基於架構簡單的原因，倒單擺、球與桿、倒三角等為控制實驗教育上或學術研究上常見之機電系統。前述的這些機電系統之共同特點為其皆具欠致動性，在過去幾年來欠致動性系統的穩定化及性能設計受到相當高的重視；又因前述之機電系統先天上為非線性且不穩定的系統，因此常被用來驗證先進的非線性控制理論的效能。回授線性化在非線性控制系統設計上不管於理論發展或實務應用方面，近幾年來皆受到相當高程度之重視。回授線性化的主要精神在於找到一個座標轉換及狀態回授，能將非線性系統轉換成線性非時變系統，然後就可以利用早已發展完善的線性系統控制理論，針對轉換過的線性系統設計控制器以達到穩定化及特定性能之控制目的。回授線性化的方法主要可分為兩種：全狀態回授線性化及輸入輸出回授線性化。令人遺憾的是上述的典型機電系統皆無法適用於全狀態回授線性化。從教育與學術的觀點而言，缺乏可全狀態回授線性化的機電實驗系統，使得控制實務與理論無法於課堂中相互驗證。基於上述之原因，本論文旨在提出一新的機電實驗系統架構，此簡單的機電系統稱為「球與輪系統」，此系統由直流馬達帶動輪盤使球能立在輪子上達到平衡。於論文中吾人將証實此系統可以利用全狀態回授線性化來設計穩定化之控制器，最後控制法則將利用數位訊號處理器來實現。

Due to structural simplicity, inverted pendulum, ball and beam, and seesaw, etc. are experimental benchmarks for control education and research. Moreover, most aforementioned mechatronic systems are underactuated. In the last few years, there has been major interest in designing controllers for underactuated systems for the closed-loop stability and performance. Due to inherent nonlinearity and instability of these experimental benchmarks, these systems provide platforms for verifying the effectiveness of the advanced methodologies in nonlinear control. Feedback linearization is an approach to nonlinear control design which has attracted a great research interest in recent years. The idea of this approach is to find a transformation that transforms the nonlinear system into a linear time-invariant system. Then, the design can be carried out on this new linear model using the well-established linear control design techniques. There are two feedback linearization approaches, namely, full-state feedback linearization and input-output feedback linearization. Unfortunately, full-state feedback linearization is not applicable to those aforementioned experimental benchmarks. Form educational and academic viewpoint, lack of such an experimental benchmark leaves a gap in the control practice and theory. Motivated by these facts, this thesis is going to introduce a novel mechatronic system, ball and wheel system. This system consists of a DC motor that drives a wheel to keep a ball staying on the wheel. It is show that the full-state feedback linearization is applicable to this system to design a stabilizing controller. Finally, the control law will be implemented through a digital signal processor.

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