參數空間法用於擾動控制系統之分析與設計

Abstract

在實體系統中使用的模型通常是不準確的。在運作期間，系統中的參數常隨著時間和環境的變化而改變，或者由於使用之模型為簡化的模型，凡此種種原因皆可導致誤差的產生，所以針對特定準確的系統而進行之分析及設計是不完全實用的。在實際控制系統設計及分析時，穩健的系統穩定性，是重要的考慮因素。由於系統中非線性元件的存在，另一個必須考慮的重要現象為極限環的產生，而通常這是設計者不希望見到的，此類問題已經被許多的研究者討論過。對帶有非線性性質的擾動系統而言，如果能夠事先預測其極限環的行為，對設計者是極有助益的。利用描述函數法將非線性元件線性化，以預測其極限環的發生，已成功的使用在許多的應用上。 本論文旨在針對具有擾動參數的控制系統，提出一完整且有效之方法，利用參數空間法及穩定性的基本觀念，以分析其增益邊際和相位邊際，並且設計控制器，調整控制器的係數，以達到系統頻域的規格要求，例如增益邊際、相位邊際和敏感度。同時對有非線性元件的系統，預測其極限環的發生。車輛模型被使用為模擬的例子。藉著求解系統之特性方程式，在選定之系統參數平面或空間上，產生增益及相位邊界曲線，以圖解方式決定控制器係數的合格區域，以使整個系統之性能達到頻域規格的要求，以此法進行分析及設計。同樣的方法也應用於模糊控制系統穩定度的分析。以上提出之方法更進一步延伸至具有擾動參數的鎖相迴路系統的設計分析。部分系統參數在給定區域擾動，於參數平面上，以圖形顯示待決之目標參數區域，選定該區域範圍內之參數，使該鎖相迴路系統能達到規格之要求。本論文模擬的結果已驗証了預期達成之目標。

The models used are usually imprecise and the parameters of physical systems vary with the operating conditions and time. Designing and implementing a system for a fixed and exact control plant is not usually practical in the natural environments. A inaccurate plant may result from a simplified model and uncertainties in system parameters can always occur in the physical world. Robustness stability is important in analysis and design of practical control systems. Another important phenomena to be considered is undesirable oscillations due to nonlinearities in a feedback closed system and it has been studied by many researchers. It is very instructive for the designer to predict the limit cycle behavior of a perturbed control system with nonlinearities. The describing function technique is mainly employed to predict the existence of constant amplitude oscillations of closed nonlinear systems and has been successfully used in many applications. The main subject of this dissertation is to propose a novel method based on parameter space method and robust stability criteria to predict limit cycles occurred, analyze the system performances of gain margin and phase margin (GM and PM), and design a desired controller by adjusting the controller coefficients for perturbed control systems to meet specified conditions including GM, PM and sensitivity in frequency domain. A vehicle model is used as an example for simulation. With the help of gain and phase boundary curves resulting from the roots of the characteristic polynomial equation of closed control systems, a methodology is proposed for portraying regions in a selected designed parameter plane so that the performance of the whole system can meet the specified requirements with perturbed parameters varying in given intervals. The same approach is extended to analyze the robust stability for a fuzzy control system. This dissertation also applies the above method on phase-locked loops (PLL) design by frequency domain approach for a perturbed PLL system. The desired system parameters of PLLs in the selected coordinate plane are determined in graphical portrayals. Simulation results have demonstrated and achieved the objectives as desired.