臺灣博碩士論文加值系統

本論文為探討在倒數狀態空間下之可變結構控制法則研究。首先利用可變結構控制法則對包含匹配式外部雜訊或非匹配式不確定項之不穩定系統進行控制。 並且利用積分式可變結構控制法則對包含匹配式外部雜訊之不穩定系統進行控制，使該系統能在初始時即進入順滑模態並且滑向順滑面。除此之外，本論文利用可變結構控制法則對包含匹配式外部雜訊及非匹配式不確定項之系統進行輸出狀態微分回授控制之研究。本論文亦利用可變結構控制法則對包含死區及扇形之非線性輸入系統，作追蹤控制之研究。
除了以上之控制法則，本論文亦提供兩種順滑模態之求法及提出三種連續型的切換函數可供一般可變結構之控制器使用。並且從模擬結果得知論文中各控制法則之可行性。

This thesis investigates variable structure control designs with state derivative feedback in reciprocal state space system. Fundamental sliding control algorithm is first carried out for unstable systems with matched external disturbance or mismatched uncertainties. To allow the systems slide onto the sliding surface at the beginning, integral sliding surface is then used in control design for system with matched external disturbance. Furthermore, for the reason of easy implementation, state derivative output feedback approach is studied and incorporated in variable structure control designs for systems with matched external disturbance and mismatched uncertainties. To deal with nonlinearities in practical applications, variable structure model-following control designs are developed for reciprocal state space system with dead-zone and sector nonlinearities.
In addition to above control algorithms, two methods for designing appropriate sliding surfaces in reciprocal state space system are provided and three novel continuous and smooth switching functions are proposed. Simulations have been performed to successfully verify the design methods in this thesis.

致謝 i
摘要 ii
Abstract iii
Nomenclature iv
Contents v
List of Figures viii
Chapter 1. Introduction1
1.1 Motivation1
1.2 Review of RSS Framework 2
1.2.1 Stability, Controllability, and Observability Criteria for RSS3
1.3 Review of VSC Method5
Chapter 2. The VSC in RSS Systems11
2.1 System Description and Problem Formulation11
2.2 The Selection of Sliding Surface12
2.3 Design the Controller14
2.4 Numerical Example 1 16
2.5 Numerical Example 2 19
Chapter 3. The VSC in RSS Systems with Mismatched Uncertainty and Matched External Disturbance22
3.1 System Description and Problem Formulation22
3.2 The Selection of Sliding Surface24
3.3 Stability in the Sliding Surface24
3.4 Design the Controller28
3.5 Numerical Example30
Chapter 4. The Integral Variable Structure Control in RSS Systems with Mismatched Uncertainty and Matched External Disturbance35
4.1 System Description and Problem Formulation35
4.2 Design the Sliding Mode36
4.3 Stability in the Sliding Surface37
4.4 Design the Controller38
4.5 Numerical Example40
Chapter 5. Output Feedback Design of VSC in RSS System with Mismatched Uncertainty43
5.1 System Description and Problem Formulation43
5.2 The Selection of Sliding Surface44
5.3 Stability in the Sliding Surface46
5.4 Design the Controller49
5.5 Numerical Example52
Chapter 6. Model-Following VSC in RSS System Consist of Input Dead-Zone Nonlinearity57
6.1 System Description and Problem Formulation57
6.2 The Selection of Sliding Surface60
6.3 Design the Controller61
6.4 Numerical Example65
Chapter 7. Virtual Eigenvalue Method for Finding Sliding Surface in RSS and Novel Switching Functions74
7.1 Virtual Eigenvalue Method74
7.1.1 Numerical Example79
7.2 Novel Switching Functions83
7.2.1 Interval Sine Function83
7.2.2 Hyperbolic Tangent Function87
7.2.3 Sigmoid Plus Function91
Chapter 8. Conclusions and Future Works95
8.1 Conclusions95
8.2 Future Works95
Reference97
List of Figures
Fig. 1.1 The state trajectory of VSC6
Fig. 1.2 Chattering Phenomenon9
Fig. 1.3 Sign function10
Fig. 1.4 Saturation function10
Fig. 2.1 Time responses of the states for system (2.1) with control law (2.19) in example 1. 17
Fig. 2.2 Time responses of the sliding surface for system (2.1) in example 1. 18
Fig. 2.3 Time responses of the control effort for system (2.1) in example 1. 18
Fig. 2.4 Time responses of the states for system (2.1) with control law (2.19) in example 2. 20
Fig. 2.5 Time responses of the sliding surface for system (2.1) in example 2. 20
Fig. 2.6 Time responses of the control effort for system (2.1) in example 2. 21
Fig. 3.1 An object on the slope surface 23
Fig. 3.2 Time responses of the states for system (3.1) with control law (3.26). 32
Fig. 3.3 Time responses of the sliding surface for system (3.1). 32
Fig. 3.4 Time responses of the control effort for system (3.1). 33
Fig. 3.5 Time responses of the states for system (3.1) without d. 34
Fig. 3.6 Time responses of the sliding surface for system (3.1) without d. 34
Fig. 4.1 Time responses of the states for system (4.1) with control law (4.12). 41
Fig. 4.2 Time responses of the sliding surface for system (4.1). 42
Fig. 4.3 Time responses of the control effort for system (4.1). 42
Fig. 5.1 Time responses of the state output for system (5.1)-(5.2) with the control law (5.27). 53
Fig. 5.2 Time responses of the sliding surface for system (5.1)-(5.2). 54
Fig. 5.3 Time responses of the control effort for system (5.1)-(5.2). 54
Fig. 5.4 Time responses of the state output for system (5.1)-(5.2) without d. 55
Fig. 5.5 Time responses of the sliding surface for system (5.1)-(5.2) without d. 56
Fig. 6.1 Dead-zone nonlinearity. 59
Fig. 6.2 Dead-zone nonlinearity with gain reduction tolerance. 59
Fig. 6.3 Sector nonlinearity. 65
Fig. 6.4 Sector nonlinearity with gain reduction tolerance. 65
Fig. 6.5 Time responses of the trajectories of x1 and xm1 for system (6.1) with input (6.2). 68
Fig. 6.6 The error of x1 and xm1 for system (6.1) with input (6.2). 68
Fig. 6.7 Time responses of the trajectories of x2 and xm2 for system (6.1) with input (6.2). 69
Fig. 6.8 The error of x2 and xm2 for system (6.1) with input (6.2). 69
Fig. 6.9 Time responses of the sliding surface for system (6.1) with input (6.2). 70
Fig. 6.10 Time responses of the control effort for system (6.1) with input (6.2). 70
Fig. 6.11 Time responses of the trajectories of x1 and xm1 for system (6.1) with input (6.32). 71
Fig. 6.12 The error of x1 and xm1 for system (6.1) with input (6.32). 71
Fig. 6.13 Time responses of the trajectories of x2 and xm2 for system (6.1) with input (6.32). 72
Fig. 6.14 The error of x2 and xm2 for system (6.1) with input (6.32). 72
Fig. 6.15 Time responses of the sliding surface for system (6.1) with input (6.32). 73
Fig. 6.16 Time responses of the control effort for system (6.1) with input (6.32). 73
Fig. 7.1 Time responses of the trajectories of x1 and x2 for system (7.1) with the control law (7.18). 80
Fig. 7.2 Time responses of the slidng surface for system (7.1) with the control law (7.18). 80
Fig. 7.3 Time responses of the control effort for system (7.1) with the control law (7.18). 81
Fig. 7.4 Time responses of the trajectories of x1 and x2 for system (7.1) without d. 82
Fig. 7.5 Time responses of the slidng surface for system (7.1) without d. 82
Fig. 7.6 Interval Sine Function. 84
Fig. 7.7 Time responses of the states for system (2.1) with switching function (7.25). 85
Fig. 7.8 Time responses of the states for system (3.1) with switching function (7.25). 85
Fig. 7.9 Time responses of the states for system (4.1) with switching function (7.25). 86
Fig. 7.10 Hyberbolic Tangent Function. 88
Fig. 7.11 Time responses of the state output for system (5.1)-(5.2) with the switching function (7.26). 88
Fig. 7.12 Time responses of the trajectories of x1 and xm1 for system (6.1) with input (6.2) and switching function (7.26). 89
Fig. 7.13 Time responses of the trajectories of x2 and xm2 for system (6.1) with input (6.2) and switching function (7.26). 89
Fig. 7.14 Time responses of the trajectories of x1 and xm1 for system (6.1) with input (6.32) and switching function (7.26). 90
Fig. 7.15 Time responses of the trajectories of x2 and xm2 for system (6.1) with input (6.32) and switching function (7.26). 90
Fig. 7.16 Sigmoid Plus function. 92
Fig. 7.17 Time responses of the state output for system (5.1)-(5.2) with the switching function (7.27). 92
Fig. 7.18 Time responses of the trajectories of x1 and xm1 for system (6.1) with input (6.2) and switching function (7.27). 93
Fig. 7.19 Time responses of the trajectories of x2 and xm2 for system (6.1) with input (6.2) and switching function (7.27).93
Fig. 7.20 Time responses of the trajectories of x1 and xm1 for system (6.1) with input (6.32) and switching function (7.27). 94
Fig. 7.21 Time responses of the trajectories of x2 and xm2 for system (6.1) with input (6.32) and switching function (7.27). 94

中文部分
陳永平, 可變結構控制設計. 全華科技圖書股份有限公司, 1999.
黃志成, 一類具有不確定的扇形或量化致動器及雜訊之非線性系統全域指數穩定控制器設計. 碩士論文, 電機工程研究所, 義守大學, 2009.
英文部分
Bahnasawi, A. A., Mahmoud, M. S., and Shawkiz, E., “Variable Structure Control of Non-Linear Adaptive Model-Following Systems,” International Journal of Systems Science, vol. 22, no. 2, pp. 351-365, 1991.
Bahnasawi, A. A., Shawkiz, E., and Mahmoud, M. S., “Adaptive Model-Following Control Based on Variable Structure System,” International Journal of Systems Science, vol. 22, no. 2, pp. 333-349, 1991.
Bunse-Gerstner, A., Mehrmann, V., and Nichols, N. K., “Regulation of Descriptor Systems by Output Feedback,” IEEE Transactions on Automatic Control, vo. 39, no. 8, 1994.
Campbell, S. L. Singular Systems of Differential Equations. in Research Notes in Math, San Francisco, CA, 1980.
Chang, J. L., Sliding –mode control design based on conventional pole-assignment method. Ph D dissertation, National Chiao Tung University, 1999.
Chern, J. L. and Wu, Y. C., “Design of integral variable structure controller and application to electrohydraulic velocity servo systems,” IEEE Proceedings D, vol. 138, pp. 439-444, 1991.
Chern, J. L. and Wu, Y. C., “Integral variable structure controller approach for robot manipulators,” IEEE Proceedings D, vol. 139, pp. 161-166, 1992.
Cobb, D. , “Controllability, Observability and Duality in Singular Systems,” IEEE Transactions on Automatic Control, vol. AC-29, no. 12, pp. 1076-1082, 1984.
DeCarlo, R. A., Zak, S. H., and Matthews, G. P., “Variable Structure Control of Nonlinear Multivariable Systems: A Tutorial,” Proceedings of IEEE, vol. 76, no. 3, pp. 212-232, 1988.
El-Khazali, R. and DeCarlo, R., “Output Feedback Variable Structure Control Design,” Automatica, vol. 31, no. 6, pp. 805-816, 1995.
Filippov, A. F., Differential Equation with Discontinuous Rightsides. Kluwer Academic Publishers, Dordrecht, Boston, London, 1988.
Hung, J. Y., Gao, W. B., and Hung, J. C., “Variable Structure Control: A Survey,” IEEE Transactions on Industrial Electronics, vol. 40, pp. 2-22, 1993.
Itkis, U., Control Systems of Variable Structure. New York: Wiley, 1976.
Kulah, H., Chae, J., Yazdi, N., and Najafi, K., “Noise Analysis and Characterization of A S-D Capacitive Silicon Micro-accelerometers,” IEEE Journal of Solid-State Circuits, vol. 41, no. 2, pp. 352-361, 2006.
Le, V. X., “Synthesis of Proportional-Plus-Derivative Feedbacks for Descriptor Systems,” IEEE Transactions on Automatic Control, vol. AC-37, no. 55, pp. 672-675, 1992.
Lin, C. L., Control System Mathematics. Chwa, Taiwan, 2002.
Lin, F. J. and Kuo, L. C., “Driving Circuit for the Ultrasonic Motor Servo Drive with Variable Structure Adaptive Model-Following Control,” IEE Proceedings, Electric Power Applications, vol. 144, no. 3, pp. 199-206, 1997.
Liu, W. J. Liu, Variable Structure Controller Design for Uncertain Systems with Dead-Zone Inputs. Ph D dissertation, National Central University, 2005.
Luenberger, D. G., “Dynamic Equations in Descriptor Form,” IEEE Transactions on Automatic Control, vol. AC-22, no. 3, pp. 312-321, 1977.
Newcomb, R. W., “The Semistate Description of Nonlinear Time Variable Circuits,” IEEE Transactions on Circuits and Systems, vol. CAS-28, no. 1, pp. 62-71, 1981.
Pai, M. C. and Sinha, A., “Sliding Mode Output Feedback Control of Time-Varying Mismatched Uncertain Systems,” IEEE International Conference on Systems, Man, and Cybernetics, Taipei, Taiwan, pp.1355-1360, 2006.
Shyu, K. K. and Liu, C. Y., “Variable Structure Controller Design for Robust Tracking and Model Following,” Journal of Guidance, Control, and Dynamics, vol. 19, no. 6, pp. 1395-1397, 1996.
Sinswat, V. and Fallside, F., “Eigenvalue/eigenvector assignment by state feedback,” International Journal of Control, vol. 23, pp.183-196, 1977.
Spurgeon, S. K. and Patton, R. J., “Robust Variable Structure Control of Model Reference System,” IEE Proceedings, Control Theory and Applications, Pt. D, vol. 137, no. 6, pp. 341-348, 1990.
Stewart, G. W. and Sun, J. G., Matrix Perturbation Theory. Academic Press, 1990.
Tseng, Y. W. and Yedavalli, R. K., “Stability, Controllability and Observability Criteria for The Reciprocal State Space Framework”, American Control Conference, Denver, Colorado, USA, 2003.
Tseng, Y. W. and Yedavalli, R. K., Control Design of Linear Dynamic System with Matrix Differential Equations for Aerospace Applications, Ph. D. Dissertation, Department of Aerospace Engineering, The Ohio State University: Columbus, 1997.
Utkin, V. I. and Shi, J., “Integral sliding mode in systems operating under uncertainty conditions,” IEEE Proceedings of Conference on Decision and Control, Kobe, Japan, pp. 4591-4596, 1996.
Utkin, V. I. Utkin, and Young, K. D., “Method for constructing discontinuity planes in multidimensional variable systems,” Automation Remote Control, vol. 39, pp. 1466-1470, 1979.
Utkin, V. I., Guldner, J., and Shi, J., Sliding Mode Control in Electromechanical Systems. Philadelphia: Taylor & Francis, 1999.
Utkin, V. I., Sliding Modes and Theirs Applications in Variable Structure Systems. Moscow: MIR, 1978.
Vatiadis, D. and Karcanias, N., “Generalized State-Space Realization from Matrix Fraction Descriptions,” IEEE Transactions on Automatic Control, vol. AC-40, no. 66, pp. 1134-1137, 1995.
Verghese, G. C., Levy, B. C., and Kailath, T., “A Generalized State-Space for Singular Systems,” IEEE Transactions on Automatic Control, vol. AC-26, no. 4, pp. 11-831, 1981.
Wang, J. D., Lee, T. L., and Juang, Y. T., 1996, “New methods to design an integral variable structure controller,” IEEE Transactions on Automatic Control, vol. 41, no. 1, pp. 140-143, 1996.
Yip, E. L. and Sincovec, R. F., “Solvability, Controllability and Observability of Continuous Descriptor Systems,” IEEE Transactions on Automatic Control, vol. AC-26, no. 3, pp. 702-707, 1981.
Young, K. D., “Design of Variable Structure Model-Following Control Systems,” IEEE Transactions on Automatic Control, vol. 23, no. 6, pp. 1079-1085, 1978.