超差特征量指标集约束下PID调节器的满意优化

针对一类具有目的域的控制系统，提出将一组由滞留时间、超差时间以及随机穿越周期时间等构成的超差特征量指标纳入满意PID调节器的目标函数集中进行研究。将PID调节器的参数设计转化为局部状态反馈问题，推导出带状目的域下超差特征量指标的解析表达式，并分析了其与稳定裕度、动态误差系数以及稳态输出方差指标之间的相容性；当上述指标相容时，给出了一种利用双群体机制下的差分进化算法和内点法相结合对PID调节器参数进行优化求解的策略；数值算例表明了所提方法的有效性。

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.