Regional anti-windup compensation for linear systems with input saturation

In this paper we propose LMI methods for designing dynamic/static anti-windup compensators to improve regional performance and stability of linear control systems with saturating actuators. Algorithms are developed for minimizing the upper bound on the regional /spl Lscr//sub 2/ gain for exogenous inputs with /spl Lscr//sub 2/ norm bounded by a given value, and for minimizing this upper bound with a guaranteed reachable set or domain of attraction. Based on the structure of the optimization problems, it is shown that for systems whose plants have poles in the closed left-half plane, plant order dynamic anti-windup can achieve semiglobal stability and finite /spl Lscr//sub 2/ gain for exogenous inputs with /spl Lscr//sub 2/ norm hounded by any finite value. The problems are studied in a general setting where the only requirement on the linear control system is well-posedness and internal stability.

[1]  Christopher Edwards,et al.  An anti-windup scheme with closed-loop stability considerations , 1999, Autom..

[2]  G. Vinnicombe,et al.  Robust control of plants with saturation nonlinearity based on coprime factor representations , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[3]  Glenn Vinnicombe,et al.  Anti-windup for local stability of unstable plants , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

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

[5]  Manfred Morari,et al.  Multivariable Anti-windup Controller Synthesis Using Bilinear Matrix Inequalities , 2000, Eur. J. Control.

[6]  S. Tarbouriech,et al.  Anti-windup design with guaranteed regions of stability: an LMI-based approach , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[7]  Luca Zaccarian,et al.  A common framework for anti-windup, bumpless transfer and reliable designs , 2002, Autom..

[8]  A. Teel,et al.  The L2 anti-winup problem: Its definition and solution , 1997, 1997 European Control Conference (ECC).

[9]  Luca Zaccarian,et al.  Linear LMI-based external anti-windup augmentation for stable linear systems , 2004, Autom..

[10]  Tingshu Hu,et al.  Analysis and design for discrete-time linear systems subject to actuator saturation , 2002, Syst. Control. Lett..

[11]  I. Postlethwaite,et al.  Anti-windup schemes with closed-loop stability considerations , 1997, 1997 European Control Conference (ECC).

[12]  Mayuresh V. Kothare,et al.  Synthesis of stabilizing anti-windup controllers using piecewise quadratic Lyapunov functions , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[13]  Matthew C. Turner,et al.  Antiwindup for stable linear systems with input saturation: an LMI-based synthesis , 2003, IEEE Trans. Autom. Control..

[14]  David G. Ward,et al.  #00 Anti-Windup Design for Linear Systems Subject to Input Saturation * , 2002 .

[15]  Luca Zaccarian,et al.  Nonlinear /spl Lscr//sub 2/ gain and regional analysis for systems with anti-windup compensation , 2005, Proceedings of the 2005, American Control Conference, 2005..

[16]  David G. Ward,et al.  An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation , 2002, IEEE Trans. Autom. Control..

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

[18]  Mayuresh V. Kothare,et al.  Synthesis of Stabilizing Antiwindup Controllers Using Piecewise Quadratic Lyapunov Functions , 2007, IEEE Transactions on Automatic Control.

[19]  S. Crawshaw.  Anti-windup synthesis for guaranteed L/sub 2/ performance , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[20]  Glenn Vinnicombe,et al.  Anti-windup synthesis for guaranteed L2 performance , 2000, CDC 2000.

[21]  Isabelle Queinnec,et al.  LMI approach for L2-Control of linear systems with saturating actuators , 2004 .

[22]  Tingshu Hu,et al.  An analysis and design method for linear systems subject to actuator saturation and disturbance , 2002, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[23]  Fen Wu,et al.  Anti-windup control design for exponentially unstable LTI systems with actuator saturation , 2004, Syst. Control. Lett..