Design of an intelligent stochastic model predictive controller for a continuous stirred tank reactor through a Fokker-Planck observer

Abstract

Over the years, different methods have been presented to control continuous stirred tank reactors (CSTRs) in which stochastic behavior of process has rarely been considered. This article uses the stochastic model of CSTR to compute the temperature of coolant as process input in order to control the joint probability density function (PDF) of process concentration and temperature. The computation is carried out based on receding horizon-model predictive control (RH-MPC). Since observer has important role in the determination of process input, we use a nonlinear stochastic Fokker-Planck observer to calculate process PDF. The CSTR model is nonlinear and complex, so the particle swarm optimization (PSO) algorithm is used for simplification of computations and for determination of the optimal value of process input. For this purpose, an MPC problem is described for which the cost function is defined based on the difference between the process PDF and a desired PDF. In this definition, temperature limitation of the coolant and the corresponding Fokker-Planck equation are both assumed as the problem constraints. When this MPC problem is solved by the use of PSO, the process input is calculated for each time window. The existence and uniqueness of our optimal solution is also studied. In the article, the Fokker-Planck equation for CSTR model will be solved by the use of path integral method. In this way, the joint PDF of process concentration and temperature is obtained for any instance of time. The simulation results are also obtained to evaluate the proposed method.