Optimal Smith-fractional PID control of pneumatic control valve opening based on adaptive differential evolution

Addressing complex control challenges such as nonlinearity, time delay, and parameter perturbations in pneumatic control valve systems, an improved Smith-fractional-order proportional–integral–derivative (FOPID) control strategy optimized by an adaptive differential evolution (ADE) algorithm is proposed to enhance the dynamic response speed and robustness of valve position control. This approach integrates the flexible adjustment capability of FOPID with the time-delay compensation advantage of an improved Smith predictor to construct a compound control structure. The ADE algorithm is employed to globally optimize the five controller parameters so as to minimize the time-weighted absolute error integral criterion (ITAE) performance index. Stability analysis indicates that the stable region of the fractional-order control system is more flexible and controllable compared to that of the integer-order system. Simulation results show that, compared with conventional PID control, the proposed strategy reduces the settling time by 44.7% and the overshoot by 10.2%. Parameter perturbation experiments further verify that the system maintains satisfactory control performance even when the pneumatic transmission delay, resistance-capacitance constant, and mechanical parameters vary by ±20%, demonstrating the robustness of the improved Smith-FOPID structure. In anti-disturbance tests under sudden step disturbances, both the fluctuation amplitude (5.2%) and the recovery stability time (1.92 seconds) significantly outperform those of comparative algorithms. The proposed control strategy effectively combines high-precision tracking, fast response, and strong disturbance rejection capability, providing a reliable solution for the precise control of industrial pneumatic regulating valves.