A Robust Controller for Output Variance Reduction and Minimum Variance with Application on a Permanent Field DC-Motor

In this paper, we present an experimental testing for a new algorithm that determines an optimal controller-s coefficients for output variance reduction related to Linear Time Invariant (LTI) Systems. The algorithm features simplicity in calculation, generalization to minimal and non-minimal phase systems, and could be configured to achieve reference tracking as well as variance reduction after compromising with the output variance. An experiment of DCmotor velocity control demonstrates the application of this new algorithm in designing the controller. The results show that the controller achieves minimum variance and reference tracking for a preset velocity reference relying on an identified model of the motor.

Authors:

• Mahmood M. Al-Imam
• M. Mustafa

Keywords:

• Output variance
• minimum variance
• overparameterization
• DC-Motor.

References:

[1] H. Kwakernaak, "Minimax frequency domain performance and robustness
optimization of linear feedback systems," IEEE Transactions on
Automatic Control, vol. AC-30, no. 10, pp. 994-1004, 1985.
[2] I. D. Landau and G. Zito, Digital Control Systems Design,Identification,
and Implementation, ser. Communications and Control Engineering.
Springer London, 2006, ch. Design of Digital Controllers in the Presence
of Random Disturbances, pp. 169-199.
[3] H.-W. Gao, G.-Y. Tang, and C. Li, "Optimal disturbance rejection with
zero steady-state error for time delay systems," in Proceedings of the
6th World Congress on Intelligent Control and Automation. Dalian,
China: IEEE, June 2006, pp. 511-515.
[4] K. J. Astrom and B. Wittenmark, Computer-controlled systems: Theory
and Design, 3rd ed. Prentice Hall Information and Sstem Sciences
Series, November 1996.
[5] D. W. Clarke and P. J. Gawthrop, "A self-tuning controller," IEEE
Procedinng, vol. 122, 1975.
[6] ÔÇöÔÇö, "A self-tuning controller," IEEE Procedinng, vol. 126, 1979.
[7] S. Ertunc, B. Akay, H. Boyacioglu, and H. Hapoglu, "Self-tuning control
of dissolved oxygen concentration in a batch bioreactor," Food and
Bioproducts Processing, vol. 87, pp. 46-55, 2009.
[8] M. Sternad and A. Ahlen, Polynomial methods in optimal Control and
filtering, ser. IEE Control Engineering. Peter Peregrinus Ltd., United
Kingdom, 1993, no. 49, ch. LQ control design and self-tuning.
[9] A. Krishnan and M. Das, "Minimum variance & lqg control for active
noise cancellation - a comparison," in Proc. 43rd IEEE Midwest Symp.
on Circuits and Systems, 2000, pp. 1358-1361.
[10] A. J. Krener, "A brief tutorial on linear and nonlinear control theory,"
Department of Mathematics, University of California, Tech. Rep., n.d.
[11] M. E. Halpern, "Modified pole-assignment controller for plant models
with exact or near pole-zero cancellation," IEE Proceeding, vol. 135,
no. 3, pp. 189-195, 1988.
[12] R. Davies and M. B. Zarrop, "On reduced variance overparameterized
pole assignment control," International Journal of Control, vol. 69, no. 1,
pp. 131-144, 1998.