基于能量成形的功率变换器非线性控制
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摘要
DC／DC变换器是一种典型的非线性对象，本文主要针对Boost和Cuk变换器，运用端口受控哈密顿系统理论中的互联和阻尼配置的无源性控制(IDA-PBC)方法进行了控制系统设计，同时对所设计的控制系统在Matlab／Simulink的软件环境下进行仿真，通过仿真结果验证了所设计的控制系统的正确性。
本文对DC／DC变换器中各种线性和非线性控制方法进行了回顾，讨论了端口受控哈密顿系统控制方法的优越性，并指出现有相关文献仅研究了DC／DC变换器中的一些无源性控制实例，没有进一步讨论哈密顿系统理论中的互联和阻尼配置的无源性控制方法，且控制效果也有进一步改善的潜力。
本文主体部分首先介绍了耗散系统和一类无源系统——哈密顿系统的一些基础知识。对这类系统的属性，出于稳定控制的考虑，我们从能量成形的角度进行了研究，介绍了无源系统的稳定性定理和耗散系统的稳定性定理，讨论了耗散的端口受控哈密顿系统的反馈镇定方法。
其次对两种基本硬开关变换器Boost和Cuk变换器的互联和阻尼配置的无源性控制(IDA-PBC)方法进行了研究，同时解决了包括反对称矩阵，阻尼矩阵的配置，期望能量函数的选择，平衡点的求取，稳定性分析等问题。利用Matlab／Simulink仿真软件，进行了仿真应用研究。
最后，利用TMSLF2407数字信号处理平台对Boost变换器的控制系统进行了实验方案分析研究。
论文最后对全文所作的工作进行了总结，并指明了未来的研究方向。
DC/DC power converter is one of typical nonlinear systems, it's control problem hasattracted many researchers. In this paper, a novel control method Port-ControlledHamiltonian (PCH) system control has been used to control the Boost and Cuk converter,and the main method is the interconnection and damping assignment passivity-basedcontrol method in the theory of Hamiltonian systems. In Matlab/Simulink, the models ofHamiltonian control systems are established. The simulation results show that the controlsystems are correct.
First of all, we introduced some basic information of dissipation system and a kindof passivity system—Hamiltonian system. We research these systems using the method ofenergy shaping from the stabilization. We have introduced the stability theory of thepassivity system and the stability theory of the dissipation system. We have discussed thefeedback stabilization theory of the Port-Controlled Hamiltonian system with dissipation.
Secondly, we established the model of Boost and Cuk converter in the theory of theport-controlled Hamiltonian system. Meanwhile we have used the interconnection anddamping assignment passivity-based control method to work out the controller of thepower converter systems. We analyzed the characteristics of the PCH model of DC/DCconverter. These included: energy balance, dissipation, passivity etc.
Thirdly, we used the TMSLF2407 DSP circuit to realize the controller of Boostconverter.
The conclusion of the research work in this dissertation is made and the futureresearch direction is given out also.
本文对DC／DC变换器中各种线性和非线性控制方法进行了回顾，讨论了端口受控哈密顿系统控制方法的优越性，并指出现有相关文献仅研究了DC／DC变换器中的一些无源性控制实例，没有进一步讨论哈密顿系统理论中的互联和阻尼配置的无源性控制方法，且控制效果也有进一步改善的潜力。
本文主体部分首先介绍了耗散系统和一类无源系统——哈密顿系统的一些基础知识。对这类系统的属性，出于稳定控制的考虑，我们从能量成形的角度进行了研究，介绍了无源系统的稳定性定理和耗散系统的稳定性定理，讨论了耗散的端口受控哈密顿系统的反馈镇定方法。
其次对两种基本硬开关变换器Boost和Cuk变换器的互联和阻尼配置的无源性控制(IDA-PBC)方法进行了研究，同时解决了包括反对称矩阵，阻尼矩阵的配置，期望能量函数的选择，平衡点的求取，稳定性分析等问题。利用Matlab／Simulink仿真软件，进行了仿真应用研究。
最后，利用TMSLF2407数字信号处理平台对Boost变换器的控制系统进行了实验方案分析研究。
论文最后对全文所作的工作进行了总结，并指明了未来的研究方向。
DC/DC power converter is one of typical nonlinear systems, it's control problem hasattracted many researchers. In this paper, a novel control method Port-ControlledHamiltonian (PCH) system control has been used to control the Boost and Cuk converter,and the main method is the interconnection and damping assignment passivity-basedcontrol method in the theory of Hamiltonian systems. In Matlab/Simulink, the models ofHamiltonian control systems are established. The simulation results show that the controlsystems are correct.
First of all, we introduced some basic information of dissipation system and a kindof passivity system—Hamiltonian system. We research these systems using the method ofenergy shaping from the stabilization. We have introduced the stability theory of thepassivity system and the stability theory of the dissipation system. We have discussed thefeedback stabilization theory of the Port-Controlled Hamiltonian system with dissipation.
Secondly, we established the model of Boost and Cuk converter in the theory of theport-controlled Hamiltonian system. Meanwhile we have used the interconnection anddamping assignment passivity-based control method to work out the controller of thepower converter systems. We analyzed the characteristics of the PCH model of DC/DCconverter. These included: energy balance, dissipation, passivity etc.
Thirdly, we used the TMSLF2407 DSP circuit to realize the controller of Boostconverter.
The conclusion of the research work in this dissertation is made and the futureresearch direction is given out also.
引文
[1] 蔡宣三，龚绍文．高频功率电子学(直流一直流变换部分)[M]．北京：科学出版社，1993．
[2] 阮新波，严仰光．DC／DC PWM全桥变换器的软开关技术[J]．第十三届全国电源技术年会论文集，2001：134～140．
[3] 陈永真，曹永刚，王国玲．基本DC／DC变换器及演化[J]．第十四届全国电源技术年会论文集，2002：576～585．
[4] 阮新波，严仰光．直流开关电源的软开关技术[M]．北京：科学出版社，2000．
[5] 陈国呈．PWM变频调速及软开关电力变换技术[M]．北京：机械工业出版社，1998．
[6] 钱照明，吕征宇，何湘宁．电力电子变换新技术[J]．江苏机械制造与自动化，2002，vol．2：3～6．
[7] I. D. Landau. Adaptive Control-the Model Reference Approach[M]. New York: 2000.
[8] 付永庆．开关稳压电源动态性能的最优化设计研究[J]．仪器仪表学报，1997，18(16)：617～621．
[9] 韩曾晋．自适应控制[M]．北京：清华大学出版社，2002．
[10] 秦娟英，张华军．基于自适应控制的逆变器实时控制系统设计[J]．微计算机信息，2005，21(5)：38～40．
[11] 邹云屏，成功，丁凯．一种基于模型参考自适应控制的软开关逆变器[J]．2000，6(3)：14～16．
[12] 高为炳．变结构控制理论基础[M]．北京：中国科学技术出版社，1990．
[13] A J van der Schaft, B M Masche. The Hamiltonian formulation of energy conservingphyscial systems with external ports[J]. Int. J. of Electronics and Communications. 1995, 49(5): 362～271.
[14] 马化胜．AC／DC Buck-Boost PFC变换器滑模变结构及PI调节器综合控制[J]．电工技术学报，2004，19(9)：69～72．
[15] R. Ortega, van der Schaft A J, B M Maschke. Stabilization of port-controlled Hamiltonian systems via energy balancing in Stability and Stabilization of nonlinear Systems[M]. London: Springer-Verlag, 1999.
[16] R. Orteg. Power Port Viewpoint to Control of Multidomain Physical Systems[M]. London: Springer-Verlag, 2001.
[17] 铁龙．机器人鲁棒控制基础[M]．北京：清华大学出版社，2000．
[18] 梅生伟，申铁龙，刘康志．现代鲁棒控制理论与应用[M]．北京：清华大学出版社，2003．
[19] Byrnes C I, Isidori A, Willems J C. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems[M]. IEEE Transaction Automatic Control, 1991, 36: 1228～1240.
[20] J. C. Willems. Dissipative dynamical systems-Part Ⅰ: General Theory. Newyork: Archive for Rational Mechanics and Analysis, 1972.
[21] R. Ortega, A J van der Scbaft. Stabilization of underactuated mechanical systems via interconnection and damping assignment[M]. In Proc. IFAC Workshop Lagrangian Hamiltonian Methods Nonlinear Systems, Princeton, NJ, 2000:74～79.
[22] Rodriguez H, R. Ortega. Stabilization of electromechanical systems via interconnection and damping assignment[J]. Int. J. Robust Nonlinear Control. 2003,13(12):1095～1111.
[23] 孙元章，刘前进，杨新林．非线性控制中的L_2增益和无源化方法[M]．北京：清华大学出版社，2002．
[24] 阮新波，严仰光．直流开关电源的软开关技术[M]．北京：科学出版社，2000．
[25] 阮新波，严仰光．脉宽调制Dc／Dc全桥变换器的软开关技术[M]．北京：科学出版社：2001．
[26] 王兆安，黄俊．电力电子技术[M]．北京：机械工业出版社，2001．
[27] R. Ortega, A. van der Schaft, B. Maschke and G. Escobar. Interconnection and damping assign-ment passivity-based control of port- controlled hamiltonian systems[J]. Automatica, April 2002,38(4):585～596.
[28] 张雄伟．DSP芯片的原理与开发应用[M]．北京：电子工业出版社，1997．
[29] 周霖，刘建存．DSP控制工程技术应用[M]．北京：国防工业出版社，2005．
[30] 张崇魏，张兴．PWM整流器及其控制[M]．北京：机械工业出版社，2003．
[31] 于海生，潘松峰，于培仁．微型计算机控制技术[M]．北京：清华大学出版社，1999．
[32] R. Ortega, A. Astolfi, G. Bastin, H. Rodriguez. Output feedback stabilization of mass-balance systems[J]. Proc. 2000 ACC, Chicago, IL, 2000, June 28-30.
[33] Ortega R., A. van der Schaft, B. Maschke, G. Escobar. Energy shaping of port-controlled'hamiltonian systems by interconnection[J]. IEEE Conf. Dec. and Control, Phoenix, AZ, USA, 1999:7-10,.
[34] C. Battle, A. Doria-Cerezo, R. Ortega. Power flow control of a doubly-fed induction machine coupled to a flywheel[J]. IEEE Conf. on Control Applications, Taipei, Taiwan, 2004: 1585～1596.
[35] R. Ortega, A. van der Sehaft, I. Mareels and B. Maschke. Putting energy back in control[J]. IEEE Control Syst. Magazine, 2001,21(2): 18～33.
[36] 于海生，赵克友，郭雷，王海亮．基于端口受控哈密顿方法的PMSM最大转距／电流控制[J]．中国电机工程学报，2006，26(8)：82～87．
[37] 李春文，冯元混．多变量非线性控制的逆系统方法[M]．北京：清华大学出版社，1990．
[38] Arian van der Schaft. L2-Gain and passivity techniques in nonlinear control[M]. London: Springer-Verlag, 2000.
[39] K. Fujimoto, K. Sakurama, T. Sugie. Trajectory tracking control of port-controlled hamiltonian systems and its application to a magnetic levitation system[J]. Proc. 40th IEEE Conference on Decision and Control, Orlando, U.S.A., 2001: 3388～3393.
[40] M. Galaz, R. Ortega, A. Bazanella, A. Stankovic. An energy-shaping approach to excitation control of synchronous generators[J]. Automatica, 2003,39(1): 111～119.
[41] H. Rodriguez, R. Ortega and G. Escobar. Energy-shaping control of switched power converters[J]. Proc. IEEE International Symposium on Industrial Electronics ISIE'2001, 2001:525～530:
[42] H. Rodriguez, R. Ortega, G. Escobar, N. Barabanov. A robustly stable output feedback saturated controller for the boost dc-to-dc converter[J]. Systems and Control Letters, 2000,40(1):1～8.
[43] R. Ortega, M. Spong, F. Gomez, G. Blankenstein. Stabilization of underactuated mechanical systems via interconnection and damping assignment[J]. IEEE Trans. Automatic Control, 2002,47(8): 1218～1233.
[44] K. Fujimoto, T. Sugie. Stabilization of hamiltonian systems with nonholonomic constraints based on time-varying generalized canonical transformations[J]. Systems and Control Letters, vol. 44, no. 4, pp. 309-319, 2001.
[45] K. Fujimoto, T. Sugie. Canonical transformations and stabilization of generalized Hamiltonian systems[J]. Systems and Control Letters, 2001,42(3):217～227.
[46] G. Blankenstein, R. Ortega, A. van der Schaft. The matching conditions of controlled lagrangians and interconnection and damping passivity-based control[J]. Int. J. of Control, 2002,75(9): 645～665.
[2] 阮新波，严仰光．DC／DC PWM全桥变换器的软开关技术[J]．第十三届全国电源技术年会论文集，2001：134～140．
[3] 陈永真，曹永刚，王国玲．基本DC／DC变换器及演化[J]．第十四届全国电源技术年会论文集，2002：576～585．
[4] 阮新波，严仰光．直流开关电源的软开关技术[M]．北京：科学出版社，2000．
[5] 陈国呈．PWM变频调速及软开关电力变换技术[M]．北京：机械工业出版社，1998．
[6] 钱照明，吕征宇，何湘宁．电力电子变换新技术[J]．江苏机械制造与自动化，2002，vol．2：3～6．
[7] I. D. Landau. Adaptive Control-the Model Reference Approach[M]. New York: 2000.
[8] 付永庆．开关稳压电源动态性能的最优化设计研究[J]．仪器仪表学报，1997，18(16)：617～621．
[9] 韩曾晋．自适应控制[M]．北京：清华大学出版社，2002．
[10] 秦娟英，张华军．基于自适应控制的逆变器实时控制系统设计[J]．微计算机信息，2005，21(5)：38～40．
[11] 邹云屏，成功，丁凯．一种基于模型参考自适应控制的软开关逆变器[J]．2000，6(3)：14～16．
[12] 高为炳．变结构控制理论基础[M]．北京：中国科学技术出版社，1990．
[13] A J van der Schaft, B M Masche. The Hamiltonian formulation of energy conservingphyscial systems with external ports[J]. Int. J. of Electronics and Communications. 1995, 49(5): 362～271.
[14] 马化胜．AC／DC Buck-Boost PFC变换器滑模变结构及PI调节器综合控制[J]．电工技术学报，2004，19(9)：69～72．
[15] R. Ortega, van der Schaft A J, B M Maschke. Stabilization of port-controlled Hamiltonian systems via energy balancing in Stability and Stabilization of nonlinear Systems[M]. London: Springer-Verlag, 1999.
[16] R. Orteg. Power Port Viewpoint to Control of Multidomain Physical Systems[M]. London: Springer-Verlag, 2001.
[17] 铁龙．机器人鲁棒控制基础[M]．北京：清华大学出版社，2000．
[18] 梅生伟，申铁龙，刘康志．现代鲁棒控制理论与应用[M]．北京：清华大学出版社，2003．
[19] Byrnes C I, Isidori A, Willems J C. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems[M]. IEEE Transaction Automatic Control, 1991, 36: 1228～1240.
[20] J. C. Willems. Dissipative dynamical systems-Part Ⅰ: General Theory. Newyork: Archive for Rational Mechanics and Analysis, 1972.
[21] R. Ortega, A J van der Scbaft. Stabilization of underactuated mechanical systems via interconnection and damping assignment[M]. In Proc. IFAC Workshop Lagrangian Hamiltonian Methods Nonlinear Systems, Princeton, NJ, 2000:74～79.
[22] Rodriguez H, R. Ortega. Stabilization of electromechanical systems via interconnection and damping assignment[J]. Int. J. Robust Nonlinear Control. 2003,13(12):1095～1111.
[23] 孙元章，刘前进，杨新林．非线性控制中的L_2增益和无源化方法[M]．北京：清华大学出版社，2002．
[24] 阮新波，严仰光．直流开关电源的软开关技术[M]．北京：科学出版社，2000．
[25] 阮新波，严仰光．脉宽调制Dc／Dc全桥变换器的软开关技术[M]．北京：科学出版社：2001．
[26] 王兆安，黄俊．电力电子技术[M]．北京：机械工业出版社，2001．
[27] R. Ortega, A. van der Schaft, B. Maschke and G. Escobar. Interconnection and damping assign-ment passivity-based control of port- controlled hamiltonian systems[J]. Automatica, April 2002,38(4):585～596.
[28] 张雄伟．DSP芯片的原理与开发应用[M]．北京：电子工业出版社，1997．
[29] 周霖，刘建存．DSP控制工程技术应用[M]．北京：国防工业出版社，2005．
[30] 张崇魏，张兴．PWM整流器及其控制[M]．北京：机械工业出版社，2003．
[31] 于海生，潘松峰，于培仁．微型计算机控制技术[M]．北京：清华大学出版社，1999．
[32] R. Ortega, A. Astolfi, G. Bastin, H. Rodriguez. Output feedback stabilization of mass-balance systems[J]. Proc. 2000 ACC, Chicago, IL, 2000, June 28-30.
[33] Ortega R., A. van der Schaft, B. Maschke, G. Escobar. Energy shaping of port-controlled'hamiltonian systems by interconnection[J]. IEEE Conf. Dec. and Control, Phoenix, AZ, USA, 1999:7-10,.
[34] C. Battle, A. Doria-Cerezo, R. Ortega. Power flow control of a doubly-fed induction machine coupled to a flywheel[J]. IEEE Conf. on Control Applications, Taipei, Taiwan, 2004: 1585～1596.
[35] R. Ortega, A. van der Sehaft, I. Mareels and B. Maschke. Putting energy back in control[J]. IEEE Control Syst. Magazine, 2001,21(2): 18～33.
[36] 于海生，赵克友，郭雷，王海亮．基于端口受控哈密顿方法的PMSM最大转距／电流控制[J]．中国电机工程学报，2006，26(8)：82～87．
[37] 李春文，冯元混．多变量非线性控制的逆系统方法[M]．北京：清华大学出版社，1990．
[38] Arian van der Schaft. L2-Gain and passivity techniques in nonlinear control[M]. London: Springer-Verlag, 2000.
[39] K. Fujimoto, K. Sakurama, T. Sugie. Trajectory tracking control of port-controlled hamiltonian systems and its application to a magnetic levitation system[J]. Proc. 40th IEEE Conference on Decision and Control, Orlando, U.S.A., 2001: 3388～3393.
[40] M. Galaz, R. Ortega, A. Bazanella, A. Stankovic. An energy-shaping approach to excitation control of synchronous generators[J]. Automatica, 2003,39(1): 111～119.
[41] H. Rodriguez, R. Ortega and G. Escobar. Energy-shaping control of switched power converters[J]. Proc. IEEE International Symposium on Industrial Electronics ISIE'2001, 2001:525～530:
[42] H. Rodriguez, R. Ortega, G. Escobar, N. Barabanov. A robustly stable output feedback saturated controller for the boost dc-to-dc converter[J]. Systems and Control Letters, 2000,40(1):1～8.
[43] R. Ortega, M. Spong, F. Gomez, G. Blankenstein. Stabilization of underactuated mechanical systems via interconnection and damping assignment[J]. IEEE Trans. Automatic Control, 2002,47(8): 1218～1233.
[44] K. Fujimoto, T. Sugie. Stabilization of hamiltonian systems with nonholonomic constraints based on time-varying generalized canonical transformations[J]. Systems and Control Letters, vol. 44, no. 4, pp. 309-319, 2001.
[45] K. Fujimoto, T. Sugie. Canonical transformations and stabilization of generalized Hamiltonian systems[J]. Systems and Control Letters, 2001,42(3):217～227.
[46] G. Blankenstein, R. Ortega, A. van der Schaft. The matching conditions of controlled lagrangians and interconnection and damping passivity-based control[J]. Int. J. of Control, 2002,75(9): 645～665.