Title: Design a Lyapunov control under input constraint for stabilisation of a CSTR

Authors: Khalil Jouili; Naceur Benhadj Braiek

Addresses: Laboratory of Advanced Systems, Polytechnic School of Tunisia (EPT), B.P. 743, 2078 Marsa, Tunisia ' Laboratory of Advanced Systems, Polytechnic School of Tunisia (EPT), B.P. 743, 2078 Marsa, Tunisia

Abstract: In this paper, a new nonlinear controller synthesis approach is presented. This approach has been developed for determination of a Lyapunov function which is computed by solving Zubov's partial differential equation of the studied controlled system. A nonlinear control law with adjustable parameters of attraction regions is derived. A Lyapunov-based control synthesis is implemented to construct an input control that guarantees stability and high precision along a steady-state. The characterisation of parameters of attraction regions can cause serious practical problems as saturation behaviour. The performance of the developed technique has been examined for temperature control of an unstable reactor and its effectiveness has been demonstrated through numerical simulation. A genetic algorithm optimisation based on linear matrix inequality are implemented to solve such problem of the proposed approach. The performance of the developed technique has been examined for temperature control of an unstable reactor and its effectiveness has been demonstrated through numerical simulation.

Keywords: Zubov method; stability region; input saturation; linear matrix inequalities; LMIs; genetic algorithms; controller design; Lyapunov control; input constraints; stabilisation; CSTR; continuous stirred tank reactors; nonlinear control; partial differential equations; PDEs; temperature control; unstable reactors; numerical simulation.

DOI: 10.1504/IJAAC.2016.075144

International Journal of Automation and Control, 2016 Vol.10 No.1, pp.52 - 72

Available online: 04 Mar 2016 *

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