Constrained control and rate or increment for linear systems with additive disturbances

This paper is devoted to the control of linear systems with constrained control and rate or increment with additive bounded disturbances. Necessary and sufficient conditions such that the system evolution respects rate or increment constraints are used to derive stabilizing feedback control. The control law respects both constraints on control and its rate or increment and is robust against additive bounded disturbances. An application to a surface mount robot, where the Y-axis of the machine uses a typical ball screw transmission driven by a DC motor to position circuits boards, is achieved.

[1]  Yu-Feng Li,et al.  DISCRETE-TIME SLIDING MODE CONTROL OF A DC MOTOR AND BALL-SCREW DRIVEN POSITIONING TABLE , 2001 .

[2]  A. Hmamed,et al.  Regulator problem for linear continuous-time systems with nonsymmetrical constrained control , 1993, IEEE Trans. Autom. Control..

[3]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[4]  A. Benzaouia,et al.  The resolution of equation XA+XBX=HX and the pole assignment problem , 1994, IEEE Trans. Autom. Control..

[5]  Tingshu Hu,et al.  The equivalence of several set invariance conditions under saturation , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[6]  F. Blanchini.  Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions , 1994, IEEE Trans. Autom. Control..

[7]  Edoardo Mosca,et al.  Predictive PI-control of linear plants under positional and incremental input saturations , 2000, Autom..

[8]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

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

[10]  David W. Clarke,et al.  Generalized predictive control - Part I. The basic algorithm , 1987, Autom..

[11]  C. Burgat,et al.  Regulator problem for linear discrete-time systems with non-symmetrical constrained control , 1988 .

[12]  Sophie Tarbouriech,et al.  Control of linear systems subject to input constraints: a polynomial approach , 2001, Autom..

[13]  Abdellah Benzaouia,et al.  Piecewise linear constrained control for continuous-time systems , 1999, IEEE Trans. Autom. Control..

[14]  M. Dahleh,et al.  Control of Uncertain Systems: A Linear Programming Approach , 1995 .

[15]  FOUAD MESQUINE,et al.  Constrained observer-based controller for linear continuous-time systems , 1996, Int. J. Syst. Sci..

[16]  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).

[17]  Zongli Lin,et al.  Semi-global Exponential Stabilization of Linear Systems Subject to \input Saturation" via Linear Feedbacks , 1993 .

[18]  Abdellah Benzaouia,et al.  Robust pole assignment in complex plane regions for linear uncertain constrained control systems , 2001 .

[19]  Ali Saberi,et al.  Performance with regulation constraints , 2000, Autom..

[20]  Franco Blanchini.  Feedback control for linear time-invariant systems with state and control bounds in the presence of disturbances , 1990 .

[21]  A. Benzaouia,et al.  Regulator problem for uncertain linear discrete-time systems with constrained control , 1994 .

[22]  Abdellah Benzaouia,et al.  REGULATOR PROBLEM FOR LINEAR SYSTEMS WITH CONSTRAINTS ON CONTROL AND ITS INCREMENT , 2002 .

[23]  David W. Clarke,et al.  Generalized Predictive Control - Part II Extensions and interpretations , 1987, Autom..

[24]  Stephen P. Boyd,et al.  Analysis of linear systems with saturation using convex optimization , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[25]  Abdellah Benzaouia,et al.  Regulator problem for linear systems with constraints on control and its increment or rate , 2004, Autom..