A hybrid sliding mode control based on a nonlinear PID surface for nonlinear chemical processes

Abstract

This work formulated and synthesized a hybrid control framework based on sliding mode control and internal model concepts. The resulting design conducts a Dynamic Sliding Mode Control (DSMC) approach based on a Nonlinear PID (NPID) sliding surface. The design procedure first uses the reaction curve identification method to obtain a reduced-order model from the nonlinear system. A First-Order Plus Dead-Time (FOPDT) model represents the reduced order model. The resulting controller is derived from the reduced-order model and the nonlinear surface. Therefore, a hybrid control framework (DSMC-NPID) is obtained and then applied to a couple of nonlinear chemical processes, a Variable Height Mixing Tank (VHMT), and a Continuous Stirred Tank Reactor (CSTR) in both cases to track reference trajectories and reject disturbances. Then, the proposed control approach is assessed and compared to a PID controller and a DSMC with a linear PID surface. Such evaluation is carried out using control performance indices such as Integral Square Error (ISE), Maximum Overshoot (MO), control total variation (TVu), and Settling Time (ST), respectively. Finally, the results of experimental trials were quantitatively compared to each controller, demonstrating that the DSMC-NPID approach could reduce the ISE by around 6.3%, MO by 89.3%, and ST by 17.6% regarding DSMC-PID. In addition, the results obtained for the CSTR system were similar, demonstrating that the proposed control strategy is suitable for different industrial processes.