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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 delay process, a proportional-integral-derivative (PID) control method with damping ratio constraint is proposed. According to the system closed-loop characteristic equation, the relationship between PID parameters and system damping ratio and natural oscillation frequency is derived, and the controller parameter value with the largest integral gain under the specified damping ratio is calculated. When the critical damping ratio is obtained, the optimal PID controller analytical formula for the first-order delay process is obtained. For other damping ratios, the solution to the transcendental equation needs to be solved. For a typical damping ratio of 0.707, a self-tuning fitting formula based on the optimal PID controller numerical solution is given. Simulation results show that the proposed PID control has good robustness to the first-order delay processes with different time delays.