Nonlinear control of input-constrained systems

Abstract This paper presents an optimization-based method for deriving model-based controllers that are applicable to input-constrained, multi-input multi-output, nonlinear processes described by a discrete-time mathematical model. By this method, nonlinear model-based control laws that inherently include optimal directionality and windup compensators are derived. The control laws can minimize the mismatch between constrained and unconstrained process responses, are input–output linearizing in the absence of input constraints, and allow one to adjust the rate of decay of the mismatch between constrained and unconstrained process responses when the constraints are no longer active. The connections between (a) the derived control laws and (b) model state feedback control and modified internal model control are established. The application and performance of the derived control laws are demonstrated by three examples.

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

[2]  F. Doyle,et al.  An anti-windup scheme for multivariable nonlinear systems , 1997 .

[3]  Jonathan P. How,et al.  Synthesizing stability regions for systems with saturating actuators , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[4]  Eric Coulibaly,et al.  Internal model predictive control (IMPC) , 1995, Autom..

[5]  Costas Kravaris,et al.  Nonlinear Model Based Process Control , 1998 .

[6]  A. Teel.  A nonlinear small gain theorem for the analysis of control systems with saturation , 1996, IEEE Trans. Autom. Control..

[7]  D. Chmielewski,et al.  On constrained infinite-time nonlinear optimal control , 2002 .

[8]  Masoud Soroush,et al.  A non-linear controller design method for processes with saturating actuators , 2003 .

[9]  Manfred Morari,et al.  Robust control of processes subject to saturation nonlinearities , 1990 .

[10]  Masoud Soroush,et al.  Optimal directionality compensation in processes with input saturation non-linearities , 1999 .

[11]  Masoud Soroush,et al.  Discrete‐Time nonlinear control of processes with actuator saturation , 1998 .

[12]  Alex Zheng,et al.  Anti-windup design for internal model control , 1994 .

[13]  Ilya Kolmanovsky,et al.  Fast reference governors for systems with state and control constraints and disturbance inputs , 1999 .

[14]  N.H. El-Farra,et al.  Bounded robust control of constrained multivariable systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[15]  Masoud Soroush,et al.  Discrete‐time nonlinear feedback control of multivariable processes , 1996 .

[16]  Alberto Bemporad,et al.  Reference governor for constrained nonlinear systems , 1998, IEEE Trans. Autom. Control..

[17]  N. El‐Farra,et al.  Integrating robustness, optimality and constraints in control of nonlinear processes , 2001 .

[18]  Edoardo Mosca,et al.  Global switching regulation of input-saturated discrete-time linear systems with arbitrary l2 disturbances , 2001, IEEE Trans. Autom. Control..

[19]  Michael J. Kurtz,et al.  Feedback linearizing control of discrete-time nonlinear systems with input constraints , 1998 .

[20]  Chong-Ho Choi,et al.  Dynamic compensation method for multivariable control systems with saturating actuators , 1995, IEEE Trans. Autom. Control..

[21]  Frank Allgöwer,et al.  A computationally attractive nonlinear predictive control scheme with guaranteed stability for stable systems , 1998 .

[22]  Ping Lu,et al.  Constrained tracking control of nonlinear systems , 1996 .

[23]  Prodromos Daoutidis,et al.  Stabilization of nonlinear processes with input constraints , 2000 .

[24]  Faryar Jabbari,et al.  Output feedback controllers for disturbance attenuation with actuator amplitude and rate saturation , 2000, Autom..