結合頻域與時域最佳化之適應性PID參數自動調整法則

Abstract

在工業4.0的時代下，智慧化生產為主要目標。在生產製造中，電腦數值控制( Computer-Numerical-Control, CNC )受到大量的使用與重視，其需要高精度與高品質的加工能力，而伺服馬達在這其中就扮演了一個非常重要的角色。在工業上控制伺服馬達最為廣泛技術，仍然是比例-積分-微分( Proportion-Integration- Differentiation, PID )控制，因其結構簡單、使用方便，但如何調整PID參數又是一門學問。因此，本研究提出一套結合頻域與時域最佳化之適應性PID參數自動調整法則，運用在伺服馬達上，達成高效能之軌跡追蹤控制。 在時域方面，選擇遞迴最小平方法(Recursive Least Squares, RLS)作為PID參數調整之準則。在頻域方面，透過頻域迴路整形的概念，設定頻域之限制，包含低頻的高增益以達到效能要求、高頻的低增益以降低模型不確定性的影響，而在中頻部分，藉由對追蹤誤差之頻域分析，自動搜尋增益交越頻率，調整系統之頻寬，來達到更好的控制效能或增強系統之強健性。 將本研究之演算法實現於東台CNC車床TC-2000之XZ平台，與Matlab之 Simulink 所提供的 PID 參數調整器進行控制效能之比較。實驗結果顯示單軸之追蹤誤差皆有80%以上之改善，循圓測試的真圓度也能有73.72%之改善。

In the era of Industry 4.0, intelligent manufacturing is the primary target. Computer-Numerical-Control (CNC) is widely used and receives a lot of attention in manufacturing, and it needs high precision and high quality control. Servo motors play a very important role in CNC motion control. The widespread control technology for servo motors is still Proportion-Integration-Differentiation (PID) control. This is because the structure of PID control is simple and easy to use, but how to tune PID parameters is a challenge. Therefore, in this research, we propose an adaptive auto-tuning method for optimal PID parameters in frequency domain and time domain, and use it in the servo motor to achieve high-performance control of trajectory tracking. In time domain, we select the recursive least square (RLS) method for PID parameter tuning. In frequency domain, we use the concept of frequency loop-shaping to set the constraints on the magnitude of the loop transfer function, including high gains in low frequencies for good performance, and low gains in high frequencies for reducing the effects of model uncertainties. In intermediate frequencies, an algorithm is developed for automatically searching the gain crossover frequency based on frequency domain analysis of the tracking errors such that the bandwidth of the closed-loop system is automatically adjusted to achieve better control performance or increase the robustness of the system. The proposed method is implemented on the XZ table of a Tongtai CNC Lathe TC-2000. The control performance is compared with that of the PID parameters tuning function provided by Matlab/Simulink. Experimental results show that the proposed method can decrease 80% of the tracking error of each axis, and improve roundness in a circular test by 73.72%.