鲁棒控制理论的应用研究——直线感应电机的鲁棒控制系统设计
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摘要
鲁棒控制是针对模型的不确定问题提出的，其研究重点是讨论控制系统的某种性能或某个指标在某种扰动下保持不变的程度。假定系统的传递函数属于一个集合(因为系统不确定性存在，所以传递函数可能有多个)，考察反馈系统的特性，给定一个控制器，如果集合中的每一个对象都能保持对这种特性成立，则称该控制器对此性能是鲁棒的。鲁棒性能的一般含义是指集合中的所有对象都满足内稳定和另外特性的性能。鲁棒控制引入权函数和增广系统的概念，使得控制系统可以同时考虑模型不确定性、稳定性、灵敏度和抗干扰能力的指标。
本论文进行的是鲁棒控制理论的应用研究，选择直线感应电机驱动的邮政分捡系统为控制对象，主要工作集中在建模和控制研究方面，满足了速度跟随迅速、抗负载扰动和抗模型摄动等控制要求。
目前对直线感应电机的控制，仍缺乏方便而有效的办法。因为直线感应电机磁极呈水平展开放置，有部分磁链不闭合，具有横向和纵向的边缘效应，表现出比旋转感应电机更强的非线性。在使用中，大多只考虑电机的静态设计性能，例如起动推力等，而对推力纹波、磁场畸变等动态性能不予考虑；在控制策略方面，也仅仅停留在开环阶段。这样的研究现状远远不能满足快速动作、精确定位、推力适当的系统控制要求，同时也不利于发挥直线感应电机推力大、速度快的性能优势。
通过探索，本文得出了一种简化直线感应电机模型的方法，可以在此基础上应用现代控制方法：1)应用矢量控制，建立直线感应电机的动态方程，并线性化输入量(电流、电压)和输出量(推力、磁通)的关系；2)建立并简化直线感应电机驱动的邮政分捡系统的动态模型；3)基于该线性动态模型，对邮政分捡系统进行控制研究。
由于直线感应电机简化模型的建立，使得我们在直线感应电机的控制策略研究方面，进展了一大步。因为由电机统一原理，可以参照旋转感应电机的各种控制方法，来进行直线感应电机的控制。而且，可以实现控制器和控制对象的一体化，使得直线感应电机的设计性能大为优化。
在本论文所述系统的鲁棒控制研究中，应用了H_∞控制理论和权函数的概念，进行系统增广，同时满足了系统速度跟随快速、抗扰动、抗模型摄动的性能要求。还引入了内模控制进行系统动态性能的改善。内模控制是将干扰信号的特征传递函数作为控制器的一个环节添加到闭环系统中去，使得控制系统有较好的对该类扰动的抑制能力。本文还研究了鲁棒控制的另一个分支——基于内模控制
浙江大学硕士学位论文。摘要
的鲁棒极点配置方法，设计了二自由度的鲁棒极点配置控制器，使得被控系统有
很好的干扰的抑制能力。
将基于内模原理的鲁棒极点配置方法、H。控制方法设计的控制系统做了仿
真研究，将控制结果与由PID控制方法得到的控制结果相比较，分析了它们对
此系统的控制优势和各自的适用性。
Robust Control is brought out to deal with system uncertainty, whose research
emphasis is to discuss the resistance of the system's certain characteristics or index to
some disturbance. Supposing the system's transfer functions belong to a set, we judge
the nature of the feedback system: given a controller, if all the objects in the set can
fulfill the demands of the nature, we say that the controller is robustic to the nature.
The general meaning of robustion is that all objects in a set can meet the requirements
of inner-stability and other characteristics. Robust control includes the concept of
weight function and augment-system, which leads to that the controlled system can
take some natures, like model uncertainty, stability, sensibility, disturbance-resistance,
into consideration at the same time.
We do the applying research of robust control theory in this paper, choose Post
Distribution System (PDS) using Linear Induction Motor (MM) as power source as
the control object. The main work focus on modeling and control research, fi.tlfill the
control demand of quick tracking, anti-loading disturbance and anti- model changing.
In the current research situation, we still lack convenient and effective way to
control LIM. Because LLM's magnetic poles are open, the magnetic chain is not
closed, it has end effect and expose strong nonlinear characteristics if compared with
Rotate Induction Motor (RIM). In the way of using, people normally only consider
the static design characteristics, and don't consider the dynamic characteristics; In the
control strategy, people only consider open-loop control. The above situation can't
meet the need of the system, such as quick tracking, accurate position and proper push,
can抰 make the LIM expose its advantages.
In this paper, we explore a method to simplify the LIIM model, and we can use
modern control method on this basis: 1) apply vector control, set up dynamic equation
of the LIM, and linearize relation of the input and output; 2) establish and simplify the
dynamic model of PDS using LIM as power system; 3) basing on this model, do some
control research on this system.
Because the establishment of the simplified LIM model, we get a big
development in the LIM control strategy. We can control LIM according to the way of
RIM control. And, the whole-design method of controller and object can optimize the
design characteristics of the LIM.
In the robust control research of this paper, we use H_∞ control theory and the
concept of weighing function, system-augment to meet the need of velocity tracking,
anti-disturbance, anti-model-change. We induce the inner model control to improve
the system's dynamic nature, which is to add a special part into controller, and make
the system has good anti-disturbance nature. We also do some research on robust pole
assignment based on inner model method, and design two-degree of freedom
controller.
We also emulate the control systems designed by PID control method, robust
pole assignment method, H_∞ Control, and compare their result and advantages.
本论文进行的是鲁棒控制理论的应用研究，选择直线感应电机驱动的邮政分捡系统为控制对象，主要工作集中在建模和控制研究方面，满足了速度跟随迅速、抗负载扰动和抗模型摄动等控制要求。
目前对直线感应电机的控制，仍缺乏方便而有效的办法。因为直线感应电机磁极呈水平展开放置，有部分磁链不闭合，具有横向和纵向的边缘效应，表现出比旋转感应电机更强的非线性。在使用中，大多只考虑电机的静态设计性能，例如起动推力等，而对推力纹波、磁场畸变等动态性能不予考虑；在控制策略方面，也仅仅停留在开环阶段。这样的研究现状远远不能满足快速动作、精确定位、推力适当的系统控制要求，同时也不利于发挥直线感应电机推力大、速度快的性能优势。
通过探索，本文得出了一种简化直线感应电机模型的方法，可以在此基础上应用现代控制方法：1)应用矢量控制，建立直线感应电机的动态方程，并线性化输入量(电流、电压)和输出量(推力、磁通)的关系；2)建立并简化直线感应电机驱动的邮政分捡系统的动态模型；3)基于该线性动态模型，对邮政分捡系统进行控制研究。
由于直线感应电机简化模型的建立，使得我们在直线感应电机的控制策略研究方面，进展了一大步。因为由电机统一原理，可以参照旋转感应电机的各种控制方法，来进行直线感应电机的控制。而且，可以实现控制器和控制对象的一体化，使得直线感应电机的设计性能大为优化。
在本论文所述系统的鲁棒控制研究中，应用了H_∞控制理论和权函数的概念，进行系统增广，同时满足了系统速度跟随快速、抗扰动、抗模型摄动的性能要求。还引入了内模控制进行系统动态性能的改善。内模控制是将干扰信号的特征传递函数作为控制器的一个环节添加到闭环系统中去，使得控制系统有较好的对该类扰动的抑制能力。本文还研究了鲁棒控制的另一个分支——基于内模控制
浙江大学硕士学位论文。摘要
的鲁棒极点配置方法，设计了二自由度的鲁棒极点配置控制器，使得被控系统有
很好的干扰的抑制能力。
将基于内模原理的鲁棒极点配置方法、H。控制方法设计的控制系统做了仿
真研究，将控制结果与由PID控制方法得到的控制结果相比较，分析了它们对
此系统的控制优势和各自的适用性。
Robust Control is brought out to deal with system uncertainty, whose research
emphasis is to discuss the resistance of the system's certain characteristics or index to
some disturbance. Supposing the system's transfer functions belong to a set, we judge
the nature of the feedback system: given a controller, if all the objects in the set can
fulfill the demands of the nature, we say that the controller is robustic to the nature.
The general meaning of robustion is that all objects in a set can meet the requirements
of inner-stability and other characteristics. Robust control includes the concept of
weight function and augment-system, which leads to that the controlled system can
take some natures, like model uncertainty, stability, sensibility, disturbance-resistance,
into consideration at the same time.
We do the applying research of robust control theory in this paper, choose Post
Distribution System (PDS) using Linear Induction Motor (MM) as power source as
the control object. The main work focus on modeling and control research, fi.tlfill the
control demand of quick tracking, anti-loading disturbance and anti- model changing.
In the current research situation, we still lack convenient and effective way to
control LIM. Because LLM's magnetic poles are open, the magnetic chain is not
closed, it has end effect and expose strong nonlinear characteristics if compared with
Rotate Induction Motor (RIM). In the way of using, people normally only consider
the static design characteristics, and don't consider the dynamic characteristics; In the
control strategy, people only consider open-loop control. The above situation can't
meet the need of the system, such as quick tracking, accurate position and proper push,
can抰 make the LIM expose its advantages.
In this paper, we explore a method to simplify the LIIM model, and we can use
modern control method on this basis: 1) apply vector control, set up dynamic equation
of the LIM, and linearize relation of the input and output; 2) establish and simplify the
dynamic model of PDS using LIM as power system; 3) basing on this model, do some
control research on this system.
Because the establishment of the simplified LIM model, we get a big
development in the LIM control strategy. We can control LIM according to the way of
RIM control. And, the whole-design method of controller and object can optimize the
design characteristics of the LIM.
In the robust control research of this paper, we use H_∞ control theory and the
concept of weighing function, system-augment to meet the need of velocity tracking,
anti-disturbance, anti-model-change. We induce the inner model control to improve
the system's dynamic nature, which is to add a special part into controller, and make
the system has good anti-disturbance nature. We also do some research on robust pole
assignment based on inner model method, and design two-degree of freedom
controller.
We also emulate the control systems designed by PID control method, robust
pole assignment method, H_∞ Control, and compare their result and advantages.
引文
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[2] 《H_∞控制理论及应用》，申铁龙，清华大学出版社，1996。
[3] 《自动控制理论》，夏得钤，机械工业出版社，1989。
[4] 《现代控制理论》，于长官，哈尔滨工业大学出版社，1988。
[5] 《线性控制系统》，郑大钟，清华大学出版社，1990。
[6] 《电力拖动自动控制系统》，陈伯时，机械工业出版社，1991。
[7] 《直线感应电机》，浙江大学《新技术译丛》编译组，1972。
[8] 《直线感应电机》(译文集)，科学出版社，1978。
[9] 《感应电动机的矢量控制及应用》，符曦(华南工学院)编，机械工业出版社，1986。
[10] 《大功率交—交变频调速及矢量控制技术》，第二版，马小亮著，机械工业出版社，1996。
[11] 《交流电机调速理论》，许大中著，浙江大学出版社，1991。
[12] 《交流调速系统》，宋中书(洛阳工业高等专科学校)主编，机械工业出版社，1999。
[13] 《特种电机》，唐任远(沈阳工业大学)主编，机械工业出版社，1998。
[14] 《直线交流伺服系统的精密控制技术》，郭庆鼎等编著，机械工业出版社，2000。
[15] 《直线电机原理与应用》，叶云岳，机械工业出版社，2000。
[16] 《控制系统计算机辅助设计——Matlab语言及应用》，薛定宇，清华大学出版社，1996。
[17] 《反馈控制系统设计与分析——Matlab语言应用》，薛定宇，清华大学出版社，2000。
[18] 《Robust Control Design——A Polynomical Approach》,Thedore E. Djaferis.
[19] 冯纯伯，费树岷，非线性控制系统分析与设计(第二版)，电子工业出版社，1998。
[20] 多变量非线性控制的逆系统方法，李春文，冯元琨，清华大学出版社，1991。
[21] Toshiharu Sugie, Tahashi Urashima, Kenji Fujimoto, A control Lyapnov Function Approach to stabilization of nonlinear systems with H_∞ control, Proceedings of the American Control Conference, Chicago, Illinois, June 2000.
[22] T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst., Man, Cybern, Vol. 15, pp. 116-132, Jan./Feb. 1985.
[23] Gwo-Ruey Yu, Gain scheduling for H_∞ control of Propulsion Aircraft, Proceedings of the American Control Conference, Chicago, Illinois, June 2000.
[24] W. Tan, Y.G. Niu, J.Z. Liu, Robust control for nonlinear boiler-turbine systems, Control Theory and Application, Vol. 16, No. 6, 1999.
[25] G.C. Loannidis, S.N. Manias, H_∞ loop-shaping control schemes for the buck converter and their evaluation using μ-analysis, IEE, Proceedings online, No. 1999990206.
[26] A. Leonessa, V. Chellaboina, W.M. Haddad, Robust stabilization of axial flow compressors with uncertain pressure-flow maps, IEEE Transaction on Control Systems Technology, Vol. 8, No.3, 2000, pp466-473.
[27] P.A. Iglesias, T.J. Urban, Loop shaping design for missile autopilots: controller configurations and weighting filter selection, Journal of Guidance, Control and Dynamics, Vol.23, No.3, 2000, pp516-525.
[28] M. Jankovic, R. Sepulchre, P.V. Kokotovic, CLF based designs with robustness to dynamic input unccrtainties, Systems & Control Letters 37 (1999) 45-54.
[29] P. Kokotovic, M. Arcak, Constructive nonlinear control: a historical perspective, Automatica 37(2001) 637-662.
[30] C.K. Chu, G.R. Yu, otc, Gain scheduling for fly-by-throttle flight control using neural networks, IEEE CDC 1996, pp1557-1562.
[31] Doyle J.C, Clover. K., Khargonekar. P.P., and Francis B.A., State-space solution to standard H_2 and H_∞ control problems, IEEE Trans. Auto. Cont., 1989, 34, (8), pp. 831-847.
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[48] 陈小峰，新型移印机用直线电机优化设计与控制，浙江大学硕士论文，2001年2月。
[49] 陈峰，一种交流电机新型非线性控制方法研究，清华大学博士论文，2000年3月。
[2] 《H_∞控制理论及应用》，申铁龙，清华大学出版社，1996。
[3] 《自动控制理论》，夏得钤，机械工业出版社，1989。
[4] 《现代控制理论》，于长官，哈尔滨工业大学出版社，1988。
[5] 《线性控制系统》，郑大钟，清华大学出版社，1990。
[6] 《电力拖动自动控制系统》，陈伯时，机械工业出版社，1991。
[7] 《直线感应电机》，浙江大学《新技术译丛》编译组，1972。
[8] 《直线感应电机》(译文集)，科学出版社，1978。
[9] 《感应电动机的矢量控制及应用》，符曦(华南工学院)编，机械工业出版社，1986。
[10] 《大功率交—交变频调速及矢量控制技术》，第二版，马小亮著，机械工业出版社，1996。
[11] 《交流电机调速理论》，许大中著，浙江大学出版社，1991。
[12] 《交流调速系统》，宋中书(洛阳工业高等专科学校)主编，机械工业出版社，1999。
[13] 《特种电机》，唐任远(沈阳工业大学)主编，机械工业出版社，1998。
[14] 《直线交流伺服系统的精密控制技术》，郭庆鼎等编著，机械工业出版社，2000。
[15] 《直线电机原理与应用》，叶云岳，机械工业出版社，2000。
[16] 《控制系统计算机辅助设计——Matlab语言及应用》，薛定宇，清华大学出版社，1996。
[17] 《反馈控制系统设计与分析——Matlab语言应用》，薛定宇，清华大学出版社，2000。
[18] 《Robust Control Design——A Polynomical Approach》,Thedore E. Djaferis.
[19] 冯纯伯，费树岷，非线性控制系统分析与设计(第二版)，电子工业出版社，1998。
[20] 多变量非线性控制的逆系统方法，李春文，冯元琨，清华大学出版社，1991。
[21] Toshiharu Sugie, Tahashi Urashima, Kenji Fujimoto, A control Lyapnov Function Approach to stabilization of nonlinear systems with H_∞ control, Proceedings of the American Control Conference, Chicago, Illinois, June 2000.
[22] T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst., Man, Cybern, Vol. 15, pp. 116-132, Jan./Feb. 1985.
[23] Gwo-Ruey Yu, Gain scheduling for H_∞ control of Propulsion Aircraft, Proceedings of the American Control Conference, Chicago, Illinois, June 2000.
[24] W. Tan, Y.G. Niu, J.Z. Liu, Robust control for nonlinear boiler-turbine systems, Control Theory and Application, Vol. 16, No. 6, 1999.
[25] G.C. Loannidis, S.N. Manias, H_∞ loop-shaping control schemes for the buck converter and their evaluation using μ-analysis, IEE, Proceedings online, No. 1999990206.
[26] A. Leonessa, V. Chellaboina, W.M. Haddad, Robust stabilization of axial flow compressors with uncertain pressure-flow maps, IEEE Transaction on Control Systems Technology, Vol. 8, No.3, 2000, pp466-473.
[27] P.A. Iglesias, T.J. Urban, Loop shaping design for missile autopilots: controller configurations and weighting filter selection, Journal of Guidance, Control and Dynamics, Vol.23, No.3, 2000, pp516-525.
[28] M. Jankovic, R. Sepulchre, P.V. Kokotovic, CLF based designs with robustness to dynamic input unccrtainties, Systems & Control Letters 37 (1999) 45-54.
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