Minimal controller synthesis algorithms with output feedback and their generalization

This paper proposes several improvements in the minimal controller synthesis algorithms, which were developed for a class of nonlinear systems with uncertainties. The major proposition is that only the output feedback is enough to control some nonlinear systems without an observer while the existing algorithms require the complete state feedback. Next, the extended version and the parameter identification technique of the minimal controller synthesis algorithm are combined in a single method estimating some more parameters for some known forms of nonlinearities. This is applicable with or without the improvement of removing the need for using the complete state feedback. It is proven that the scaling factors in the algorithms can be variable and different for each component. The algorithms are applicable to some noncanonical forms of systems. All the propositions and some of the existing algorithms are generalized in a single form with some options. A speed-sensorless DC motor control simulation is also included with quite exaggerated noisy conditions and the results verify that the proposed modifications make the minimal controller synthesis algorithms much more efficient model reference adaptive control algorithms for certain types of systems. The proposed method, which does not use the speed measurement, yields fewer ripples than the existing method, which uses the speed measurement. In addition, the proposed method accurately estimates the armature resistance and inductance while the existing method fails to do this.

Anahtar Kelimeler:

Output feedback control, identification and control methods, DC motor control

Minimal controller synthesis algorithms with output feedback and their generalization

Keywords:

Output feedback control, identification and control methods, DC motor control,

PDF

___

D.P. Stoten, H. Benchoubane, “Empirical studies of an MRAC algorithm with minimal controller synthesis”, International Journal of Control, Vol. 51, pp. 823–849, 1990.
D.P. Stoten, H. Benchoubane, “Robustness of a minimal controller synthesis algorithm”, International Journal of Control, Vol. 51, pp. 851–861, 1990.
D.P. Stoten, H. Benchoubane, “The decentralized minimal controller synthesis algorithm”, International Journal of Control, Vol. 56, pp. 967–983, 1992.
D.P. Stoten, H. Benchoubane, “The extended minimal controller synthesis algorithm”, International Journal of Control, Vol. 56, pp. 1139–1165, 1992.
D.P. Stoten, H. Benchoubane, “The minimal control synthesis identification algorithm”, International Journal of Control, Vol. 58, pp. 685–696, 1993.
Y.D. Landau, Adaptive Control: The Model Reference Approach, New York, Marcel Dekker, 1979.
S.P. Hodgson, D.P. Stoten, “Robustness of the minimal control synthesis algorithm with minimal phase plant dynamics of unknown order but known relative degree”, International Journal of Control, Vol. 71, pp. 1–17, 1998. T.T. Arif, “A modified minimal controller synthesis for satellite attitude control”, IEEE Aerospace Conference, Paper No. 8.0404, 2006.
S.R. Bowes, J. Li, D.P. Stoten, “Novel robust adaptive control for high performance field oriented control drives”, Conference Record of the IEEE 31st Industry Applications Conference, Vol. 1, pp. 418–425, 1996.
T.S. Richardson, G.A. Charles, D.P. Stoten, M. di Bernardo, M.H. Lowenberg, “Continuation based control of aircraft dynamics”, Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 4932–4938, 2003.
W.S.H. Wong, W.K.S. Pao, D. Holliday, “Minimal controller synthesis adaptive control for direct torque controlled induction motor drives”, First International Power and Energy Conference, pp. 330–336, 2006.
T.T. Arif, “A decentralized adaptive control of flexible satellite”, IEEE Aerospace Conference, Paper No. 8.0405, 200
K. Koganezawa, D.P. Stoten, “Adaptive control of manipulators via an extension to the error-based minimal control synthesis with integral action algorithm”, IEEE International Conference on Robotics and Automation, pp. 1960– 1967, 2007.
D.G. Luenberger, “Canonical forms for linear multivariable systems”, IEEE Transactions on Automatic Control, Vol. 12, pp. 290–293, 1967.
V.M. Popov, Hyperstability of Automatic Control Systems, New York, Springer-Verlag, 1973.
M. di Bernardo, D.P. Stoten, “A new extended minimal control synthesis algorithm with an application to control of chaotic systems”, Proceedings of the 36th Conference on Decision and Control, Vol. 2, pp. 1902–1907, 1997.
A.P. Morgan, K.S. Narendra, “On the stability of nonautonomous differential equations ·x = A+B(t)x, with skew symmetric matrix B(t)”, SIAM Journal on Control and Optimization, Vol. 15, pp. 163–176, 1977.
K.S. Narendra, L.S. Valavani, “Stable adaptive controller design-direct control”, IEEE Transactions on Automatic Control, Vol. 23, pp. 570–583, 1978.
P.C. Krause, O. Wasynczuk, S.D. Sudhoff, Analysis of Electric Machinery and Drive Systems, New York, Wiley Press, 1994.
A. Sevin¸ c, “A full adaptive observer for DC servo motors”, Turkish Journal of Electrical Engineering & Computer Sciences, Vol. 11, No. 2, pp. 117–130, 2003.