基於最小追蹤誤差與頻域限制條件之伺服馬達PID控制器參數自動調整法則

Abstract

有鑑於伺服馬達控制架構中大多數仍然使用PI或PID控制器，故本論文首先蒐集比較數種針對PID控制器之設計方法與其性能，並提出新的設計方法。前述文獻中大部分的設計方法可經由簡單的公式求得PID控制器參數，但多數的調整方法往往無法兼顧系統的強健與性能。甚至PID控制器在設計過程中，並無明確地考量系統強健性的性能指標。所以，本論文提出一套調整方法，同時考慮到時域與頻域的性能指標，在最小化平方積分誤差時，亦同時加入頻域限制。利用頻率整形(frequency shaping)的概念，調整系統之頻率響應，以達成符合相位邊界(phase margin)且使頻寬最大化的最佳控制器參數調整方法，使設計出的控制系統能兼顧強健性與性能，再由此最佳化參數調整方法發展出一整套的參數調整流程，最後將此調整流程整合於人機介面，並實際運用在Faulhaber伺服馬達的速度控制與位置控制上。實驗結果顯示，與Faulhaber的參數自動調整演算法相比，本研究之所得到的控制器參數可達到更好之控制效能。

In view of the widespread use of PID controllers in servo motors, this study first collects some widely used PID tuning methods and compares their performance. These methods use simple formulas to find the PID gains, but they cannot satisfy the requirements of robustness and performance at the same time. Some of the tuning methods tune the PID gains without explicit consideration of the robustness margin. To improve the tuning process, this study proposes a new tuning method which considers the performance of time domain and frequency domain at the same time. While minimizing the integral of squared errors, the proposed method also imposes frequency domain constraints. Using the frequency shaping techniques, the proposed method can satisfy the requirement of the user specified phase margin and maximize the bandwidth of the system. Therefore both robustness and performance are explicitly taken into account. Graphic user interfaces are designed to facilitate the whole tuning process of the proposed method. Then experiments are conducted in the position and velocity loops of a servo motor from Faulhaber. The results show that a better performance is achieved in comparison with the Faulhaber’s auto-tuning algorithm.