Stability analysis for systems with saturation and backlash in the loop

This paper deals with the stability analysis problem for linear systems with saturation and backlash in the loop. The resulting system controlled by a static output feedback is a dynamical model with nested backlash and saturation operators. Uniform ultimate boundedness stability is tackled in a regional (local) or global context depending on the stability property of the open-loop system. Suitable regions of the state space in which the closed-loop trajectories can be captured are characterized, together with estimates of the basin of attraction of such regions. Convex optimization problems are proposed in order to give a constructive solution (in the sense of theoretical conditions associated to numerical procedures).

[1]  Thomas Kailath,et al.  The asymptotic stability of nonlinear (Lur'e) systems with multiple slope restrictions , 1998, IEEE Trans. Autom. Control..

[2]  M. Brokate,et al.  Hysteresis and Phase Transitions , 1996 .

[3]  Sophie Tarbouriech,et al.  Stability analysis and stabilization of systems presenting nested saturations , 2006, IEEE Transactions on Automatic Control.

[4]  H. Logemann,et al.  The Circle Criterion and Input-to-State Stability , 2011, IEEE Control Systems.

[5]  Isabelle Queinnec,et al.  Stability Analysis and Stabilization of Systems With Input Backlash , 2014, IEEE Transactions on Automatic Control.

[6]  Gang Tao,et al.  Control of sandwich nonlinear systems , 2003 .

[7]  Isabelle Queinnec,et al.  Stability analysis for linear systems with input backlash through sufficient LMI conditions , 2010, Autom..

[8]  Jonathan P. How,et al.  A KYP lemma and invariance principle for systems with multiple hysteresis non-linearities , 2001 .

[9]  Mattias Nordin,et al.  Controlling mechanical systems with backlash - a survey , 2002, Autom..

[10]  Isabelle Queinnec,et al.  Ultimate bounded stability and stabilization of linear systems interconnected with generalized saturated functions , 2011, Autom..

[11]  Mayergoyz,et al.  Mathematical models of hysteresis. , 1986, Physical review letters.

[12]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[13]  Maria Letizia Corradini,et al.  Robust stabilization of nonlinear uncertain plants with backlash or dead zone in the actuator , 2002, IEEE Trans. Control. Syst. Technol..

[14]  I Queinnec,et al.  Global stability for systems with nested backlash and saturation operators , 2010, Proceedings of the 2010 American Control Conference.

[15]  Karolos M. Grigoriadis,et al.  Actuator saturation control , 2002 .

[16]  Alfonso Baños,et al.  Input-output stability of systems with backlash , 2006, Autom..

[17]  I-Kong Fong,et al.  State feedback stabilization of single input systems through actuators with saturation and deadzone characteristics , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[18]  William P. Heath,et al.  Controller structure for plants with combined saturation and deadzone/backlash , 2012, 2012 IEEE International Conference on Control Applications.

[19]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[20]  P. Olver.  Nonlinear Systems , 2013 .

[21]  M. Brokate,et al.  Phase Transitions and Hysteresis , 1994 .

[22]  Sophie Tarbouriech,et al.  Stability and Stabilization of Linear Systems with Saturating Actuators , 2011 .