Patent Publication Number: US-2007121485-A1

Title: System and method for adjusting a pid controller in a limited rotation motor system

Description:
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  
      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.  
      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.  
      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.  
      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.  
      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).  
       FIG. 1  shows a model of a limited rotation torque motor system  10  of the prior art. The system  10  includes a controller 12  (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.  
      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).  
      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.  
      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.  
      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.  
      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  
      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 p  of a proportional unit of the system, for the coefficient k i  of an integral unit for the system, and for the coefficient k 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  
      The following description may be further understood with reference to the accompanying drawings in which:  
       FIG. 1  shows an illustrative diagrammatic functional view of a limited rotation motor and control system in accordance with the prior art;  
       FIG. 2  shows an illustrative diagrammatic functional view of a limited rotation motor and control system in accordance with an embodiment of the invention;  
       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;  
       FIG. 4  shows an illustrative diagrammatic representation of a controller in accordance with an embodiment of the invention;  
       FIG. 5  shows an illustrative graphical representation of a measured frequency response of a system in accordance with an embodiment of the invention;  
       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;  
       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;  
       FIG. 8  shows an illustrative graphical representation of a control system transfer function of a system in accordance with an embodiment of the invention;  
       FIG. 9  shows an illustrative diagrammatic functional view of a galvanometer and control system in accordance with another embodiment of the invention;  
       FIG. 10  shows an illustrative diagrammatic functional view of a galvanometer and control system in accordance with a further embodiment of the invention; and  
       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. 
    
    
      The drawings are shown for illustrative purposes only.  
     DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS  
      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.  
      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.  
      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.  
       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 p ), a integrating element  46  (k i ), and a derivative element  48  (k 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.  
      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.  
      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 0 w 0 , a 1 w 1 , a 2 w 2  . . . a n w n , where n may, for example, be 512. A sequence of the ratios of the values a 0 , a 1 , a 2  . . . a n  for the position detection signal  42  over the respective values a 0 , a 1 , a 2  . . . a n  for the control signal yields a sequence of magnitudes m 0 , m 1 , m 2  . . . m n . This ratio sequence is provided by the ratio sequence unit  68 . These magnitudes m 0 , m 1 , m 2  . . . m 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 μsec for a 1024 PBRS sequence.  
      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  52   a,    52   b  and  52   c  may be provided to the PID units  44 ,  46  and  48  of the controller  32 .  
      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   ⁢     s   3       -     10.47   ⁢     s   2       -     15.82   ⁢   s     -   6.642         0.3259   ⁢     s   3       +     2.942   ⁢     s   2       +     2.951   ⁢   s     -   0.0067         
 
      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 p =1.05, k d =1 and k i =2.25, with the transfer function of  
           s   2     +     1.05   ⁢   s     +   2.25     s       
 
      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.  
      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   ⁢           ⁢   all   ⁢           ⁢   w   ⁢           ⁢   interest       ⁢     [     (       mag   ⁡     (     C   ⁡     (   w   )       )       -       mag   ⁡     (     D   ⁡     (   w   )       )       2       ]               
     and     
       Q   =         ∑     for   ⁢           ⁢   all   ⁢           ⁢   w   ⁢           ⁢   interest       ⁢     [     (       ang   ⁡     (     C   ⁡     (   w   )       )       -       ang   ⁡     (     D   ⁡     (   w   )       )       2       ]               
 
 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   ⁡     (     C   ⁡     (   w   )       )       -       real   ⁡     (     D   ⁡     (   w   )       )       2     +                 (       image   ⁡     (     C   ⁡     (   w   )       )       -       image   ⁡     (     D   ⁡     (   w   )       )       2               ]             
 
 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. 
 
      For a PID controller as shown in  FIG. 2 , therefore, the frequency response may be generalized as 
 
 C ( w )=( k   d   *jw+k   i   −k   p   *w   2 )/ jw  
 
 where k p , k i  and k 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. 
 
      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 p ), the integral unit  128  (k i ) and the derivative unit  130  (k d ).  
      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   p   *jw+k   i )/ jw *(1 +k   d   *jw*P ( w )) 
 
 where P(w) is the frequency response of the system to be controlled. Again, the controller coefficients k p , k i , k d  may be designed using frequency matching by substituting the above equation for C(w) into the functions for Q discussed above. 
 
      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 p ), the integral unit  158  (k i ) and the derivative unit  160  (k d ).  
      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 i )/ jw *(1+( k   d   *jw+k   p )* P ( w )) 
 
 where P(w) is the frequency response of the system to be controlled. Again, the controller coefficients k p , k i , k d  may be designed using frequency matching by substituting the above equation for C(w) into the functions for Q discussed above. 
 
      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.  
      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.