使用狀態相關Riccati方程式控制器設計實現雙輪機器人

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姓名

郭俊廷(Jun-Ting Kuo) 查詢紙本館藏

畢業系所

光機電工程研究所

論文名稱

使用狀態相關Riccati方程式控制器設計實現雙輪機器人
(Real Implementation of Two-Wheeled Robot Based on Novel Analysis and Design of State-Dependent Riccati Equation Controller)

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摘要(中)

本論文主要研究使用狀態相關Riccati方程式(state-dependent Riccati equation, SDRE) 方案於兩輪倒單擺機器人的非線性控制器設計和實現。根據系統數學模型設計兩輪平衡機器人的車體機構，通過Inventor軟體建構3D模型獲得一些重要參數，並以MATLAB®撰寫程式設計SDRE控制器，完成機器人的姿態平衡控制目標。系統軟硬件架構主要以搭載Windows系統的LattePanda開發版為上位機，結合運用RS-485以Modbus RTU通訊協定、馬達驅動控制技術、IMU 姿態量測技術等等，擷取必要之系統狀態變量。本研究進一步分析了狀態相關矩陣對應的逐點代數Riccati 方程式的可解性，通過降維得出的可解性簡單等價條件，可以有效減少逐點檢驗SDRE 方案可解性的大量計算負擔。然後設計SDRE 控制器以獲得最優控制律，通過輸出電壓Duty 模式驅動電機旋轉，成功控制兩輪機器人完成姿態平衡。

摘要(英)

This thesis mainly studies the design and implementation of nonlinear controllers for two-wheeled inverted pendulum robots using the state-dependent Riccati equation (SDRE) scheme. According to the mathematical model of the system, the body mechanism of the two-wheeled balancing robot is designed, some important parameters are obtained by constructing a 3D model with Inventor software, and the SDRE controller is programmed with MATLAB® to complete the robot’s postural balance control goal. The system software and hardware architecture are mainly based on the LattePanda development version equipped with Windows system as the host computer, combined with the use of RS-485, Modbus RTU communication protocol, motor drive control technology, IMU attitude measurement technology, etc., to capture necessary system state variables. This study further analyzes the solvability of the pointwise algebraic Riccati equation (ARE) corresponding to the state-dependent coefficients (SDCs) matrix. The simple equivalence conditions for solvability obtained through dimensionality reduction can effectively reduce the computational burden of pointwise testing of the solvability of the SDRE scheme. Then design the SDRE controller to obtain the optimal control law, drive the motor to rotate through the output voltage Duty mode, and successfully control the two-wheeled robot to complete the postural balance.

關鍵字(中)

★ 非線性控制
★ 兩輪倒單擺
★ 狀態相關Riccati方程式

關鍵字(英)

★ Nonlinear control
★ two-wheeled inverted pendulum
★ state-dependent Riccati equation (SDRE)

論文目次

摘要iv
Abstract v
誌謝vii
目錄viii
圖目錄xi
表目錄xiii
符號說明xiv
一、緒論1
1.1 研究動機.................................................................. 1
1.2 本文結構.................................................................. 4
二、機構設計與系統架構6
2.1 車體機構設計............................................................ 7
2.1.1 Inventor 3D 建模................................................ 8
2.1.2 擺體長度l 與慣性矩I1、I2、I3 ............................. 8
2.1.3 車輪的轉動慣量J 與轉動動能K .......................... 10
2.2 系統硬體架構............................................................ 10
2.2.1 LattePanda Board................................................ 12
2.2.2 充電鋰電池...................................................... 13
2.2.3 直流無刷馬達(BLDC Motor) ................................ 14
2.2.4 馬達驅動器...................................................... 17
2.2.5 慣性量測元件(IMU)........................................... 18
2.2.6 RS-485 通訊..................................................... 20
三、SDRE 控制器設計24
3.1 SDRE 方案概論.......................................................... 24
3.1.1 引理1 (Lemma 1) ............................................... 27
3.2 SDRE 設計流程.......................................................... 29
四、TWIP 系統動態模型32
4.1 TWIP 狀態空間模型.................................................... 32
4.2 SDC 矩陣設計............................................................ 35
4.2.1 引理2 (Lemma 2) ............................................... 38
4.2.2 可解性分析(Solvability Analysis) ........................... 38
4.2.3 定理一(Theorem 1)............................................. 44
4.3 TWIP 系統模擬.......................................................... 46
五、SDRE 控制器實現48
5.1 實驗方法.................................................................. 48
5.2 實驗結果.................................................................. 50
5.2.1 姿態平衡實驗一................................................ 50
5.2.2 姿態平衡實驗二................................................ 53
六、結論57
6.1 結論........................................................................ 57
6.2 未來展望.................................................................. 58
參考文獻60

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指導教授

林立岡(Li-Gang Lin)

審核日期

2022-8-4

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