Nonlinear model predictive control of a simulated multivariable polymerization reactor using second-order Volterra models

Abstract

Two formulations of a nonlinear model predictive control scheme based on the second-order Volterra series model are presented. The first formulation determines the control action using successive substitution, and the second method directly solves a fourth-order nonlinear programming problem on-line. One case study is presented for the SISO control of an isothermal reactor which utilizes the first controller formulation. A second case study is presented for the multivariable control of a large reactor, and uses the nonlinear programming formulation for the controller. The model coefficients for both examples are obtained by discretizing the bilinear Taylor series approximation of the fundamental model and calculating Markov parameters. The relationships between discrete and continuous-time bilinear model matrices using an explicit fourth-order Runge-Kutta method are also included. The responses to setpoint changes of both reactors controlled with a linear model predictive control scheme and the second-order Volterra model predictive control scheme are compared to desired, linear reference trajectories. In the majority of the cases examined, the responses obtained by the Volterra controller followed the reference trajectories more closely. Practical issues, including the reduction of the number of model parameters, are addressed in both case studies.