摘要

對於完全可控的多輸入多輸出線性非時變系統，可以使用狀態迴授，將極點放置在任意位置，讓系統狀態以期望的性能，回到原點。當進行追蹤控制時，則必需在狀態迴授控制器裡，外加一個參考訊號項。該項的權重矩陣，則必需適當設計，使輸出入訊號向量之間，有單位直流增益。這些設計，在系統皆為已知時，已頗有技巧性了，一旦系統含有匹配式的外擾時，就變得非常具有挑戰性。即使外加了強健項在控制器中，也因多輸入多輸出的特性，使推導難度大為增加。本文以滑動控制方式，提出多輸入多輸出線性非時變系統的強健追蹤控制器，企圖讓系統能容忍匹配式的外擾。其中使用Lyapunov穩定性理論，以證明閉迴路系統有漸近收斂的追蹤性能。另外，亦以電腦模擬來驗證其可行性。

Abstract

For regulation control of a completely controllable MIMO LTI system, the state feedback controller is able to place the closed-loop poles to desired locations so that the system states will converge to zero with satisfactory performance. For tracking control, in addition to the state feedback controller, a reference signal term has to be included whose weighting matrix is with a unity DC gain. Even for known systems, state feedback tracking controller design is not straightforward. When the system contains matched uncertainties, the state feedback tracking controller design problem for a MIMO LTI system becomes more involved. In this thesis, a sliding controller is proposed for the state feedback tracking control of MIMO LTI systems subject to matched uncertainties with known variation bounds. The Lyapunov stability theory is employed to prove closed-loop stability so that tracking performance can be ensured. Simulation studies are given to verify effectiveness of the proposed scheme.

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