本文提出符號函數技術來解決多輸入多輸出系統的輸入飽和限制問題。傳統的線性二次式類比追蹤器雖有良好的追蹤效果，但是在暫態響應或追蹤軌跡為劇烈變化時會產生很大的輸入能量，如此巨大的輸入能量甚至在自然界是難以實現的。因此運用符號函數的特性來抑制巨大的輸入訊號。首先，根據最佳線性化方法可分析符號函數的特性。接著，將符號函數應用在線性二次式類比追蹤器，以達到壓縮控制輸入的效果。此外，合理壓縮控制的過程也已被詳細的驗證。最後，運用這些線性模型設計具有壓縮控制輸入的數位重新設計追蹤器。儘管使用符號函數的模型跟其它的輸入限制飽和致動器一樣會損失少部份追蹤的效果，但是卻不須如其他的限制飽和致動器(例如:windup)須設定較多參數，其只須使用簡單且基本的最佳化控制概念即可。

In this thesis, a sign function control is proposed to resolve the input constraint problem for MIMO systems. A conventional linear quadratic analog tracker with the high-gain property has good tracking performance. However, the great energy of the control input is usually required and may not exist in nature world due to the violent variation of the transient response and the specific reference. Hence, the sign function is applied to constrain the huge control input. Firstly, the sign function property can be analyzed by optimal linearization algorithm. Then, using the sign function control for the linear quadratic analog tracker can compress the control input. Finally, these models are applied to design the digital redesign tracker which still can compress the control input. Although the sign function control loses slightly tracking performance as well as other constrained actuators, the parameters of the proposed controller which just applies optimization control theorem are less than other constraint actuators (e.g. windup).

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