Nonlinear Finite-Time PID Control Method with Gain Tuning by Frequency Domain Analysis

Modern control theory has developed vigorously so far, and most of them are still the PD type controller. However, PID control is still applied in most practical industries. Therefore, the PD type feedback control in this paper is improved to nonlinear finite-time PID control under time domain state space model for affine nonlinear systems. Concretely, the feedback linearization method is adopted to do the coordinate transformation of the nonlinear system and then the nonsmooth controller is skillfully designed. This closed-loop system is proved to be finite-time stable by Lyapunov method. Compared with the time domain analysis, frequency domain analysis can observe the potential robustness metrics of control system to tune the control gain. Considering that the frequency domain analysis exists obstacles for the nonlinear system, linear parameter-varying framework is adopted for the nonlinear system under the proposed method for further analysis, which is conducive to the better gain tuning of the control system. At last, simulations of the controls of data based electrostatic precipitator models are given for the validation of the proposed method.