摘 要
本論文主要探討用強健性之H∞控制器，來控制一個脈寬模組（Pulse Width Modular,PWM）切換式降壓型DC-DC轉換器（Buck DC-DC Converter）的方法，並推導其交流（Alternating Current）小訊號數學模式。本文首先推導出拓撲電路（Topological Circuit）的狀態空間方程式，藉由建立一DC擾動操作點，將系統在操作點線性化，獲得系統之線性化狀態空間方程式。但是此狀態空間方程式，必須再加上PWM轉移函數及切換開關轉移函數形成一個完整的受控體（Plant）。接著，再根據其數學模式設計H∞控制器，使得輸出電壓外在干擾（Disturbance）及負載變動的影響降至最低程度。最後再針對不同的輸入信號，在雜訊（Noise）造成系統參數擾動的情況下，分別驗證本文控制架構的可行性及強健性（Robustness）。

Abstract
An H∞-Control design of the Pulse Width Modulator (PWM) switch buck DC-DC converter is studied in this thesis. The AC small-signal mathematical model for the PWM switch buck DC-DC converter is derived in this research and the state space equation of a topological circuit through a DC perturbation operating point is then established and linearized around the operating point. The composite model to be controlled is then composed of a AC small-signal model , a PWM transfer function and a switch transfer function. To minimize the ill-effects of the noises , disturbances and the parameter variations , the H∞-control methodolody is applied on the composite model to achieve the desired performance. Finally , computer simulations results are made to verify the feasibility and the robustness of the proposed control design under the presence of system parameter uncertainties and noises.

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