利用雙性能指標作伺服控制系統之最佳化設計

Abstract

本文旨在探討一種兼具指令追蹤與排除雜訊功能的控制系統設計法則。此 法應用兩個較新的觀念，即（一）設定控制器的起始狀態值與（二）依 照"混合式"準則作最佳化設計。在控制器的起始狀態可自行調整的前提下 ，設計自由度將得以加大。因此，僅用單一控制器即可讓兩個性能指標同 時達到最佳化的目的。此二性能指標，其一顯示追蹤能力；另一以反映排 除雜訊的能力為主。前者係一確定式代價函數；後者為包含隨機性及確定 性訊號的混合式代價函數。其中，根據後者而做的最佳化設計，可讓吾人 在兼顧指令追蹤的需求下，同時加強排除雜訊的能力。本法所獲致之最佳 控制器，包含指令追蹤所須的內造模型。因之，即使在控制器起始狀態無 法準確設定的情況下，亦能達到確定性指令"漸進追蹤"的目標。本法另一 優點為：控制器的動態參數不必隨著系統起始值的改變而重行設計。 In this thesis, we investigate a design method for command tracking with noise rejection. Two relatively new concepts are applied in this method: (1) assignment of a controller's initial state and (2) optimization according to a mixed-type criterion. The design variable, "controller's initial state," has broadened the freedom of design, so that two performance indices can be optimized simultaneously. About these two performance indices, one is a deterministic-type cost function for command tracking, and the other is a mixed-type cost function for noise rejection. The application of the latter one allows us to improve the ability of noise rejection while also take care of the need for command tracking. Furthermore, the resulting optimal controller contains an internal model, so that asymptotic tracking occurs for the deterministic command, even with an inaccurate assignment of the controller's initial state. Another advantage with this method is an invariance property in the sense that the assignment of the controller's dynamic parameters is independent of the system's initial state.