无模型SISO时滞系统的PID参数稳定域研究

针对无精确模型的单输入单输出(SISO)时滞系统, 利用频率响应数据, 给出确定PID参数稳定域的解析方法. 首先通过继电反馈频域辨识法得到系统的频率响应数据, 然后基于该数据确定控制参数的奇异边界线和非奇异边界线, 并判断边界线的哪一侧具有更少的不稳定极点, 从而给出能使闭环系统稳定的控制参数区域. 该方法避免了模型辨识的复杂计算过程, 为无模型SISO时滞系统的PID控制器设计和调节提供了一条简单有效的途径. 仿真结果验证了方法的有效性.

Stability regions of PID parameters for model-free SISO systems with time delay

For the single-input and single-output (SISO) time-delay system with no accurate model, we propose an analytical method for determining the stability regions of PID parameters by using the frequency response data. The frequency response data are obtained by using the method of frequency response identification from relay feedback. Then, the singular and nonsingular boundaries of the PID parameters are determined from the frequency response data. By comparing the number of unstable poles on both sides of a boundary, we select the side with less unstable poles for determining the regions of PID parameters which make the closed-loop system stable. For the model-free SISO system with time delay, the proposed method avoids the complexity of the model identification, and thus provides a convenient approach for the design and tuning of the PID controller. The simulation results demonstrate the validity of this method.