An Output Feedback Controller Design for Linear Systems Subject to Sensor Nonlinearities

Abstract— In this paper, the output feedback controllerdesign problem is addressed for linear systems subject to sensornonlinearity. First, the existence condition of an output feedbackcontroller is derived for systems with sensor sector nonlinearity. Adesign method for the output feedback controller is proposedusing a linear-matrix inequality (LMI) based approach. The resultis then applied to the design of a regional output feedbackcontroller for the systems subject to sensor saturation. An LMI op-timization based approach is proposed to computing the feedbackmatrices of the regional output feedback controller. At lasta numerical example is presented to show the effectiveness of theresults.Index Terms— Linear systems, sector nonlinearity, sensor satu-ration, control, 2 gain. I. I NTRODUCTION I N FEEDBACK control systems, feedback device non-linearities, including actuator and sensor saturation, arisefrequently. They can severely degrade the closed-loop systemperformance and sometimes even make an otherwise stableclosed-loop system unstable. The issue of closed-loop systemstability and performance in the presence of feedback devicenonlinearities thus carries a great deal of practical importance.While in practice it is desirable to choose actuators and sensorsthat are large enough so that they operate in their linear regions,cheaper actuators and sensors can be used if their saturationcan be satisfactorily handled.While actuator nonlinearity has been addressed in muchdetail, (see, for example, [1], [13], [5] and the referencestherein), few results are available that deal with the sensornonlinearity. Among these few results, observability of a linearsystem subject to sensor saturation was studied in detail in[12]. A discontinuous dead beat controller was constructedfor single-input–single-output (SISO) linear systems in thepresence of output saturation in [11]. A semiglobal stabilizinglinear output feedback controller design method was proposedfor the SISO linear systems subject to sensor saturation in [14].In this paper, we will use the circle criterion theory to ad-dress the issues related to analysis and design for linear sys-

[1]  Tingshu Hu,et al.  Semi-global stabilization of linear systems subject to output saturation , 2001, Syst. Control. Lett..

[2]  Zongli Lin,et al.  Low gain feedback , 1999 .

[3]  G. Kreisselmeier.  Stabilization of linear systems in the presence of output measurement saturation , 1996 .

[4]  Karolos M. Grigoriadis,et al.  Anti-windup controller design using linear parameter-varying control methods , 2000 .

[5]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[6]  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).

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

[8]  Pascal Gahinet,et al.  Explicit controller formulas for LMI-based H∞ synthesis , 1996, Autom..

[9]  R. Skelton,et al.  Linear quadratic suboptimal control with static output feedback , 1994 .

[10]  Tetsuya Iwasaki,et al.  All controllers for the general H∞ control problem: LMI existence conditions and state space formulas , 1994, Autom..

[11]  Wassim M. Haddad,et al.  Fixed-structure controller design for systems with actuator amplitude and rate non-linearities , 2000 .

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

[13]  Wassim M. Haddad,et al.  Fixed-structure controller design for systems with actuator amplitude and rate nonlinearities , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[14]  Faryar Jabbari,et al.  Output feedback controllers for disturbance attenuation with actuator amplitude and rate saturation , 2000, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

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

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

[17]  D. Bernstein,et al.  A chronological bibliography on saturating actuators , 1995 .

[18]  Eduardo Sontag,et al.  Observability of linear systems with saturated outputs , 1994 .