Research Of Deterministic Performance Assessment Of PID Controller

Accessing the cuurent PID controller performance provide useful guidelines for mproving the performance of the control loop. Controller performance in terms of the deterministic, stochastic and robustness measures are the most popular in performance assessment field. The deterministic performance assessment of PID controller has been studied in this thesis.First, performance in terms of the deterministic, stochastic and robustness characteristics is introduced, and the methods of calculating performance indexes are illustrated by some simulation examples. The most commonly used deterministic control performance, i.e. resistance to load disturbance and setpiont tracking, has been further studied. For the resistance to load disturbance, the PID controller based on direct synthesis (DS-PID) is used as the benchmark controller. The analytical expression of performance indexes and range of application are derived by analyzing the DS-PID closed loop transfer function, including integral absolute error (IAE), integral time absolute error (ITAE), integrated square error (ISE) and integral time square error (ITSE). For the setpiont tracking performance, the PID controller based on internal model control (IMC-PID) is used as the benchmark controller. The analytical expression of performance indexes and range of application are derived by analyzing the IMC-PID closed loop transfer function. Numerical fitting is used to generate the analytical expression where the theoretical value cannot predict the true value.This thesis mainly focuses on studing the methods of setpoint tracking performance assessment of PID controller with actuators saturation. Tracking performance could be affected by actuator saturation in many cases. In order to evaluate the PID setpiont tracking performance under actuator saturation accurately, the IAE is used to access system performance and PID controller is designed based on the IMC. With the plant approximated by first order or second order stable systems plus time delay (FOPDT/SOPDT), the characteristics of the IMC - PID controller output is studied by studying the close loop characteristic equation, and then the relationship between control output overshoot and the controller parameters is identified. The methods of choosing the PID controller parameters which make the optimal IAE are discussed and produced to 4 conclusions. Thus the optimal IAE value can be used as the benchmark for performance evaluation. At last, setpiont tracking performance evaluation method of the PID controller under actuators saturated is came up. Simulation examples point that ignoring the situation to calculate benchmark indexes can lead to inaccurate evaluation results. The effectiveness of the proposed method to calculate the lower bound of IAE is verified by the simulation results of FOPDT/SOPDT.