μ-Suboptimal design of a robustly performing controller for a chemical reactor

Abstract The design of robustly performing controllers for an important class of control problems is treated. The problem is dealt with in the structured singular value (μ)-framework. The systems considered are characterized by weak nonlineari-ties and parametric and unstructured uncertainties. Nonlinear effects are taken into account via linearization families. Parametric uncertainty is included in a non-conservative way. Both lead to a μ-synthesis problem with repeated scalar real perturbations. As no direct solution to such a μ-synthesis problem is known to date, an iterative approach comprising both μ-analysis of the actual problem and D-K-iteration for a modified problem is shown. This approach is applied to a realistic continuous stirred-tank reactor for production of cyclopen-tenol to show the applicability to non-trivial MIMO process control problems.

[1]  J. Freudenberg,et al.  Right half plane poles and zeros and design tradeoffs in feedback systems , 1985 .

[2]  R. Vitthal,et al.  Process control via artificial neural networks and learning automata , 1995, Proceedings of IEEE/IAS International Conference on Industrial Automation and Control.

[3]  A. Tits,et al.  Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics , 1991 .

[4]  J. Kantor.  Stability of State Feedback Transformations for Nonlinear Systems - Some Practical Considerations , 1986, 1986 American Control Conference.

[5]  J. Hauser.  Nonlinear control via uniform system approximation , 1991 .

[6]  J. Doyle,et al.  mu analysis with real parametric uncertainty , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[7]  David M. Himmelblau,et al.  Process control via artificial neural networks and reinforcement learning , 1992 .

[8]  J. Doyle,et al.  Computation of mu with real and complex uncertainties , 1990, 29th IEEE Conference on Decision and Control.

[9]  W. Baumann,et al.  Feedback control of nonlinear systems by extended linearization , 1986 .

[10]  Kurt Dirk Bettenhausen.  Kontinuierlicher Rührkesselreaktor mit Neben- und Folgereaktionen , 1993 .

[11]  Ian Postlethwaite,et al.  μ-K iteration: A new algorithm for μ-synthesis , 1993, Autom..

[12]  Ferenc Szeifert,et al.  Adaptive optimizing control algorithm for a CSTR , 1992 .

[13]  Evanghelos Zafiriou,et al.  Robust process control , 1987 .

[14]  G. Stein,et al.  Multivariable feedback design: Concepts for a classical/modern synthesis , 1981 .

[15]  Richard D. Braatz,et al.  Robust control for a noncollocated spring-mass system , 1992 .

[16]  G. Stein,et al.  Performance and robustness analysis for structured uncertainty , 1982, 1982 21st IEEE Conference on Decision and Control.

[17]  M. Morari,et al.  On Nonlinear Systems with Poorly Behaved Zero Dynamics , 1992, 1992 American Control Conference.

[18]  J. Doyle,et al.  Review of LFTs, LMIs, and mu , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[19]  W. Rugh,et al.  Feedback linearization families for nonlinear systems , 1987 .

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

[21]  Masoud Soroush,et al.  Multivariable Nonlinear Control of a Continuous Polymerization Reactor , 1992, 1992 American Control Conference.

[22]  John C. Doyle,et al.  Matrix interpolation and H∞ performance bounds , 1985, 1985 American Control Conference.

[23]  C. Reboulet,et al.  "Pseudolinearization of multi-input nonlinear systems" , 1984, The 23rd IEEE Conference on Decision and Control.