臺灣博碩士論文加值系統

倒單擺系統(Inverted Pendulum System)是極為不穩定的系統，如何穩定的控制倒單擺系統平衡倒立，成為重要的研究課題。本文首先研究倒單擺車的系統模型，再探討用線性二次調節器(Linear Quadratic Regulator, LQR)的設計方法，來設計倒單擺車的控制器。藉由Matlab程式完成LQR控制器的設計，並模擬倒單擺車的系統響應了解倒單擺車系統參數與LQR控制器增益之間的關係。本文設計的倒單擺車系統是使用直流伺服馬達驅動車輪，以嵌入式系統作為控制器。將傾斜感測器裝置於單擺車的框架，量測倒單擺車的傾斜角度，經A/D轉換器作資料轉換後由嵌入式控制器讀取，倒單擺車的位置是利用直流伺服馬達的編碼器，經數位輸入(Digital Input, DI)由嵌入式控制器進行讀取，倒單擺車的傾斜度及位置輸入用LQR所設計的控制器，其輸出經D/A轉換器，輸出控制命令給直流伺服馬達，控制單擺車成為直立的狀態。模擬結果顯示利用LQR的方法所設計的控制器，能控制倒單擺車達到直立穩定的狀態。

Inverted Pendulum System is an extremely unstable system. It’s an important research topic to stabilize upside down control for balancing the inverted pendulum system This thesis studies the system model of an inverted pendulum cart and investigates the design method using linear quadratic regulator (LQR). A Matlab-based LQR controller is designed to simulate system responses and conduct the relationships between the inverted pendulum cart system parameters and the LQR controller gains. In this thesis, the DC servo motors are used to drive the wheels of inverted pendulum, and an embedded system is used for implementation the controller. The tilt sensor in the pendulum cart frame is used to measure the inclination angle of the pendulum cart. The tilt sensor output is read by the embedded controller through an A/D converter. The DC servo motor encoders are used to measuring the inverted pendulum cart position that are read by the embedded controller using the Digital Inputs (DI). The inclination angle and the position of the inverted pendulum cart are the input the LQR controller, control command output to the DC servo motor through the D/A converter to maintain the cart in its inverted state. The simulation results show that the inverted pendulum cart can be controlled by the proposed LQR controller to reach a balancing upright state.

摘要 i
ABSTRACT ii
謝誌 iii
目錄 iv
圖目錄 vi
表目錄 ix
第一章　緒論 1
1.1 研究動機 1
1.2 文獻探討 1
1.3 論文架構 7
第二章　倒單擺車系統模型及LQR控制器 9
2.1 倒單擺車數學模型 9
2.2 LQR控制器設計 13
2.3 極點安置 15
第三章　倒單擺車系統硬體架構 17
3.1 系統架構 17
3.2 傾斜感測器 19
3.3 嵌入式控制器 22
3.4 馬達、馬達驅動器、編碼器及減速機 23
第四章　模擬與實驗結果 27
4.1 車身參數模擬結果 27
4.2 系統響應模擬 30
4.3 感測器量測 42
4.4 倒單擺車傾斜狀態量測 46
4.5 倒單擺車位置狀態量測 50
4.6 狀態回授控制器 53
4.7 實驗結果討論 60
第五章　結論與未來研究建議 68
5.1 結論 68
5.2 未來研究建議 70
參考文獻 71

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