Observer-based anti-windup compensator design for saturated control systems using an LMI approach

In practical control systems, actuator saturation usually induces a windup phenomenon and potentially results in system instability. Accordingly, this paper develops an observer-based auxiliary anti-windup compensation scheme to mitigate the effects of actuator limitations on the performance and stability of the controlled system. In the proposed approach, the controller output signal passing through the saturation element is treated as an external disturbance imported to the designed controller and an auxiliary controller is designed to minimize the difference between the controller output signal and the system input signal. The conditions required to maintain the system performance in the presence of actuator saturation are formulated as an LMI criterion. The L"2-stability criterion of the anti-windup compensator design is also formulated as an LMI condition. It is shown that by integrating the two LMI conditions and solving the resulting optimization problem, the resulting anti-windup controller both minimizes the performance attenuation of the saturated control system and guarantees its L"2-stability.

[1]  Luca Zaccarian,et al.  Robust linear anti‐windup synthesis for recovery of unconstrained performance , 2004 .

[2]  Bor-Sen Chen,et al.  The stability of feedback control with nonlinear saturating actuator: time domain approach , 1988 .

[3]  G. Bitsoris.  Positively invariant polyhedral sets of discrete-time linear systems , 1988 .

[4]  Roy S. Smith,et al.  Control of Plants with Input Saturation Nonlinearities , 1987, 1987 American Control Conference.

[5]  Manfred Morari,et al.  Multiplier theory for stability analysis of anti-windup control systems , 1999, Autom..

[6]  Jyh-Horng Chou.  Stabilization of linear discrete-time systems with actuator saturation , 1991 .

[7]  Per Hagander,et al.  A new design of constrained controllers for linear systems , 1982, 1982 21st IEEE Conference on Decision and Control.

[8]  Manfred Morari,et al.  Multivariable anti-windup controller synthesis using linear matrix inequalities , 2001, Autom..

[9]  An-Chen Lee,et al.  Sliding Observer for Friction Compensation in a Linear-Motor-Driven Motion System , 2011 .

[10]  Manfred Morari,et al.  A unified framework for the study of anti-windup designs , 1994, Autom..

[11]  C. Scherer,et al.  Lecture Notes DISC Course on Linear Matrix Inequalities in Control , 1999 .

[12]  Michael Athans,et al.  Design of feedback control systems for stable plants with saturating actuators , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[13]  C. Scherer,et al.  Linear Matrix Inequalities in Control , 2011 .

[14]  Chieh-Li Chen,et al.  Performance improvement of saturated system using loop shaping approach , 2009 .

[15]  Victor M. Becerra,et al.  Optimal control , 2008, Scholarpedia.

[16]  Manfred Morari,et al.  Robust control of processes subject to saturation nonlinearities , 1990 .

[17]  A.S.I. Zinober.  Optimal Relay and Saturating Control System Synthesis , 1982 .

[18]  Mayuresh V. Kothare,et al.  Simultaneous linear and anti-windup controller synthesis using multiobjective convex optimization , 2009, Autom..

[19]  Michel Kinnaert,et al.  Conditioning technique, a general anti-windup and bumpless transfer method , 1987, Autom..

[20]  Brian D. O. Anderson,et al.  Linear Optimal Control , 1971 .

[21]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[22]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .