基于期望系统的PID频域逼近设计

Desired System Based Approximation in Frequency Domain for PID Design

摘要:

为了能在时域和频域同时具有期望的系统性能，提出了一种基于期望系统的频域逼近设计方法：在开环幅相频率特性的低频段，待设计系统频率特性模型的实部与虚部分别逼近期望开环频率特性模型的实部与虚部，从而得到PID控制器的比例增益Kp和积分增益Ki；在开环幅相频率特性的中频段，以高于期望稳定裕度的幅值条件，获得微分增益Kd的置信区间，从而确保PID控制系统的稳定性。纯滞后系统和非最小相位系统的仿真研究表明，该方法能够获得与期望系统更近的时域跟踪性能以及不低于期望系统的频域稳定裕度；同时，与其它三种PID设计方法进行了频域性能对比和时域阶跃响应测试，结果表明所提出的PID设计方法能够获得更好的性能指标。液位控制实验显示：采用所提出的方法可以实现超调量为0，系统响应速度为被控对象开环响应的的4~5倍。

Abstract:

In order to have the desired performance both in time domain and frequency domain, an approximation method based on a desired system in frequency domain is proposed. In the low frequency band of the open-loop amplitude-phase frequency curve, the real part and the imaginary part of the system to be designed respectively approximate to those of the desired one such that the proportional gain Kp and the integral gain Ki of the PID controller can be obtained. In the mid-band of frequency, the confidence interval of the differential gain Kd is calculated by expecting a higher gain margin than the desired one which ensures the stability of the closed-loop system. The simulations for time-delay system and non-minimum phase system show that the proposed method out-performers the others in set-point tracking. Meanwhile, the comparison to the other three kinds of PID design methods in frequency-domain performance and step response demonstrates that the proposed PID controller outperforms the others. The resulted stability margin by the proposed method is not less than the desired one. The experiment of water level control demonstrates that the proposed system can have zero overshoot or 5 time faster than the open loop system response.