高性能紅外線變焦鏡組伺服之分數階控制器設計與實現

Abstract

分數階微積分(fractional calculus) 的理論發展至今已有三個世紀之久，但最近這三、四十年才真正發展出適用於工程上的分數階微積分運算方法，本論文主要研究分數階微積分理論在控制器設計上的應用。首先，本文將從分數階系統的特性來開始研究，利用其特性來設計分數階控制器，討論分數階控制器在連續時間的特性、穩定性與強健性，並將控制器以直接離散化與非直接離散化兩種方法來實現分數階控制器，同時搭配不同的演算法，比較這些方法的差異性並找出適合應用在分數階控制器上。最後本文以兩段式紅外線變焦鏡機構為對象，用PIC單晶片微處理機來實現控制器，並依據紅外線變焦鏡機構與感測器特性，設計出切換式控制法則，實際驗證分數階控制器的性能。

The theory of fractional calculus has been established for over 300 years. However, the algorithm of fractional calculus was developed in the last 40 years. In this thesis, the fractional-order controllers are designed according to the characteristics of fractional-order systems in continuous time. Then, the stability and robustness of these controllers are discussed. The fractional-order controllers are achieved by direct and indirect discretizations and different algorithms. The research focuses in an application of fractional-order controllers for an infrared zoom lens servo. The implementation of the controllers is accomplished with a microprocessor PIC, which is used to switch the infrared zoom lens. Finally, the performance of fractional-order controller is shown in the experiment results.