H-Infinity Controller Design for a Continuous Stirred Tank Reactor

The paper presents a method for H-infinity controller design for a system affected by parametric uncertainty. The proposed method is based on minimising infinity norm of sensitivity function of the nominal system. The design approach is verified by robust stabilization and control of an unstable and perturbed continuous stirred tank reactor (CSTR) with hydrolysis of Propylene Glycol. The control input is volumetric flow rate of coolant and the controlled output is the temperature of CSTR. The reactor has three uncertain parameters and an unstable process, is controlled with the help of proposed controller. The results obtained justify that designed H-infinity controller provides good tracking and disturbance rejection performances. KeywordsContinuous stirred tank reactor (CSTR), H-infinity, infinity norm, linear fractional transformation (LFT), structured uncertainty. 1-INTRODUCTION: CSTR is a very essential and important plant for chemical process industry. The distinguished property of CSTR is that it posses nonlinearity, potential safety problem and possibility to have multiple steady states. Moreover some of CSTRs parameters are not exactly known. These parameters are reaction rate constants, reaction enthalpies, heat transfer coefficients, etc [1, 2]. Hence, there is always some variation between mathematical model and true process. Because of all these facts CSTR is a very challenging plant from the control point of view and it is very important to design robust controllers for such uncertain and nonlinear plants like CSTR [3, 4]. H-infinity controller design methods are used in control theory to synthesize controllers achieving stability with guaranteed performance. To use H-infinity method a control designer expresses the control problem as a mathematical optimization 768 Ashutosh Kumar Mishra, Vijander Singh, Asha Rani problem and then evaluates the controller parameters, these methods were introduced into control theory in the late 1970’s-early 1980’s by Zames [5] and Zames and Francis [6]. The aim of this paper is to design H-infinity controller for stabilization of a CSTR which is open loop unstable. 2-PROCESS DESCRIPTION: The process under consideration is a continuous stirred tank reactor for production of propylene glycol from hydrolysis of propylene oxide with sulphuric acid as catalyst [1, 7]. The reaction is given by − − − + → − − (1) The simplified model of the CSTR system is governed by equation 3, 4 and 5. The mass balance of any component in reactor is given as