A Novel Six-DOF Precision Positioner Utilizing Hybrid Mechanism with Magnetism and Fluid

本論文提出一種同時利用磁力與流體浮力的混合式機構實現新型多自由度電磁致動精密定位平臺；其中，不論是其新式硬體架構、電磁致動器以及有效的控制器都有完整的介紹。在平臺主體設計，首次利用了流體的特性，來提高平臺本身的可控性，也大大的降低電磁線圈所需消耗的功率，進而達到系統低功率損耗的一大特性。本新型精密定位平臺達成四大目標：第一，擁有大移動行程的能力（此指公釐的範疇）; 第二，精密定位的能力; 第三，採用簡潔而低本的機構設計; 第四，達到系統低功率損耗的需求。 在系統中，共有八個永久磁鐵黏附在可移動的載台上，以及共有八個相對應的電磁鐵安裝在固定的基座上。在進一步控制永久磁鐵及電磁鐵間的磁力後，即可推導及分析本系統完整的動態模型。再則，由於此系統的先天不穩定現象及系統具有的不確定因素，為了能確保在定位及追蹤時所有的自由度都能保持穩定，在此，我們設計了一種強健可適應性滑動模式控制器。同時，為了有比較的基礎，一個傳統的PID控制器也將一併提出。最後，為了展現系統的性能，我們執行了一系列的實驗。實驗結果顯示出，精密定位平台之行程為3mm×3mm×4mm，且其定位解析度為10um，此解析度已達到所採用之光學位移量測器精度之極限。This thesis proposes a novel six-degree-of-freedom (DOF) electromagnetic precision positioner made of a hybrid mechanism utilizing both magnetic driving force and fluid upper lifting power, in which the new structure, the electromagnetic actuator, and the effective controller are developed. The concept of the mechanism design not only involves the magnetic driving mechanism but also the fluid buoyancy and damping properties, of which the latter help counter-balance weight of the platen so as to achieve very low steady-state power consumption. The four goals of novel system design include: (1) to have large moving range (in mm level), (2) to achieve precision positioning, (3) to design compact but low-cost mechanism, and (4) to achieve low power consumption. In this system, totally there are eight permanent magnets (PMs) attached to the movable carrier, and eight electromagnetic coils appropriately mounted on a fixed based. After exploring the characteristics of the magnetic forces between PMs and electromagnetic coils, the general 6-DOF dynamic model of this system is derived and analyzed. Then, because of the naturally unstable behavior and uncertainties of the underlying system, a robust adaptive sliding-mode controller is proposed to guarantee the system stability for both regulation and tracking tasks. Meanwhile, a traditional PID controller is presented for comparison with the hereby developed robust adaptive sliding-mode controller. Finally, we have conducted extensive experiments to demonstrate the performance of the proposed system. The experimental results show that traveling range is 3mm×3mm×4mm, and the tracking error in each axis is kept within 10um, which is up to the limit of our optical sensors.摘要 i Abstract ii Table of Contents iv List of Figures vii List of Tables xiii Chapter 1 Introduction 1 1.1 Motivation and Goal 1 1.2 6-DOF Positioning System Survey and Related Research 3 1.2.1 David L. Trumper and Won-jong Kim 3 1.2.2 Won-jong Kim and Shobhit Verma 4 1.2.3 Chia-Hsiang Menq and Shih-Kang Kuo 4 1.3 Contribution 5 1.4 Thesis Organization 6 Chapter 2 Preliminaries 7 2.1 Basic Theories of Fluid Mechanics 7 2.1.1 Drag Concepts 7 2.1.2 General Drag 9 2.1.3 Drag at Low Velocity 9 2.1.4 Drag at High Velocity 10 2.2 Basic Theories of Electromagneitcs 11 2.2.1 Lorentz Force Principle 11 2.2.2 The Vector Potential and Vector Poisson Equation 13 2.2.3 Superposition Integral of the Biot-Savart Law 16 2.3 Magnetic Field Resulting from Electromagnet 18 2.3.1 Magnetic Field due to Cylindrical Electromagnet 18 2.3.2 Magnetic Field due to Current-Carrying Straight Wire 20 2.4 Force and Torque between Permanent Magnet (PM) and electromagnet 22 Chapter 3 Design Concepts 25 3.1 Design Strategies 25 3.1.1 High Positioning Accuracy 26 3.1.2 Large Moving Range 26 3.1.3 Low Power Consumption 26 3.1.4 Low Cost 27 3.1.5 Compact System 27 3.2 Fluid Mechanics 27 3.3 Mechanism Introduction 29 3.3.1 Overall System Description 29 3.3.2 Moving Platen 31 3.4 Stability of Moving Platen 31 3.5 Electromagnetic Actuator 34 3.5.1 Voice Coil Motor 34 3.5.2 Our VCM electromagnetic Actuator 35 3.5.3 Repulsive Electromagnetic Actuator 36 Chapter 4 Modeling and Dynamic Behavior 39 4.1 Sensing Methodology 40 4.2 Force Representation and Allocation 43 4.2.1 Force Characteristics of the Electromagnetic Actuator 43 4.2.2 Linear Force Formulation 50 4.2.3 Force Allocation 51 4.3 Dynamic Formulation 53 4.3.1 Assumptions 53 4.3.2 Mathematical Modeling 54 Chapter 5 Controller Design 59 5.1 PID Controller Design 60 5.1.1 PID Controller Design 62 5.1.2 Determination of PID Controller Gains 63 5.2 Adaptive Sliding-Mode Controller Design 65 5.2.1 Sliding Surface 66 5.2.2 Controller Formulation 67 5.2.3 Stability Analysis 68 5.2.4 Numerical Simulation Results 72 Chapter 6 Experimental Results 75 6.1 System Setup and Experimental Environment 75 6.2 Experimental Results Based on PID Controller 79 6.2.1 Regulation Response 79 6.2.2 Large Moving Range 80 6.2.3 Step-Train Response 82 6.2.4 Slower Sinusoidal Motion 83 6.2.5 Faster Sinusoidal Motion 85 6.2.6 Slower Circling Motion 86 6.2.7 Faster Circling Motion 87 6.2.8 Rotational Motion 89 6.2.9 Wobble motion 91 6.2.10 3-Dimentional Contour – Spiral Motion 92 6.3 Experimental Results Based on Adaptive Sliding-Mode Controller 93 6.3.1 Regulation Response 93 6.3.2 Large-Moving Range 95 6.3.3 Step-Train Response 96 6.3.4 Slower Sinusoidal Motion 98 6.3.5 Faster Sinusoidal Motion 99 6.3.6 Slower Circling Motion 100 6.3.7 Faster Circling Motion 102 6.3.8 Rotational Motion 103 6.3.9 Wobble Motion 105 6.3.10 3-Dimentional Contour – Spiral Motion 106 6.4 Summary 109 Chapter 7 Conclusion 111 References 11