多軸運動系統之整合式控制器及參數化插值器設計

Abstract

近年來，由於電腦應用技術的快速發展，使得運動系統架構不斷創新以建立高速高精密度的加工環境。一般而言，運動系統可以分成兩個主要部份：插值器與控制系統，因此本論文以兩部份分別討論控制器設計(第二章∼第五章)與插值器設計(第六章∼第八章)，以獲得多軸運動系統的高速高精密度特性。本人延伸碩士論文中單軸及雙軸運動控制的研究成果，在博士論文中分別完成多軸控制器及插值器設計。 在傳統的運動控制技術上是採用PID的迴授控制器設計，因此無法克服系統因各軸間動態特性的不匹配、伺服落後、與外界擾動所引起的加工誤差。有鑑於此，在本文中首先是耦合各軸動態特性的迴授控制器設計，藉由極零點的對消與動態響應的補償設計位置迴授控制器，使各軸的動態特性能夠一致，以減少輪廓誤差。而在降低外界擾動的性能上，本文提出干擾觀測器與非線性函數的速度迴授控制方式。在改善系統的伺服落後上，藉由系統增益的最佳化調整與落後相位的補償，本文採用匹配零相位誤差追跡控制的設計方式，可以明顯地改善位置控制系統的追跡響應。在改善系統輪廓響應方面，本文發展多軸的交叉耦合控制的設計，藉由及時的輪廓誤差估測與補償，可以改善位置控制系統的輪廓響應。而在控制器的設計上，本文同時推導出輪廓誤差轉移函數CETF的控制器設計方式，以簡化耦合系統的控制器設計。為同時改善多軸位置運動控制系統的追跡與輪廓響應，結合(1)位置迴授控制、(2)位置前置控制、與(3)交叉耦合控制的整合運動控制架構在本文中被提出討論。藉由誤差訊號的分析，本文提出控制器設計的獨立性與輪廓誤差轉移函數的設計方式，可以大幅簡化控制器的設計。 雖然先進的控制器設計可以改善位置控制系統的運動精度，然而不適當的位置命令將破壞系統的性能。因此本文的第二部份將討論精確的參數化曲線命令產生方式。然而，由於參數化曲線的複雜性，使得插值器的設計在近年來才伴隨電腦而發展。本文首先討論非一致性分式B類曲線 (Non-uniform rational B-spline; NURBS)的實現。由於NURBS的基底函數具有多層次迭代的特性，因此本文提出使用共通資料暫存器的設計方式以降低計算的問題，同時也可以一併求出NURBS的一次與二次微分資訊。而在插值方式的設計上，本文分別提出固定曲線速率與固定弦高誤差的插值方式。採用對傳統參數疊代方式的幾何補償，固定曲線速率的插值方式可以使命令的曲線速率在運動過程中維持定值。固定弦高誤差的插值方式，採用的方法是對傳統參數疊代方式中的速率估測，可以使命令的位置誤差在運動過程中低於設定值，以提供更精確的位置命令。本文結合所討論的控制器與插值器的設計，以實驗證明可達成高速高精度的運動控制。

In general, motion control and interpolator are the most important parts in multi-axis motion systems. Therefore, six advanced motion control algorithms (Chapter 2~5) and three parametric curve interpolators (Chapter 6~8) are proposed to achieve motion accuracy under high speed operations for multi-axis motion systems in this dissertation. To reduce contouring errors due to the mismatched dynamics among multiple axes, the perfectly matched feedback control design is developed to achieve identical frequency responses among all axes by applying the stable pole-zero cancellation and complementary zeros. To decrease perturbations caused by external disturbances, a digital disturbance observer (DDOB) control and a practical nonlinear function feedback compensation algorithms are also proposed. Moreover, by applying the design of the optimal digital pre-filter (DPF) and perfectly matched feedforward control, the perfectly matched feedforward control (PMFFC) is proposed to increases bandwidth of multi-axis systems. Furthermore, the robust multi-axis cross-coupled control (CCC) is developed to improve contouring accuracy by applying estimation and compensation of the newly developed contouring error vector. The contouring error transfer function (CETF) for multi-axis motion systems is also derived to simplify the CCC design. Accordingly, the multi-axis integrated control which combines (1) feedback control, (2) feedforward control, and (3) multi-axis cross-coupled control is proposed to significantly improve both tracking and contouring accuracy. Also, systematic control design procedures are obtained by applying the error signals analysis. Furthermore, machining quality may be deteriorated by the incorrect position command generation. The second part of this thesis discusses the design of precise interpolation algorithms for parametric curve of non-uniform rational B-spline (NURBS). In the second part of this dissertation, the implementation complexity of NURBS interpolator is solved by the newly developed method which uses the common data registers to realize an efficient interpolation algorithm for NURBS. Also, based on the common data registers, the 1st and 2nd derivatives of NURBS are efficiently obtained. Moreover, the speed-controlled interpolation algorithm generates precise position commands with a constant curve speed by applying the trajectory dependent compensatory value. By estimating the curve speed corresponding to the specified chord errors, the chord-error-controlled interpolation algorithm improves the position accuracy between two interpolating points. Feasibility of all proposed motion controllers and interpolators has been verified on an industrial DYNA CNC machining center. ABSTRACT (CHINESE) i ABSTRACT (ENGLISH) iii ACKNOWLEDGMENT v TABLE OF CONTENTS vi LIST OF TABLES x LIST OF FIGURES xiii CHAPTER 1 INTRODUCTION 1 1.1 General review 1 1.2 Problem statement 5 1.3 Proposed approach 7 1.4 Experimental setup 9 1.5 Organization of thesis 10 CHAPTER 2 FEEDBACK CONTROL DESIGN FOR MULTI-AXIS MOTION SYSTEMS 12 2.1 Perfectly matched feedback control design for multiple axes 13 2.2 Digital disturbance observer (DDOB) 23 2.3 Nonlinear compensation 34 2.4 Summary 48 CHAPTER 3 PERFECTLY MATCHED FEEDFORWARD CONTROL 49 3.1 Optimal ZPETC (Yeh and Hsu, 1999c) 49 3.2 Perfectly matched feedforward control 68 3.3 Summary 76 CHAPTER 4 ROBUST CROSS-COUPLED CONTROL 78 4.1 Robust CCC (Yeh and Hsu, 1999a) 78 4.2 Cross-coupled control by using the contouring error vector 94 4.3 Multi-axis cross-coupled control 102 4.4 Summary 110 CHAPTER 5 INTEGRATED CONTROL FOR MULTI-AXIS SYSTEMS 112 5.1 Biaxial integrated control (Yeh and Hsu, 1999b) 112 5.2 Multi-axis integrated control 127 5.3 Summary 137 CHAPTER 6 IMPLEMENTATION OF NURBS INTERPOLATORS 139 6.1 Review of NURBS 139 6.2 Structure of the basis function 141 6.3 The moving data registers 144 6.4 The branch structure and the extended basis function 145 6.5 The implementation of the proposed algorithm 147 6.6 Simulation results 149 6.7 Summary 151 CHAPTER 7 CONSTANT SPEED INTERPOLATION ALGORITHM 152 7.1 Parametric curve formulation 152 7.2 The speed-controlled interpolation algorithm 154 7.3 Applications 160 7.4 Summary 168 CHAPTER 8 CHORD-ERROR-CONTROLLED INTERPOLATION ALGORITHM 169 8.1 Parametric curve formulation and interpolations 169 8.2 Chord error controlled interpolation algorithm 170 8.3 Simulation results 173 8.4 Summary 177 CHAPTER 9 CONCLUSIONS 179 REFERENCES 181 VITA 191 PUBLICATION LIST 194