Fractional Order Internal Model PID Control for Pulp Batch Cooking Process

Abstract

Pulp batch cooking is performed in a sealed high-temperature and high-pressure digester and is a complex black-box process. Based on the analysis of the mechanism of batch cooking, a model with nonlinear characteristics was established. To optimize the nonlinear part of the model, function fitting and numerical approximation were used for the simple cooking process. A novel fractional-order model is proposed to solve the problems of model inaccuracy and uncertain system parameters during batch cooking. For fractional-order systems, a two-degree-of-freedom fractional-order PID (FO-PID) controller based on internal model control is designed. The internal model control simplifies the number of parameter settings of the fractional-order controller and allows accurate adjustment of the adjustable parameters of the FO-PID controller based on the maximum sensitivity and stability margin. The simulation results show that the fractional-order internal model control in the batch cooking process is superior to the integer-order control in terms of overshoot, response speed, and robustness. Compared to internal model control, it provides better setpoint tracking dynamics and better robustness to system parameter disturbances. The practical application results in paper mills are given to illustrate the effectiveness of the method.