阻尼比约束的时滞过程最优PID控制

Optimal PID Control on Damping Ratio Constraints for Dead-time Processes

对一阶时滞过程,提出一种阻尼比约束的比例积分微分(PID)控制方法。依据系统闭环特征方程导出PID参数与系统阻尼比和自然振荡频率之间的显示关系,由此算出指定阻尼比下积分增益最大的控制器参数值。临界阻尼比时,可得一阶时滞过程的最优PID控制器解析公式,其他阻尼比时,需要求解超越方程。对典型阻尼比0.707的情况,给出一个基于最优PID控制器数值解的自整定拟合公式。仿真表明,该法所得PID控制针对不同时滞的一阶时滞过程都有好的鲁棒性能。

For the first-order plus dead-time process （FOPDT）, damping ratio based proportional-integral-derivative （PID） control method is introduced. Derived from the closed-loop characteristic equation, the Pit） parameters can be expressed explicitly with the damping ratio and the natural frequency of the control system. Thus, PID parameters can be solved to optimize its integral gain. With critical damping ratio condition, analytical formulas of the optimal PID are derived on seeking the peak of the integral gain for FOPDT, while with other damping ratios, solving the transcendental equation is needed. With the typical damping ratio, 0.707, auto-tune formulas for PID controllers are fitted through the optimal values on integral gain peak. Simulations show that the proposed PID control method can achieve satisfied robustness and performance for different time-delayed FOPDT processes.