Satisfactory Optimization for PID Regulator with Constraints on Exceeding Tolerance Characteristic Indices

With regard to a class of control systems with target areas,a set of exceeding tolerance characteristic(ETC) indices combined by residence time,exceeding tolerance time and random passage period time are added to the objective functions for a satisfactory PID regulator design.Firstly,the design of PID regulator's parameters is transformed into a partial state feedback problem,and analytical formulas of the ETC indices on zonal target area are deduced.Then,on this basis,the consistency of ETC indices,stability margin index,dynamic error coefficient index and steady output covariance index,are analyzed.When the above indices are consistent,a differential evolution algorithm based on double populations is utilized together with interior point method to find a set of optimal parameters for the PID regulator.A numerical example is presented finally to show the effectiveness of the proposed method.