逼近速率可調之離散型順滑模態控制器設計

Abstract

本論文研製逼近速率可調之離散型順滑模態控制器，適用於具有匹配式雜訊干擾的離散型系統，可改善傳統順滑模態控制器設計時必須事先掌握雜訊上限的缺點，並掌控迫近模態之系統軌跡，以避免高頻暫態響應，及減抑控制輸入之高增益需求。此離散型順滑模態控制器包括兩個設計步驟：首先設計適當之超曲面，當受控系統沿此超曲面運動時，可穩定地接近控制目標，再選取順滑函數使系統軌跡在順滑層內，依設定之逼近速率朝此超曲面前進；其次，設計滿足迫近及順滑條件之控制法則，使系統軌跡得以在有限時間內進入順滑層，達到控制目的。最後，為了驗證逼近速率可調之順滑模態控制器的可行性，以線性單輸入二階系統及多輸入四階系統進行數值模擬，由模擬結果可知系統確實對於匹配式外界干擾具有強健性，也可經由逼近速率的選取來調控順滑模態的系統軌跡。

This thesis proposes a novel discrete sliding-mode controller with adjustable reaching rate for discrete systems encountering matched disturbance with unknown upper bound. In addition, by suitably designing the approaching mode, high frequency transient response and high gain control input can be avoided. There are two steps to design the discrete sliding-mode control. First, choose an appropriate hyper-surface and the system will reach the control goal when it moves along the hyper-surface. Besides, select sliding functions such that the system trajectory in the sliding layer will move toward hyper-surface under specific reaching rate. Next, design the control algorithms such that the approaching and sliding condition is satisfied, which completes the controller design. Finally, to verify the feasibility of the proposed sliding-mode controller, numerical simulation is adopted for a linear single-input second order system and a multi-input fourth order system. From the simulation results, the controller is indeed robust to the matched disturbance and the system trajectory in the sliding mode can be steered to reach the hyper-surface in a specific reaching rate.