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为进一步改进分散PID控制系统的性能,提出一种基于极限点求解的整定方法。首先,在对角优势系统Nyquist稳定性判据的基础上,推导了多变量系统对角元素的Gersh-gorin圆族的包络线方程,并获得其与负实轴交点的解析表达式,从而求解各回路的极限增益和极限频率的近似值,再利用修正的Z-N(MZN)整定公式或Tyreus-Luyben(T-L)整定公式,设计多变量系统的PID控制器。设计实例的仿真表明,所设计的控制系统具有较小的超调量和较强的抑制回路间扰动的能力,并具有良好的性能鲁棒性。
In order to further improve the performance of decentralized PID control system, a tuning method based on the solution of the limit point is proposed. First, based on Nyquist stability criterion of diagonal dominant system, the envelope equation of Gersh-gorin circle of diagonal elements of multivariable system is deduced and the analytic expression of intersection with the real axis is obtained. Solve the approximate gain and limit frequency of each circuit, and then design the PID controller of multivariable system by using the modified formula of ZN (MZN) or the formula of Tyreus-Luyben (TL). The simulation of the design example shows that the designed control system has less overshoot and strong ability to restrain inter-loop disturbance and has good performance robustness.