伺服系統使用PID控制器已有多年歷史。一般來說，欠阻尼系統的響應較快，但常伴隨有超越量；而過阻尼系統不會有振盪問題，但其響應緩慢，以往的工程師在使用傳統的PID控制器的，常必須在二者之間取捨。比較理想的是系統在運動初期能像欠阻系統一樣有較快速的響應，而在運動結束時能像過阻尼系統一樣沒有振盪。
對此，我們提出以軌跡位置為依據，利用模糊邏輯進行PID制器之增益排程。藉以兼俱響應快速及抑振之利。文中選擇兩個軌跡點；在第一個軌跡點前，PID控制器有較大的比例增益及積分增益，故系統表現為欠阻尼者；而在第二個軌跡點後，設定一組不同PID參數，使系統表現過阻尼特徵。在兩者間，增益呈線性改變。為得PID控制器增益排程的最佳值，本研究使用 Powell’s method對3個參數同時最佳化，並在一維的線搜尋上使用golden section method，以期快速收斂。
本研究使用ADLink運動控制卡PCI 8366、三菱驅動器及一組以伺服馬達驅動滾珠螺桿之線性平台，利用LabView設計程式來驗証所提方法的有效性。結果顯示線性平台有極佳的定位能力。

PID controllers have been employed in servo systems for decades. It is well known that an underdamped system has a faster response but accompanied by undesired overshoot, while an overdamped system has no oscillation at all but its response is too slow. In the past, the system engineers had to make a compromise in between with the conventional PID controllers. It is desired that a system would act like an underdamped one to have a faster response in the beginning, while it’d act like an overdamped one to have almost no oscillation.
We propose a setpoint gain scheduling scheme for PID controllers using fuzzy logic to take the advantages of fast response and oscillation suppression. Two set points are used in scheduling PID gains. The PID controller will have fixed high proportional and integral gains for quick response before reaching the first set point, so the system is underdamped. Also, the system is overdamped to yield no oscillation with a different set of PID parameters after passing the second set point. And the gains vary linearly between the first and second setpoints.
Our objective is to make the positioning system reach the target position and settle down as soon as possible. In optimizing the parameters, we use Powell’s method, a non-gradient based method, to provide conjugate direction search for faster convergence. An optimal step size along each search direction will be found using the golden section method to achieved better performance.
The experimental setup consists of an ADLink motion control card PCI 8366 installed in a desktop PC, a Mitsubishi amplifier, an AC servo motor, and a Hiwin ballscrew linear stage. LabView software is used to program the suggested methods.
The setup is used to demonstrate the effectiveness of our proposed setpoint gain scheduling scheme. The results show that the optimized setpoint gain scheduled Fuzzy-PID controller has much better performance in positioning than the optimized conventional PID controller.

摘要 i
Abstract ii
Acknowledgements iv
Table of Contents v
List of Figures vii
List of Tables x
Chapter 1 Introduction 1
1.1 Introduction 1
1.2 Literature review 3
1.3 Research Approach 7
Chapter 2 Controller design 9
2.1 PID controller 9
2.2 Fuzzy Gain Scheduling 11
2.2.1 Gain Scheduling 11
2.2.2 Fuzzy Logic 13
2.2.3 Fuzzy Gain Scheduling 14
2.3 Gain Scheduled Fuzzy-PID Using T-curve Setpoints 16
2.3.1 Trapezoidal Veclocity Profile 17
2.3.2 Setpoint Selection 17
2.4 Gain Optimization Using Powell’s Method 21
2.4.1 Settling Time 21
2.4.2 Golden Section Algorithm 22
2.4.3 Powell’s Method 24
Chapter 3 System Descriptions 26
3.1 ADLink Motion Control Card PCI 8366 28
3.2 Servo MR-J2S Mitsubishi Amplifier 29
3.3 Servo Motor 33
3.4 Linear Stage 34
Chapter 4 Results and Discussions 35
4.1 PID Auto Tuning Result 37
4.2 Fixed PID With Different KP 38
4.3 Fixed PID With Different KI 44
4.4 Fixed PID With Different KD 52
4.5 Setpoint Fuzzy PID Gain Scheduling 68
4.6 Optimized Setpoint Gain Scheduled Fuzzy-PID Controller 70
Chapter 5 Conclusions and Future works 72
5.1 Conclusions 72
5.2 Future works 73
References 74

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