增益调度控制方法及其在热工对象中的应用
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摘要
一般的热工对象具有较强的非线性,系统参数随着工况变化而具有较大的变化。论文结合增益调度控制方法、状态反馈控制理论和PID控制器设计方法,得到一些适用于非线性热工对象全工况运行的控制方案。
论文采用结合状态反馈控制、Kharitonov 理论、广义Hermite-Biehler定理等理论进行稳定性分析,并通过计算机仿真进行验证的研究方法,研究了增益调度的设计方法及其在热工对象中的应用。取得了下列主要成果:[1]基于状态反馈控制理论,得到了一种稳态工况之间简单可行的控制器参数计算方法,避免了经典增益调度插值算法所面临的实时解两个线性矩阵不等式以及采用矩阵进行插值运算的问题,并应用于非线性机炉协调工况变换的控制问题上;[2]针对非线性控制器切换问题,通过设计控制器的无扰切换方法,得到全工况控制器参数的选择方法,并应用于单级倒立摆的摆角全程控制和位移控制中。这部分内容是把增益调度理论扩展到使用不同形式控制器的对象全工况控制问题上;[3]基于 Kharitonov 理论,针对一类二阶对象,设计了保证系统稳定的PI增益调度方法,并应用于车用分轴燃气轮机的全程控制中。这部分内容是增益调度和PI 控制器相结合的一种方案。[4]通过仿真研究,得到一种适用热工对象变工况控制的增益调度应用方案,包括:对未知系统的阶次和参数同时辨识的系统辨识方法,以及基于广义Hermite-Biehler定理的保证系统稳定的PID无扰切换方法。这个方案应用在核电站蒸汽发生器的水位控制仿真模型中。它为增益调度在工业生产过程,尤其是在热工对象变工况控制领域的应用提供一定的设计经验。研究结果显示了增益调度在热工控制问题上有一定的应用前景。
Thermal objects are usually nonlinear systems whose parameters vary in a large region. In this dissertation, some control schemes based on gain scheduled and state feedback control theory and PID controller were proposed to control the nonlinear parameter-varying thermal objects.
In present dissertation, through the stability analysis with the state feedback control, Kharitonov theory, and generalized Hermite-Biehler theorem, gain scheduled was studied for thermal control problems, which were confirmed by the computer simulations. Firstly, a stability-preserving interpolation method was proposed to compute the controller parameters in the operation regions between those equilibrium points. It averted the problem of real-time computation for two matrix inequations and interpolation with matrixes, which the classical gain scheduled interpolation method had to meet. This method was implemented in controlling a three-input and three-output nonlinear boiler-turbine unit with parameters varying in a wide range. Secondly, bumpless switching methods were proposed to extend gain scheduled to those plants which used different form controllers in the operation region. These methods were implemented in global control for the angle and distance of the inverted pendulum. Thirdly, based on Kharitonov theory, stability-preserving gain-scheduled PI controllers were designed for a kind of two-order plants whose parameters varied in a large range. This method was applied in a separate-axis gas turbine for automobile use with operation points varying globally. In addition, this method provided a scheme to combine gain scheduled and PI controllers. Finally, based on simulation study, a control scheme for the nonlinear unknown system, especially for thermal objects, was provided. It included a system identification method proposed to identify the order and parameters of an unknown system and PID-controller bumpless
switching method which was based on the generalized Hermite-Biehler theorem to guarantee the system stability. This control scheme was confirmed to control a simulation model of the nuclear steam generator water level. In addition, this control scheme provided design experience for gain scheduled to be implemented in industry, especially in thermal object control. The study of this dissertation illusrtated the promising future of gain scheduled in thermal object control.
论文采用结合状态反馈控制、Kharitonov 理论、广义Hermite-Biehler定理等理论进行稳定性分析,并通过计算机仿真进行验证的研究方法,研究了增益调度的设计方法及其在热工对象中的应用。取得了下列主要成果:[1]基于状态反馈控制理论,得到了一种稳态工况之间简单可行的控制器参数计算方法,避免了经典增益调度插值算法所面临的实时解两个线性矩阵不等式以及采用矩阵进行插值运算的问题,并应用于非线性机炉协调工况变换的控制问题上;[2]针对非线性控制器切换问题,通过设计控制器的无扰切换方法,得到全工况控制器参数的选择方法,并应用于单级倒立摆的摆角全程控制和位移控制中。这部分内容是把增益调度理论扩展到使用不同形式控制器的对象全工况控制问题上;[3]基于 Kharitonov 理论,针对一类二阶对象,设计了保证系统稳定的PI增益调度方法,并应用于车用分轴燃气轮机的全程控制中。这部分内容是增益调度和PI 控制器相结合的一种方案。[4]通过仿真研究,得到一种适用热工对象变工况控制的增益调度应用方案,包括:对未知系统的阶次和参数同时辨识的系统辨识方法,以及基于广义Hermite-Biehler定理的保证系统稳定的PID无扰切换方法。这个方案应用在核电站蒸汽发生器的水位控制仿真模型中。它为增益调度在工业生产过程,尤其是在热工对象变工况控制领域的应用提供一定的设计经验。研究结果显示了增益调度在热工控制问题上有一定的应用前景。
Thermal objects are usually nonlinear systems whose parameters vary in a large region. In this dissertation, some control schemes based on gain scheduled and state feedback control theory and PID controller were proposed to control the nonlinear parameter-varying thermal objects.
In present dissertation, through the stability analysis with the state feedback control, Kharitonov theory, and generalized Hermite-Biehler theorem, gain scheduled was studied for thermal control problems, which were confirmed by the computer simulations. Firstly, a stability-preserving interpolation method was proposed to compute the controller parameters in the operation regions between those equilibrium points. It averted the problem of real-time computation for two matrix inequations and interpolation with matrixes, which the classical gain scheduled interpolation method had to meet. This method was implemented in controlling a three-input and three-output nonlinear boiler-turbine unit with parameters varying in a wide range. Secondly, bumpless switching methods were proposed to extend gain scheduled to those plants which used different form controllers in the operation region. These methods were implemented in global control for the angle and distance of the inverted pendulum. Thirdly, based on Kharitonov theory, stability-preserving gain-scheduled PI controllers were designed for a kind of two-order plants whose parameters varied in a large range. This method was applied in a separate-axis gas turbine for automobile use with operation points varying globally. In addition, this method provided a scheme to combine gain scheduled and PI controllers. Finally, based on simulation study, a control scheme for the nonlinear unknown system, especially for thermal objects, was provided. It included a system identification method proposed to identify the order and parameters of an unknown system and PID-controller bumpless
switching method which was based on the generalized Hermite-Biehler theorem to guarantee the system stability. This control scheme was confirmed to control a simulation model of the nuclear steam generator water level. In addition, this control scheme provided design experience for gain scheduled to be implemented in industry, especially in thermal object control. The study of this dissertation illusrtated the promising future of gain scheduled in thermal object control.
引文
钟庆昌,谢剑英,李 辉. 变参数PID控制器. 信息与控制,1999,28(4):273~277
C. C. Kuan, C. Lin, and C. C. Hsu. Fuzzy logic control of steam generator water level in pressurized water reactors. Nucl. Tech. 1992, 100: 125~134
G. Y. Park, P. H. Seong. Application of a fuzzy learning algorithm to nuclear steam generator level control. Ann. Nucl. Energy. 1995, 22(3/4): 135~146
B. H. Cho, H. C. No. Design of stability-guaranteed fuzzy logic controller for nuclear steam generators. IEEE Trans. Nucl. Sci. 1996, 43: 716~730
M. G. Na. Design of a genetic-fuzzy controller for the nuclear steam generator water level control. IEEE Trans. Nucl. Sci. 1998, 45: 2261~2271
M. G. Na. A model predictive controller for the water level of nuclear steam generators. J. Korean Nucl. Soc. 2001, 33(1): 102~110
M. G. Na. Auto-Tuned PID Controller Using a Model Predictive Control Method for the Steam Generator Water Level. IEEE TRANSACTIONS ON NUCLEAR SCIENCE. 2001, 48(5):1664~1671
E. Irving, C. Miossec, and J. Tassart. Toward efficient full automatic operation of the pwr steam generator with water level adaptive control. U.K.: 2nd Int. Conf. Boiler Dynamics and Control in Nuclear Power Stations, Bournemouth. 1979: 309~329
M. G. Na, H. C. No. Design of an adaptive observer-based controller for the water level of steam generators. Nucl. Eng. Des.1992, 135(3): 379~394
Mads E.Hangstrup, Jakob Stoustrup, etc. Gain-Scheduled Control of a Fossil-Fired Power Plant Boiler. Proceeding of the 1997 IEEE International Conference on Control Applications.1999:907~909
Byung Hak Cho, Hee Cheon No. Design of stability and performance robust fuzzy logic gain scheduler for nuclear steam generators. IEEE Transactions on nuclear science.1997, 44(3):1431~1441
Wataro Shinohara, D.E.Koditschek. Intelligent control of a boiler-turbine plant based on switching control scheme. Proceedings of the 34th Conference on Decision and control.1995: 1762-1763
Wilson J.Rugh, Jeff S.Shamma. a survey of Research on Gain Scheduling. Elsevier Preprint.1999: 1~58
Jeff S.Shamma. Analysis and design of gain scheduled control systems. Massachusetts Institute of Technology Cambridge, Mass. 1988
Daniel J.Stilwell, Wilson J.Rugh. Interpolation methods for gain scheduling. Proceedings of the 37th IEEE Conference on Decision & Control.1998: 3003~3009
D. J. Stilwell, W. J. Rugh. Interpolation of Observer State Feedback Controllers for Gain Scheduling. IEEE Transaction on Automatic control, 1999, 44(6):1225-1229
Benoit Clement, Gilles Duc. An Interpolation Method for Gain-scheduling. Proceedings of the 40th IEEE Conference on Decision and Control, 2001:1310-1315
黄祖毅,李东海,姜学智,孙立明. Gain Scheduled Servo System for Boiler-Turbine Unit. 中国电机工程学报,2003,23(10):191~198
黄祖毅,李东海,姜学智,孙立明. 倒立摆控制的无扰切换问题研究. 清华大学学报(自然科学版),2004,44(2):266~269
黄祖毅,李东海,姜学智,孙立明. 倒立摆摆角全程控制的增益调度方法. 电机与控制学报,2004,已收录
黄祖毅,陈建清,李东海. 基于有理分式等价的系统阶次和参数同时辨识. 清华大学学报(自然科学版),2003,43(6):794~797
W. J. Rugh. Analytical framework for gain scheduling. IEEE Control Syst. Mag., 1991, 11(1): 79-84
谭文,牛玉广,刘吉臻. 非线性锅炉-汽轮机系统的鲁棒控制. 控制理论与应用, 1999,16(6):863~867
葛友,李春文. 反馈线性化在锅炉-汽机系统控制中的应用. 清华大学学报(自然科学版),2001,41(7):125~128
Cori R, Maffezzori C. Practical optimal control of a drum boiler power plant. Automatica, 1984, 20(2): 163~173
ohansson L, Koivo H N. Inverse nyquist array technique in the design of a multivariable controller for a solid-fuel boiler. Int. J. Control, 1984, 40(5): 1077-1088
JKatsuhiko Ogata. Modern Control Engineering. USA, New Jersey: Prentice Hall, 2002
Adel Ben-Abdenmour, Kwang Y. Lee. A Decentralized Controller Design for a Power Plant Using Robust Local Controllers and Function Mapping. IEEE Transactions on Energy Conversion, 1996, 11(2): 394-400
Robert Dimeo, Kwang Y. Lee. Boiler-Turbine Control System Design Using a Genetic Algorithm. IEEE Transactions on Energy Conversion, 1995, 10(4): 752-759
Robert Dimeo and Kwang Y. Lee. Boiler-Turbine Control System Design Using a Genetic Algorithm. IEEE Transactions on Energy Conversion. 1995, 10(4): 752-759
李祖欣,张榆锋,施心陵. 一种基于模糊规则切换的双模控制器. 贵州科学, 2002,20(4):31-34
Isabelle Fantoni, Rogelio Lozano. Non-linear Control for Underactuated Mechanical Systems. UK: Springer, 2002
从 爽,张冬军,魏衡华. 单级倒立摆三种控制方法的对比研究. 系统工程与电子技术,2001,23(11):47~49
张飞舟,范跃祖,沈程智,等. 利用云模型实现智能控制倒立摆. 控制理论与应用,2000,17(4):519~523
孙立明,姜学智,李东海,余涛. 水轮机水门非线性控制--动态反馈线性化方法的研究. 电力系统自动化,2003,27(16):45~49
HAO Jianbin, TAN Shaohua, Joos Vandewalle. A rule-based neural controller for inverted pendulum system. IEEE International Conference on Neural Networks, 1993, 1: 534~539
黎浩荣,李立勤,李东海,等. 对一种高精度模糊控制方案的研究与改进. 清华大学学报(自然科学版),2000,40(2):114~117
李宁,张乃尧,靳开岩. 输入隶属函数不均匀分布时典型模糊控制器的结构分析. 清华大学学报(自然科学版),2000,40(1):120~123
Yasunobu Seiji, Mori Munehito. Swing up Fuzzy controller for Inverted Pendulum based on a human control strategy. Proceedings of the Sixth IEEE International Conference on Fuzzy Systems, 1997, 3: 1621~1625
范醒哲,张乃尧. 输出隶属函数不均匀分布时典型模糊控制器的结构分析. 清华大学学报(自然科学版),2001,41(7):121~124
李春文,冯元琨. 多变量非线性控制的逆系统方法. 北京:清华大学出版社,1991
N. Ajlouni, A. H. Jones, S.B. Kenway. Genetic Design of a Gain-Scheduled Controller for a Non-linear Concentration Control System. Proceedings of the 1996 IEEE International Symposium on Intelligent Control, 1996: 366~371
A. Jimenez, F. Matia. A fast piecewise-linear implementation of Fuzzy Controllers. Proceedings of the First International Joint Conference of the North American Fuzzy Information and Processing Society Biannual Conference and The Industrial Fuzzy Control and Intelligent Systems Conference, and the NASA Joint Technolo ,? 1994: 27~31
徐峰. 鲁棒PID控制器研究及其在热工对象控制中的应用. 北京:清华大学热能工程系,2002
Kharitonov V L. Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differentsialjnie Uravnenia, 1978, 14:2086~2088
Chapellat H and Bhattacharyya S P. A generalization of Kharitonov’s Theorem: Robust stability of interval plants, IEEE Tr. Auto. Control, 1990, 34(3): 306~311
C Houck, J Joines, M Kay. A Genetic Algorithm for Function Optimization: A MATLAB Implementation. NCSU-IE TR 95-09, U.S.A.: North Carolina State University, 1995
张立群,李东海,薛亚丽,等. 基于参数稳定空间的 PID控制器. 清华大学学报(自然科学版),2004,44(2):274~277
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Datta A, Ho M T, Bhattacharyya S P. Structure and Synthesis of PID Controllers. London: Springer, 2000
C. C. Kuan, C. Lin, and C. C. Hsu. Fuzzy logic control of steam generator water level in pressurized water reactors. Nucl. Tech. 1992, 100: 125~134
G. Y. Park, P. H. Seong. Application of a fuzzy learning algorithm to nuclear steam generator level control. Ann. Nucl. Energy. 1995, 22(3/4): 135~146
B. H. Cho, H. C. No. Design of stability-guaranteed fuzzy logic controller for nuclear steam generators. IEEE Trans. Nucl. Sci. 1996, 43: 716~730
M. G. Na. Design of a genetic-fuzzy controller for the nuclear steam generator water level control. IEEE Trans. Nucl. Sci. 1998, 45: 2261~2271
M. G. Na. A model predictive controller for the water level of nuclear steam generators. J. Korean Nucl. Soc. 2001, 33(1): 102~110
M. G. Na. Auto-Tuned PID Controller Using a Model Predictive Control Method for the Steam Generator Water Level. IEEE TRANSACTIONS ON NUCLEAR SCIENCE. 2001, 48(5):1664~1671
E. Irving, C. Miossec, and J. Tassart. Toward efficient full automatic operation of the pwr steam generator with water level adaptive control. U.K.: 2nd Int. Conf. Boiler Dynamics and Control in Nuclear Power Stations, Bournemouth. 1979: 309~329
M. G. Na, H. C. No. Design of an adaptive observer-based controller for the water level of steam generators. Nucl. Eng. Des.1992, 135(3): 379~394
Mads E.Hangstrup, Jakob Stoustrup, etc. Gain-Scheduled Control of a Fossil-Fired Power Plant Boiler. Proceeding of the 1997 IEEE International Conference on Control Applications.1999:907~909
Byung Hak Cho, Hee Cheon No. Design of stability and performance robust fuzzy logic gain scheduler for nuclear steam generators. IEEE Transactions on nuclear science.1997, 44(3):1431~1441
Wataro Shinohara, D.E.Koditschek. Intelligent control of a boiler-turbine plant based on switching control scheme. Proceedings of the 34th Conference on Decision and control.1995: 1762-1763
Wilson J.Rugh, Jeff S.Shamma. a survey of Research on Gain Scheduling. Elsevier Preprint.1999: 1~58
Jeff S.Shamma. Analysis and design of gain scheduled control systems. Massachusetts Institute of Technology Cambridge, Mass. 1988
Daniel J.Stilwell, Wilson J.Rugh. Interpolation methods for gain scheduling. Proceedings of the 37th IEEE Conference on Decision & Control.1998: 3003~3009
D. J. Stilwell, W. J. Rugh. Interpolation of Observer State Feedback Controllers for Gain Scheduling. IEEE Transaction on Automatic control, 1999, 44(6):1225-1229
Benoit Clement, Gilles Duc. An Interpolation Method for Gain-scheduling. Proceedings of the 40th IEEE Conference on Decision and Control, 2001:1310-1315
黄祖毅,李东海,姜学智,孙立明. Gain Scheduled Servo System for Boiler-Turbine Unit. 中国电机工程学报,2003,23(10):191~198
黄祖毅,李东海,姜学智,孙立明. 倒立摆控制的无扰切换问题研究. 清华大学学报(自然科学版),2004,44(2):266~269
黄祖毅,李东海,姜学智,孙立明. 倒立摆摆角全程控制的增益调度方法. 电机与控制学报,2004,已收录
黄祖毅,陈建清,李东海. 基于有理分式等价的系统阶次和参数同时辨识. 清华大学学报(自然科学版),2003,43(6):794~797
W. J. Rugh. Analytical framework for gain scheduling. IEEE Control Syst. Mag., 1991, 11(1): 79-84
谭文,牛玉广,刘吉臻. 非线性锅炉-汽轮机系统的鲁棒控制. 控制理论与应用, 1999,16(6):863~867
葛友,李春文. 反馈线性化在锅炉-汽机系统控制中的应用. 清华大学学报(自然科学版),2001,41(7):125~128
Cori R, Maffezzori C. Practical optimal control of a drum boiler power plant. Automatica, 1984, 20(2): 163~173
ohansson L, Koivo H N. Inverse nyquist array technique in the design of a multivariable controller for a solid-fuel boiler. Int. J. Control, 1984, 40(5): 1077-1088
JKatsuhiko Ogata. Modern Control Engineering. USA, New Jersey: Prentice Hall, 2002
Adel Ben-Abdenmour, Kwang Y. Lee. A Decentralized Controller Design for a Power Plant Using Robust Local Controllers and Function Mapping. IEEE Transactions on Energy Conversion, 1996, 11(2): 394-400
Robert Dimeo, Kwang Y. Lee. Boiler-Turbine Control System Design Using a Genetic Algorithm. IEEE Transactions on Energy Conversion, 1995, 10(4): 752-759
Robert Dimeo and Kwang Y. Lee. Boiler-Turbine Control System Design Using a Genetic Algorithm. IEEE Transactions on Energy Conversion. 1995, 10(4): 752-759
李祖欣,张榆锋,施心陵. 一种基于模糊规则切换的双模控制器. 贵州科学, 2002,20(4):31-34
Isabelle Fantoni, Rogelio Lozano. Non-linear Control for Underactuated Mechanical Systems. UK: Springer, 2002
从 爽,张冬军,魏衡华. 单级倒立摆三种控制方法的对比研究. 系统工程与电子技术,2001,23(11):47~49
张飞舟,范跃祖,沈程智,等. 利用云模型实现智能控制倒立摆. 控制理论与应用,2000,17(4):519~523
孙立明,姜学智,李东海,余涛. 水轮机水门非线性控制--动态反馈线性化方法的研究. 电力系统自动化,2003,27(16):45~49
HAO Jianbin, TAN Shaohua, Joos Vandewalle. A rule-based neural controller for inverted pendulum system. IEEE International Conference on Neural Networks, 1993, 1: 534~539
黎浩荣,李立勤,李东海,等. 对一种高精度模糊控制方案的研究与改进. 清华大学学报(自然科学版),2000,40(2):114~117
李宁,张乃尧,靳开岩. 输入隶属函数不均匀分布时典型模糊控制器的结构分析. 清华大学学报(自然科学版),2000,40(1):120~123
Yasunobu Seiji, Mori Munehito. Swing up Fuzzy controller for Inverted Pendulum based on a human control strategy. Proceedings of the Sixth IEEE International Conference on Fuzzy Systems, 1997, 3: 1621~1625
范醒哲,张乃尧. 输出隶属函数不均匀分布时典型模糊控制器的结构分析. 清华大学学报(自然科学版),2001,41(7):121~124
李春文,冯元琨. 多变量非线性控制的逆系统方法. 北京:清华大学出版社,1991
N. Ajlouni, A. H. Jones, S.B. Kenway. Genetic Design of a Gain-Scheduled Controller for a Non-linear Concentration Control System. Proceedings of the 1996 IEEE International Symposium on Intelligent Control, 1996: 366~371
A. Jimenez, F. Matia. A fast piecewise-linear implementation of Fuzzy Controllers. Proceedings of the First International Joint Conference of the North American Fuzzy Information and Processing Society Biannual Conference and The Industrial Fuzzy Control and Intelligent Systems Conference, and the NASA Joint Technolo ,? 1994: 27~31
徐峰. 鲁棒PID控制器研究及其在热工对象控制中的应用. 北京:清华大学热能工程系,2002
Kharitonov V L. Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differentsialjnie Uravnenia, 1978, 14:2086~2088
Chapellat H and Bhattacharyya S P. A generalization of Kharitonov’s Theorem: Robust stability of interval plants, IEEE Tr. Auto. Control, 1990, 34(3): 306~311
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张立群,李东海,薛亚丽,等. 基于参数稳定空间的 PID控制器. 清华大学学报(自然科学版),2004,44(2):274~277
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