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研究生:余文俊
研究生(外文):Wen-ChunYu
論文名稱:交流伺服馬達之全數位化強健精密定位控制
論文名稱(外文):Robust Digital Control for AC Servomotor Precise Positioning
指導教授:王國禎
指導教授(外文):Gou-Jen Wang
學位類別:博士
校院名稱:國立中興大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
中文關鍵詞:自我調諧PID控制器最佳化滑動模式控制器最佳化選頻滑動模式控制器顫動遺忘滑動表面
外文關鍵詞:self-tuning PID controlleroptimal sliding model controloptimal frequency-shaping sliding mode controlchatteringforgetting sliding surface
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本研究對於交流伺服馬達精密定位控制提出四種數位式控制設計架構:自我調諧PID控制器、最佳化滑動模式控制器、最佳化選頻滑動模式控制器、結合前饋控制器(Feedforward controller)與最佳化選頻滑動模式控制器之融合控制器(Hybrid controller)。
本論文所提出之自我調諧PID控制器是一種不需要系統數學模式之控制發法,本研究方法乃基於參考模式控制(Model reference control)法則。以系統之輸出入反應趨勢所推導出之調諧機制,線上調整PID控制器之控制參數。本方法之穩定性可以Lyapunov定理證明。
最佳化滑動模式控制器乃是以最佳控制之最佳化理論計算滑動模式之最佳滑動表面,並以奇異擾動理論(Singular perturbation theorem),簡化交流伺服馬達為二階線性動態方程式,以系統化之設計方式設計以電壓控制為基礎,簡單又適合工業界使用之單迴路交流馬達數位控制器。
本研究所發展之選頻滑動模式控制器乃將選頻之問題轉化成LQR (Linear quadratic regular)之最佳化問題後,再選擇一高通無限脈衝響應濾波器(Infinite impulse response filter),以Parseval定理推導出控制法則以去除外在之週期性干擾。最後再選擇適當之遺忘滑動表面(Forgetting sliding surface)來消除顫動現象(Chattering)。
由於前饋控制具有設計簡單及不影響閉迴路穩定性之優點,本論文將它與選頻滑動模式控制器結合以改善選頻滑動模式控制器之暫態響應。
電腦模擬與實驗結果證明本文所提之系統化設計之可行性。又由於僅需使用單一迴路之電壓控制模式,使得控制器之硬體設計及軟體寫作更趨簡單。

Four discrete-type control schemes proposed in this dissertation for precise AC servomotor positioning control are divided up into modeled and un-modeled approach. i) modeled approach: the self-tuning PID control scheme, ii) un-modeled approach: the optimal sliding mode control scheme, the optimal frequency-shaping sliding mode control scheme, and the hybrid control scheme. Computer simulations and experiments are performed to demonstrate their performance and robustness.
The self-tuning PID control scheme is based on the model reference method and the trend of system output verse control input. A simple tuning rule is derived to on-line update the PID control parameters. The stability of the control method is proved by Lyapunov theory. In discrete optimal approach, the sliding surface that determines the response properties is designed based on the optimal LQR approach. This new discrete sliding mode control algorithm possesses the properties of the optimal control and the sliding mode control. The frequency-shaping sliding mode control scheme is proposed to deal with periodic disturbances. The discrete frequency-shaping problem is firstly converted to the LQR optimal formation. A suitable high-pass infinite impulse response filter is then selected to reject the vibration disturbances. The equivalent control algorithm is derived by Parseval’s theory. A proper forgetting sliding surface to suppress the chattering is determined; the optimal solution is finally calculated. The hybrid control is used to progress the system transient response by adding an additional feedforward control input to the frequency-shaping control input.
To reduce the structure of the controller and satisfy the necessary condition of the sliding mode control, the fourth order AC servomotor is simplified into a second-order reduced model such that only the q-axis voltage control loop is required.
Computer simulations and experiments show that the proposed discrete-type heuristic self-tuning PID (DHSPID) controller possesses advantages such as easy implementation, insensitive to initial parameter assignment, good responses and robust to the external load. For the optimal sliding mode control scheme, computer simulations and experiments were demonstrated by advantages such as easy implementation, fast response and robust to the external loads. AC servomotor position control with a flexible rod was conducted to verify the performances of the discrete optimal frequency-shaping sliding mode control (DSFSMC) scheme. Simulation results showed that the DSFSMC possesses characteristics such as good periodic disturbance rejection and chattering suppressing. Simulation results also illustrate that the hybrid control scheme is able to improve the transient response of the DSFSMC.

CONTENTS
Pages
ABSTRACT ………………………………………………….. i
CONTENTS ………………………………………………….. ii
LIST OF TABLES …………………………………………… vii
LIST OF FIGURES……………………………………………… viii
NOMENCLATURE ……………………………………………. x
CHAPTER 1 INTROSUCTION…… 1
CHAPTER 2 SYSTEM MODELONG……………………………...6
2.1 Reduced Model of AC Servomotor………………………………………… ...6
2.1.1 Electrical Governing Equation……………………………………. …….6
2.1.2 Mechanical Governing Equation…………………………………… ..7
2.2 Necessary Condition of Sliding Mode Control……………….……………. 10
2.3 Apparatus for Experiments……………………………………………… …..11
CHAPTER 3 DISCRETE-TYPE HEURISTIC SELF-TUNING PID
CONTROLLER……………………………… 12
3.1 Discrete-Type Heuristic Self-Tuning PID Controller…………….…..…. …..12
3.2 Design Procedures for DHSPID…………………………………………. …..15
3.3 Computer Simulations ……………………………………………………….15
3.4 Experimental Verification……………………………………………………. 21
3.4.1Apparatus for Experiments…………………………………………. …21
3.4.2 Experiments…………………………………………………………… 22
CHAPTER 4 DISCRETE SLIDING MODE CONTROLLER
DESIGN BASED ON THE SUPOPTIMAL APPROACH 26
4.1 Discrete LQR Optimal Control………………………………………..……. .26
4.2 Design of Discrete Optimal Sliding Mode Controller (DSSMC)…………... .28
4.2.1 Canonical Form for Sliding Mode Controller Design………………… 28
4.2.2 Hyperplane…………………………………...……………….…..…... .30
4.2.3 Optimal Sliding Mode Control…………………….……………..….... .30
4.2.4 Disturbance Rejection…………………………………………...…….. 32
4.3 Design Procedures for DSSMC………………….……………………..…… 33
4.4 Computer Simulations ………………………….…………………………… 33
4.5 Experiments………..……………………………………………………….. ..38
CHAPTER 5 DISCRETE OPTIMAL FREQUENCY-SHAPING
SLIDING MODE CONTROL……………………….43
5.1 Linear Operator on Hyperplane………………………………………….. .….43
5.2 Sliding Surface for Discrete LQR Problem…………………………………. .45
5.3 Discrete Frequency-shaping Sliding Mode Control……………………….. ...47
5.4 Sliding Surface Smoothing………………………………………………….. .54
5.5 Design of the IIR Filter……………………………………….. ……….….….57
5.5.1 Low-Pass Filter……………………………………………………… …58
5.5.2 High-Pass Filter……………………………………………………. ..…59
5.6 Controller Design……………………………………………………..……. ..61
5.7 Computer Simulations………………………………………………….... ..…61
CHAPTER 6 HYBRID CONTROL: FEEDFORWARD CONTROL AND FREQUENCY-SHAPING SLIDING MODE CONTROL………………………………………... 68
6.1 Control Scheme of Hybrid Control……………………………………. ……68
6.1.1 Frequency-shaping Sliding Model control………………………….. …68
6.1.2 Feedforward Control…………………………………………….….. …69
6.1.3 Hybrid Control…………………………………………………… …….71
6.2 Controller Design Processes……………………………………………….. ..72
6.3 Computer Simulations…………………………………………………….. …72
CHAPTER 7 CONCLUSIONS ………………….………………... 74
REFERENCES……………………………………………………..76
VITA…………………………………………………..…………… 80

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