional, integral, derivative
controller in a limited rotation motor system. The method includes
the step of providing a first frequency domain sequence that is
representative of a frequency domain representation of a motor
control signal responsive to a first digital signal that is
representative of the motor control signal. The method also
includes the step of providing a second frequency domain sequence
that is representative of a frequency domain representation of a
position detection signal responsive to a second digital signal
that is representative of the position detection signal. The method
further includes the steps of identifying a representation of a
ratio of the first and second frequency domain sequences, and
identifying appropriate values for the coefficient k.sub.p of a
proportional unit of the system, for the coefficient k.sub.i of an
integral unit for the system, and for the coefficient k.sub.d of a
derivative unit for the system responsive to the ratio of the first
and second frequency domain signals.
BRIEF DESCRIPTION OF THE DRAWINGS
[0014] The following description may be further understood with
reference to the accompanying drawings in which:
[0015] FIG. 1 shows an illustrative diagrammatic functional view of
a limited rotation motor and control system in accordance with the
prior art;
[0016] FIG. 2 shows an illustrative diagrammatic functional view of
a limited rotation motor and control system in accordance with an
embodiment of the invention;
[0017] FIGS. 3A and 3B show illustrative graphical representations
of a pseudo random binary sequence position signal that is provided
to a motor controller, and the associated position detection signal
that is produced by the motor in response to the pseudo random
binary sequence;
[0018] FIG. 4 shows an illustrative diagrammatic representation of
a controller in accordance with an embodiment of the invention;
[0019] FIG. 5 shows an illustrative graphical representation of a
measured frequency response of a system in accordance with an
embodiment of the invention;
[0020] FIG. 6 shows illustrative graphical representations of
magnitude response curves of various PID controllers that may be
employed in accordance with certain embodiments of the
invention;
[0021] FIG. 7 shows an illustrative graphical representation of a
motor transfer function in a system to be controlled in accordance
with an embodiment of the invention;
[0022] FIG. 8 shows an illustrative graphical representation of a
control system transfer function of a system in accordance with an
embodiment of the invention;
[0023] FIG. 9 shows an illustrative diagrammatic functional view of
a galvanometer and control system in accordance with another
embodiment of the invention;
[0024] FIG. 10 shows an illustrative diagrammatic functional view
of a galvanometer and control system in accordance with a further
embodiment of the invention; and
[0025] FIGS. 11A and 11B show illustrative graphical
representations of step response signals in a control system with
and without employing a tuning system in accordance with an
embodiment of the invention.
[0026] The drawings are shown for illustrative purposes only.
DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS
[0027] In accordance with various embodiments of the invention,
limited rotation motor performance data is captured from a motor
system. A pseudo random binary signal is input to the system. The
signal that is input to the motor (the motor input signal) is
recorded, and the position signal that is received from the
position detector (the PD signal) is also recorded. A Fast Fourier
Transform (FFT) is performed on each signal, and a frequency
response representation for the PD signal is compared to the
frequency response representation for the motor input signal by
taking the ratio of these two representations. The ratio provides a
sequence (the ratio sequence) that represents the open loop
frequency response for the system. The open loop frequency response
may be provided in a Bode plot of the magnitude versus frequency. A
mathematical system model may then be generated that represents the
transfer function of the motor system. Knowing the mathematical
model for a motor system permits the system to be designed to
provide optimal output, e.g., by adjusting the PID coefficients to
achieve optimal performance, or by designing a controller that best
complements the motor system transfer function to achieve optimal
performance.
[0028] The system provides that the identification of the open loop
cross over frequency variations in the motor system may be
identified automatically (even via a remote digital network) as a
result of changes in mirror inertia, operating temperature and
operation angle. The automatic identification may be performed
closed-loop so that system stability is not affected during the
procedure. A data collection procedure may be performed in
milliseconds.
[0029] An automatic identification system in accordance with an
embodiment of the invention may involve system excitation using a
pseudo random binary sequence (PRBS), then conducting a Fast
Fourier Transform (FFT) on the captured time responses. The system
identification is then modeled using the FFT data.
[0030] FIG. 2 shows an illustrative diagrammatic view of a system
30 in accordance with an embodiment of the invention. The system 30
includes a PID controller 32 that receives an input command 34. The
controller 32 provides a control signal 35 to a motor 36, which
moves an optical element such as a mirror to provide position
changes 38 responsive to the input command 34. The system 30 also
includes a position detector 40 that provides a position detection
signal 42 that is also provided to the controller 42 with the input
command 34. The controller 32 includes proportional amplifier 44
(k.sub.p), a integrating element 46 (k.sub.i), and a derivative
element 48 (k.sub.d). The system also includes a PID adjustment
unit 50 that receives the motor control signal that is provided by
the controller 32 and the position detection signal 42. The motor
control signal and the position detection signal are provided in
digital form to a FFT converter within the adjustment unit 50 to
determine the closed loop frequency responses, and the open loop
frequency response is derived from the closed loop frequency
response.
[0031] In particular, a pseudo random binary sequence is input to
the system either as the input command 34 or is provided as a
perturbation to the output of the controller 32. The data points
for the PRBS excitation signal may be powers of twos. FIG. 3A shows
at 60 a PRBS signal, and FIG. 3B shows at 62 a position detection
provided by the motor in response to the PRBS signal shown in FIG.
3A. The input process may capture, for example, 1024 data points
for each input signal.
[0032] As shown in FIG. 4, the captured control signal 35 and
position detection signal 42 may be converted to digital signals by
A/D converters 54 and 56 is either signal is not already in digital
form. Once the input signals are in digital form, they may be
transmitted any distance, for example, via a network, and the
output PID adjustment signals may also be transmitted via a network
in a digital environment. The digital input time domain signals are
then converted to frequency domain representations of the signals
by FFT converter units 64 and 66 respectively. Each FFT provides a
complex polynomial of the form a.sub.0w.sub.0, a.sub.1w.sub.1,
a.sub.2w.sub.2 . . . a.sub.nw.sub.n, where n may, for example, be
512. A sequence of the ratios of the values a.sub.0, a.sub.1,
a.sub.2 . . . a.sub.n for the position detection signal 42 over the
respective values a.sub.0, a.sub.1, a.sub.2 . . . a.sub.n for the
control signal yields a sequence of magnitudes m.sub.0, m.sub.1,
m.sub.2 . . . m.sub.n. This ratio sequence is provided by the ratio
sequence unit 68. These magnitudes m.sub.0, m.sub.1, m.sub.2 . . .
m.sub.n provide the open loop frequency responses for the system
and may be plotted in graphical form as shown at 90 in FIG. 5. As
shown in FIG. 5, the system may experience some distortion at low
frequencies 92, some harmonic resonance at high frequencies 94, and
may be operated in the mid frequency range 96. The data collection
procedure may require very little time, for example 13.44 .mu.sec
for a 1024 PBRS sequence.
[0033] Having determined the open loop frequency responses, the
system may then identify a model for the system (using
identification unit 70), then interpolate the open loop gain from
the identified model (at interpolation unit 72) and then adjust the
controller gain accordingly using the proportional adjust unit 74,
the integral adjust unit 76 and the derivative adjust unit 78. The
outputs of the adjust units 74, 76 and 78 may be provided to D/A
converters 80, 82 and 84 respectively, and these analog PID outputs
52a, 52b and 52c may be provided to the PID units 44, 46 and 48 of
the controller 32.
[0034] The system model may be identified in a variety of ways,
including for example, frequency matching using stored information
regarding a plurality of frequency curves for known systems. For
example, FIG. 6 shows examples of magnitude response curves 100 for
various PID controllers. When a system model has been developed,
the best fit frequency curve may be selected. For example, FIG. 7
shows at 102 a model for a controller over a desired range having
the transfer function - s 4 - 3.085 .times. s 3 - 10.47 .times. s 2
- 15.82 .times. s - 6.642 0.3259 .times. s 3 + 2.942 .times. s 2 +
2.951 .times. s - 0.0067 ##EQU1##
[0035] Using a best fit analysis, the closest matching frequency
curve (from 100) may be chosen, and the controller P, I and D
values may be adjusted accordingly. For example, FIG. 8 shows at
104 a fitted PID controller with k.sub.p=1.05, k.sub.d=1 and
k.sub.i=2.25, with the transfer function of s 2 + 1.05 .times. s +
2.25 s ##EQU2##
[0036] The system, therefore, first provides a higher order
controller that meets the design specifications, and then
identifies a PID controller that matches the frequency response of
the high order controller. Examples of matching criteria include
(1) identifying the PID parameters so that the differences between
magnitudes of the frequency responses of the optimal controller and
that of the PID controller is minimized in the least mean square
(LMS) sense, and (2) identifying the PID parameters so that the
distance on the s-plane between magnitudes of the frequency
responses of the optimal controller and that of the PID controller
is minimized in the LMS sense. Frequency weighting functions may be
used for each of the above. In further embodiments, other
identification methods may involve linear least square with
weighting, non-linear search with weighting, and linear least
square followed by non-linear search, each with weighting.
[0037] The objective, therefore, of frequency matching is to select
the appropriate controller coefficients for a given controller
architecture so that the difference between the frequency responses
C(w) and D(w) is minimized, where C(w) is the controller to be
designed, D(w) is the desired controller and w is the frequency
variable in radians/sec. For optimization methods employing LMS,
this is equivalent to minimizing the following Q = for .times.
.times. all .times. .times. w .times. .times. interest .times. [ (
mag .function. ( C .function. ( w ) ) - mag .function. ( D
.function. ( w ) ) 2 ] ##EQU3## and ##EQU3.2## Q = for .times.
.times. all .times. .times. w .times. .times. interest .times. [ (
ang .function. ( C .function. ( w ) ) - ang .function. ( D
.function. ( w ) ) 2 ] ##EQU3.3## where real( ) and image( )
represent the real and imaginary part of the frequency responses
respectively. For a linear time-invariant minimal phase system, the
phase of the frequency response is uniquely defined by the
magnitude of the frequency response. The equivalent function may be
defined as Q = [ ( real .function. ( C .function. ( w ) ) - real
.function. ( D .function. ( w ) ) 2 + ( image .function. ( C
.function. ( w ) ) - image .function. ( D .function. ( w ) ) 2 ]
##EQU4## where mag( ) and ang( ) represent the magnitude and phase
angle of the frequency responses respectively. When the frequency
responses at certain frequencies are more significant than at other
frequencies, the desired frequency response D(w) may be replaced by
D(w)*W(w) in the above functions where W(w) is the weighting
function. For example, if the weighting of all other frequencies
are 1 in the weighting function W(w), the value of 10 may be
assigned to frequencies that are more critical. This provides a
weighted LMS method.
[0038] For a PID controller as shown in FIG. 2, therefore, the
frequency response may be generalized as
C(w)=(k.sub.d*jw+k.sub.i-k.sub.p*w.sup.2)/jw where k.sub.p, k.sub.i
and k.sub.d are the gains of the proportional, integral and
derivative of the error respectively. These three coefficients
fully define the PID controller and may be designed by substituting
the above equation for C(w) into the functions discussed above for
Q.
[0039] As shown in FIG. 9, a PI plus D controller system 110 in
accordance with a further embodiment of the invention may include a
PID controller 112 that receives an input command 114. The
controller 112 provides a control signal to a motor 116, which
moves an optical element such as a minor to provide position
changes 118 responsive to the input command 114. The system also
includes a position detector 120 that provides a position detection
signal 122 that is also provided to the controller 112 with the
input command 114. The system also includes a PID adjustment unit
124 the receives the motor control signal and the position
detection signal, and provide output adjustment signals to the
proportional amplifier 126 (k.sub.p), the integral unit 128
(k.sub.i) and the derivative unit 130 (k.sub.d).
[0040] Instead of feeding back the derivative of the error signal
as with the PID controller discussed above, the PI plus D
controller provides feedback of the derivative of the velocity
signal only. The frequency response of the PI plus D controller
therefore is C(w)=(k.sub.p*jw+k.sub.i)/jw*(1+k.sub.d*jw*P(w)) where
P(w) is the frequency response of the system to be controlled.
Again, the controller coefficients k.sub.p, k.sub.i, k.sub.d may be
designed using frequency matching by substituting the above
equation for C(w) into the functions for Q discussed above.
[0041] As shown in FIG. 10, a P plus I plus D controller system 140
in accordance with a further embodiment of the invention may
include a PID controller 142 that receives an input command 144.
The controller 142 provides a control signal to a motor 146, which
moves an optical element such as a mirror to provide position
changes 148 responsive to the input command 144. The system also
includes a position detector 150 that provides a position detection
signal 152 that is also provided to the controller 142 with the
input command 144. The system also includes a PID adjustment unit
154 the receives the motor control signal and the position
detection signal, and provide output adjustment signals to the
proportional amplifier 156 (k.sub.p), the integral unit 158
(k.sub.i) and the derivative unit 160 (k.sub.d).
[0042] The error proportional term in the PI plus D controller is
therefore replaced with the position proportional term. The
frequency response of the P plus I plus D controller therefore is
C(w)=i k.sub.i)/jw*(1+(k.sub.d*jw+k.sub.p)*P(w)) where P(w) is the
frequency response of the system to be controlled. Again, the
controller coefficients k.sub.p, k.sub.i, k.sub.d may be designed
using frequency matching by substituting the above equation for
C(w) into the functions for Q discussed above.
[0043] The invention provides, therefore, that a PID controlled
limited rotation motor system may be adjusted to provide improved
performance by adjusting the coefficients for the proportional,
integral and derivative elements of the PID controller. FIG. 11A
shows a command measurement 170 and a corresponding position
measurement 172 for a PID controller system prior to performing an
adjustment in accordance with an embodiment, and FIG. 11B shows a
command measurement 174 and a corresponding position measurement
176 for a the PID controller system after an adjustment is made to
the PID coefficients in accordance with an embodiment of the
invention.
[0044] Those skilled in the art will appreciate that numerous
modifications and variations may be made to the above disclosed
embodiments without departing from the spirit and scope of the
invention.
* * * * *