Robust control in presence of parametric uncertainties: Observer-based feedback controller design

Abstract This paper proposes a complete procedure for the design of a robust controller for a nonlinear process, taking into account the various issues arising in the design and using the main theoretical results from the Literature about this topic. An extended model is set up, linking performance and robustness to the control law: the H ∞ norm of the extended system in closed loop measures the achievement of the objectives. The result is a state feedback control law which guarantees robust performance. The problem of the design of an observer to estimate the state of the system is also addressed, as the complete knowledge of the state is required to calculate the control action; moreover, the implications of the use of the observer in the design of the controller are pointed out. The methodology is illustrated via simulation of a regulation problem in a continuous stirred tank reactor (CSTR). The application of this methodology to more complex systems will be discussed.

[1]  Panagiotis D. Christofides,et al.  Robust hybrid predictive control of nonlinear systems , 2005, Autom..

[2]  C. Kravaris,et al.  Nonlinear State Feedback Synthesis by Global Input/Output Linearization , 1986, 1986 American Control Conference.

[3]  A. Isidori Nonlinear Control Systems , 1985 .

[4]  Vishak Sampath,et al.  Robust nonlinear control of polymethylmethacrylate production in a batch reactor , 1998 .

[5]  C. Kravaris,et al.  Robust nonlinear state feedback under structured uncertainty , 1988 .

[6]  Nael H. Ei-Farra,et al.  Output feedback control of switched nonlinear systems using multiple Lyapunov functions , 2001 .

[7]  N. El‐Farra,et al.  Bounded robust control of constrained multivariable nonlinear processes , 2003 .

[8]  G. Zames On the input-output stability of time-varying nonlinear feedback systems--Part II: Conditions involving circles in the frequency plane and sector nonlinearities , 1966 .

[9]  G. Leitmann,et al.  Robustness of uncertain systems in the absence of matching assumptions , 1987 .

[10]  John C. Doyle Analysis of Feedback Systems with Structured Uncertainty , 1982 .

[11]  Prashant Mhaskar,et al.  Robust Model Predictive Control Design for Fault-Tolerant Control of Process Systems , 2006 .

[12]  Patrizio Colaneri,et al.  Control Theory and Design. A RH2-RHinf viewpoint , 1997 .

[13]  Sahjendra N. Singh,et al.  Decoupling in a Class of Nonlinear Systems by State Variable Feedback , 1972 .

[14]  Jose A. Romagnoli,et al.  Robust H∞ control of nonlinear plants based on multi-linear models : an application to a bench-scale pH neutralization reactor , 2000 .

[15]  A. Isidori,et al.  On the synthesis of linear input-output responses for nonlinear systems , 1984 .

[16]  G. Zames On the input-output stability of time-varying nonlinear feedback systems Part one: Conditions derived using concepts of loop gain, conicity, and positivity , 1966 .

[17]  Srinivas Palanki,et al.  Robust control of I/O linearizable systems via multi-model H2/H∞ synthesis , 2000 .

[18]  F. G. Greg Shinskey,et al.  Process Control Systems: Application, Design and Tuning , 1990 .

[19]  Kumpati S. Narendra,et al.  Stability of nonlinear time-varying feedback systems , 1968, Autom..

[20]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.