Observer-based relay feedback controller design for LTI systems

This paper presents a design approach for observer-based relay feedback controllers. A switching law dependent on the estimation state is designed while using a Luenberger observer. The stabilization problem leads to qualitative conditions. A numerical example is provided to assess the effectiveness of the developed method.

[1]  D. Luenberger.  Observing the State of a Linear System , 1964, IEEE Transactions on Military Electronics.

[2]  Tao Liu,et al.  Industrial Process Identification and Control Design: Step-test and Relay-experiment-based Methods , 2011 .

[3]  Neil Genzlinger.  A. and Q , 2006 .

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

[5]  Osvaldo Simeone,et al.  Relay Feedback Analysis Identification And Control , 2007 .

[6]  Irmgard Flugge-Lotz,et al.  Discontinuous Automatic Control , 1953 .

[7]  K. Henrik,et al.  Limit Cycles with Chattering in Relay Feedback Systems , 1997 .

[8]  Vadim I. Utkin,et al.  Sliding mode control in electromechanical systems , 1999 .

[9]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

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

[11]  Emilia Fridman,et al.  Variable Structure Control With Generalized Relays: A Simple Convex Optimization Approach , 2015, IEEE Transactions on Automatic Control.

[12]  Karl Henrik Johansson,et al.  Fast switches in relay feedback systems , 1999, Autom..

[13]  D. Luenberger.  Observers for multivariable systems , 1966 .

[14]  B. Ross Barmish,et al.  Robustness of Luenberger Observers: Linear Systems Stabilized via Nonlinear Control , 1984 .

[15]  Jean-Pierre Barbot,et al.  Sliding Mode Control In Engineering , 2002 .

[16]  Romain Delpoux,et al.  Parameter-Dependent Relay Control: Application to PMSM , 2015, IEEE Transactions on Control Systems Technology.

[17]  Cheng-Ching Yu,et al.  Autotuning of PID Controllers: Relay Feedback Approach , 1999 .

[18]  Karl Henrik Johansson,et al.  Stability of limit cycles with chattering in relay feedback systems , 2003, 2003 European Control Conference (ECC).

[19]  J. Aubin,et al.  Differential inclusions set-valued maps and viability theory , 1984 .

[20]  Jamal Daafouz,et al.  Observabilité d'un convertisseur multi-niveaux via le principe d'invariance de Lasalle , 2010 .

[21]  Munther A. Dahleh,et al.  Global stability of relay feedback systems , 2001, IEEE Trans. Autom. Control..

[22]  A. Polyakov,et al.  On practical stabilization of systems with delayed relay control , 2010 .

[23]  Alexander S. Poznyak,et al.  Attractive Ellipsoids in Robust Control , 2014 .

[24]  Andrey Polyakov,et al.  On relay control for discrete time systems using linear matrix inequalities , 2014, 2014 European Control Conference (ECC).

[25]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[26]  Christopher Edwards,et al.  An output feedback sliding mode control strategy for MIMO systems of arbitrary relative degree , 2007, 2007 46th IEEE Conference on Decision and Control.

[27]  A. Bacciotti,et al.  Liapunov functions and stability in control theory , 2001 .

[28]  Andrei Polyakov,et al.  Practical stabilization via relay delayed control , 2008, 2008 47th IEEE Conference on Decision and Control.

[29]  I︠a︡. Z. T︠S︡ypkin.  Relay Control Systems , 1985 .

[30]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[31]  J. Cortés.  Discontinuous dynamical systems , 2008, IEEE Control Systems.

[32]  Karl Johan Åström,et al.  Relay Feedback Auto-tuning of Process Controllers – A Tutorial Review , 2002 .

[33]  W. Marsden.  I and J , 2012 .