一阶时滞过程PID控制器优化准则

Criteria for Optimization of PID Controllers for First Order Plus Delay-time Processes

对单回路控制系统,期望得到控制器的统一优化准则。以误差积分性能指标描述系统时间响应,以环路函数的频域约束表示系统稳定裕度,从而建立一种综合的鲁棒性能(RP)指标,即系统的稳定裕度和积分性能的指数加权指标。针对比例积分微分(PID)控制器串联一阶时滞过程(FOPDT)的系统,通过计算机数值运算,选择出RP的合理加权因子范围为1～2。以加权因子取1.5的RP作为控制器优化准则,对时滞比从0到∞的FOPDT过程获得了最优PID控制。仿真表明,该法对鲁棒性和积分性能的折中是合适的,对一般工业过程的控制器参数优化有较大的借鉴意义。

Of single-loop control system, we expect the unified controller optimization criterion. With the integral performance index of error function to describe the behavior of system time-domain response, and the frequency domain constraints of loop function to indicate the system stablity margin, we established a comprehensive robust performance（RP） index, which is the exponential weighted index of stability margin and integral performance of the system. For the case of proportional integral derivative （PID） controller series the first- order plus delay time（FOPDT） process in system, through computer numerical computing, the range of RP weighted factor is reasona- bly determined from 1 to 2. With the weighted factor of 1.5 in the RP as the controller optimization criterion, the optimal PID control for FOPDT processes with the time ratio, of delay time to lag time, from 0 to infinity, were achieved. Simulation examples show that the compromise between robustness and dynamic performance of closed-loop system is appropriate and satisfactory. So, this proposed criterion can be as the best general guidelines for optimal control for common industrial processes.