Randomized analysis and synthesis of robust linear static anti-windup

We consider robust linear static anti-windup design for linear control systems subject to input saturation with uncertain parameters. Within this context, we use scenario-based randomized techniques and revisit the well known LMI-based static anti-windup design technique for continuous-time linear control systems. The proposed approach leads to convex (LMI-based) techniques to construct a randomized robust nonlinear L2 gain estimate and to design an optimal robust static linear anti-windup compensator. The advantages of the proposed technique are illustrated on a simulation example.

[1]  A. Teel,et al.  Stability and performance for saturated systems via quadratic and non-quadratic Lyapunov functions ∗ , 2022 .

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

[3]  Matthew C. Turner,et al.  An Architecture for Design and Analysis of High-Performance Robust Antiwindup Compensators , 2007, IEEE Transactions on Automatic Control.

[4]  Andrew R. Teel,et al.  On a performance-robustness trade-off intrinsic to the natural anti-windup problem , 2006, Autom..

[5]  Matthew C. Turner,et al.  Anti-windup synthesis using Riccati equations , 2007, Int. J. Control.

[6]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[7]  Giuseppe Carlo Calafiore,et al.  Notes on the Scenario Design Approach , 2009, IEEE Transactions on Automatic Control.

[8]  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).

[9]  Mario Garcia-Sanz.  Special Issue on ‘Wind Turbines: New Challenges and Advanced Control Solutions’ International Journal of Robust and Nonlinear Control , 2007 .

[10]  Matthew C. Turner,et al.  A tutorial on modern anti-windup design , 2009, 2009 European Control Conference (ECC).

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

[12]  Jean-Marc Biannic,et al.  Convex Design of a Robust Antiwindup Controller for an LFT Model , 2007, IEEE Transactions on Automatic Control.

[13]  Guido Herrmann,et al.  Incorporating Robustness Requirements Into Antiwindup Design , 2007, IEEE Transactions on Automatic Control.

[14]  S. Tarbouriech,et al.  Anti-windup design: an overview of some recent advances and open problems , 2009 .

[15]  Luca Zaccarian,et al.  Modern Anti-windup Synthesis: Control Augmentation for Actuator Saturation , 2011 .

[16]  Giuseppe Carlo Calafiore,et al.  Research on probabilistic methods for control system design , 2011, Autom..

[17]  Luca Zaccarian,et al.  Stability and Performance for Saturated Systems via Quadratic and Nonquadratic Lyapunov Functions , 2006, IEEE Transactions on Automatic Control.

[18]  Giuseppe Carlo Calafiore,et al.  RACT: Randomized Algorithms Control Toolbox for MATLAB , 2008 .

[19]  Roberto Tempo,et al.  On the Sample Complexity of Probabilistic Analysis and Design Methods , 2010 .

[20]  M. Campi,et al.  The scenario approach for systems and control design , 2008 .

[21]  Marco C. Campi,et al.  The exact feasibility of randomized solutions of robust convex programs , 2008 .

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

[23]  R. Tempo,et al.  Randomized Algorithms for Analysis and Control of Uncertain Systems , 2004 .

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

[25]  Alan J. Laub,et al.  The LMI control toolbox , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[26]  Giuseppe Carlo Calafiore,et al.  The scenario approach to robust control design , 2006, IEEE Transactions on Automatic Control.