Multiplier theory for stability analysis of anti-windup control systems

Applies the passivity theorem with appropriate choice of multipliers to develop sufficient conditions for stability of the anti-windup bumpless transfer (AWBT) framework presented in Kothare et al. (1994). For particular choices of the multipliers, the authors show that these tests can be performed using convex optimization over linear matrix inequalities (LMIs). The sufficient conditions are complemented by necessary conditions for internal stability of the AWBT compensated system.

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

[2]  J. Doyle,et al.  Uncertain Multivariable Systems from a State Space Perspective , 1987, 1987 American Control Conference.

[3]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

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

[5]  Michael G. Safonov,et al.  Computer-aided stability analysis renders Papov criterion obsolete , 1987 .

[6]  Michael Athans,et al.  Multivariable Control Systems with Saturating Actuators Antireset Windup Strategies , 1985, 1985 American Control Conference.

[7]  G. Zames.  On the input-output stability of time-varying nonlinear feedback systems Part one: Conditions derived using concepts of loop gain, conicity, and positivity , 1966 .

[8]  G. Zames.  Stability of systems with sector nonlinearities: A comparison of various inequalities , 1968 .

[9]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[10]  A. H. Glattfelder,et al.  Stability of discrete override and cascade-limiter single-loop control systems , 1988 .

[11]  I. W. Sandberg,et al.  On the L 2 -boundedness of solutions of nonlinear functional equations , 1964 .

[12]  I. Sandberg.  Some results on the theory of physical systems governed by nonlinear functional equations , 1965 .

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

[14]  P. Falb,et al.  Stability Conditions for Systems with Monotone and Slope-Restricted Nonlinearities , 1968 .

[15]  Andrew Packard,et al.  The complex structured singular value , 1993, Autom..

[16]  Alex Zheng,et al.  Anti-windup design for internal model control , 1994 .

[17]  K. Narendra,et al.  An off-axis circle criterion for stability of feedback systems with a monotonic nonlinearity , 1968 .

[18]  A. Packard,et al.  Linear matrix inequalities in analysis with multipliers , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[19]  M. Morari,et al.  Multivariable Anti-Windup and Bumpless Transfer: A General Theory , 1989, 1989 American Control Conference.

[20]  A. H. Glattfelder,et al.  Stability of override control systems , 1983 .

[21]  Michael Safonov,et al.  Computer-aided stability analysis renders Papov criterion obsolete , 1987, 26th IEEE Conference on Decision and Control.

[22]  V. Balakrishnan.  Linear matrix inequalities in robustness analysis with multipliers , 1995 .

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

[24]  Lars Rundqwist,et al.  Integrator Windup and How to Avoid It , 1989, 1989 American Control Conference.

[25]  R. W. Brockett,et al.  Frequency domain stability criteria. II. , 1965 .

[26]  R. Fitts,et al.  Two counterexamples to Aizerman's conjecture , 1966 .

[27]  A. Glattfelder,et al.  Stability analysis of single loop control systems with saturation and antireset-windup circuits , 1983 .

[28]  J. Wen,et al.  Robustness analysis of LTI systems with structured incrementally sector bounded nonlinearities , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[29]  G. Zames.  On the input-output stability of time-varying nonlinear feedback systems--Part II: Conditions involving circles in the frequency plane and sector nonlinearities , 1966 .