Optimal metaheuristic state-dependent parameter proportional-integral-plus control: Alternative to gain-scheduled controller for control of a nonlinear continuous stirred tank reactor

Abstract

The continuous stirred-tank reactors have complex dynamic behavior. In the reactor, the residual concentration decreases during an exothermic chemical reaction. In this transition proper cooling is essential to stabilize the reaction, and to prevent reactor overheating. This paper presents the data-driven metaheuristic state-dependent parameter proportional-integration-plus (M-SDP-PIP) control as an alternative of gain-scheduled control for adjusting the coolant temperature of the reactor. In fact, the parameters of the discrete transfer function were identified in the non-minimal state space using state-dependent parameter which is a nonlinear method; and weighting matrixes of linear quadratic servomechanism cost function of the optimal controller were achieved by metaheuristic methods, genetic algorithm, and particle swarm optimization, according to the minimization of the integral absolute error index and energy consumption. The proposed controller was compared to gain-scheduled and non-gain-scheduled controllers in the closed-loop condition in terms of tracking performance. The results show particle swarm optimization algorithm converge to the same optimal solution as genetic algorithm using fewer number of function evaluation, so that proposed controller has more effective offset-free servo-regulatory performance than other control schemes. In addition, it is simpler and more comprehensible because it requires no auxiliary equations and models to determine and manage the control gain, as opposed to the gain-scheduled structure.