Model Predictive Control with Variable Sampling Time for Nonlinear Continuous Time Chemical Processes

Chemical processes often involve nonlinear continuous-time ordinary or partial differential equations. When implementing advanced control strategies like Model Predictive Control, it is necessary to discretize the continuous-time system to accommodate digital control systems. Typically, a fixed sampling time is used, but this can lead to high computational costs and subpar control performance when the system exhibits significant nonlinearity. In this paper, we propose a model predictive control scheme with time varying sampling time. Specifically, we discretize the continuous-time ordinary differential equation using both low and high order models based on the Runge-Kutta method. The sampling time is then treated as a decision variable in the MPC design. To ensure accurate predictions from the discrete-time model, an additional constraint is introduced to regulate the differences between the predictions from the two sets of models. This approach effectively balances computational costs and control performance. Numerical experiments were conducted on the control of a batch reactor to validate the efficiency of the proposed method.