基于T-S模糊模型的约束预测控制研究
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摘要
基于线性模型的预测控制研究已经相当成熟并得到了广泛的工业应用,然而在实际控制系统中,被控对象往往具有非线性、时变性和不确定性,针对高度非线性系统则很难取得令人满意的控制效果。而T-S模糊模型可以以任意精度逼近非线性系统,并且由于其结构的特殊性,可以通过局部动态线性化,把非线性系统表示成为线性形式,使得对其设计GPC控制器成为可能。本文首先简要介绍了广义预测控制的基本原理、基本算法步骤和模糊系统模型的基本原理,然后针对非线性系统提出了几种基于T-S模糊模型的有约束广义预测控制算法,并通过matlab仿真试验验证了这些算法的有效性。全文主要创新点有:
1.针对单变量非线性系统,在利用T-S模糊模型充分逼近的基础上,基于一步近似计算的思想,通过对输入变量的适当处理,提出了一种带约束输入的快速广义预测控制算法,该方法充分考虑了控制输入及其增量受约束的情况,并且计算量不大。
2.针对多变量非线性系统,基于T-S模糊模型建模,提出了一种带约束输入的快速广义预测控制算法,该方法充分考虑了控制输入及其增量受约束的情况,并避免了非线性搜索方法求解受约束的优化问题和求Diophantine方程,并且计算量不大。
在本文的最后,总结全文,并提出在该方向上需进一步做的工作。
Research on linear predictive control has become mature and linear MPC has gained wide applications in industrial processes. However, mostprocesses in industry are nonlinear, time-variant and bear uncertainty,for a highly nonlinear system, it may not give rise to satisfactory dynamic performance. The T-S fuzzy model can approaching any nonlinear systems, and its structure is simple. So the controlled plant can be expressed as a linear model, then the GPC controller can designed for it. In this dissertation, the development about predictive control and the T-S fuzzy system's strongpoints and deficiencies are introduced firstly. The basic identification steps of Takagi-Sugeno fuzzy model are presented in detail. And then some new algorithms of constrained fuzzy generalized predictive control are presented for nonlinear systems. The simulation results show their superior performance for nonlinear systems. In conclusion the main contents are as follows:
1) one kind of quickly constrained generalized predictive control algorithm is presented based on the T-S fuzzy model which is used to approach the SISO nonlinear systems, its computer load is not too large;
2) one kind of quickly constrained generalized predictive control algorithm is presented based on the T-S fuzzy model which is used to approach the MIMO nonlinear systems,it avoids the nonlinear search and need not to solve Diophantine functions by using a soft gene of input,so its computer load is not too large;
In the last section of this dissertation, a conclusion is presented, and some jobs needed to be done in the future are drawn.
1.针对单变量非线性系统,在利用T-S模糊模型充分逼近的基础上,基于一步近似计算的思想,通过对输入变量的适当处理,提出了一种带约束输入的快速广义预测控制算法,该方法充分考虑了控制输入及其增量受约束的情况,并且计算量不大。
2.针对多变量非线性系统,基于T-S模糊模型建模,提出了一种带约束输入的快速广义预测控制算法,该方法充分考虑了控制输入及其增量受约束的情况,并避免了非线性搜索方法求解受约束的优化问题和求Diophantine方程,并且计算量不大。
在本文的最后,总结全文,并提出在该方向上需进一步做的工作。
Research on linear predictive control has become mature and linear MPC has gained wide applications in industrial processes. However, mostprocesses in industry are nonlinear, time-variant and bear uncertainty,for a highly nonlinear system, it may not give rise to satisfactory dynamic performance. The T-S fuzzy model can approaching any nonlinear systems, and its structure is simple. So the controlled plant can be expressed as a linear model, then the GPC controller can designed for it. In this dissertation, the development about predictive control and the T-S fuzzy system's strongpoints and deficiencies are introduced firstly. The basic identification steps of Takagi-Sugeno fuzzy model are presented in detail. And then some new algorithms of constrained fuzzy generalized predictive control are presented for nonlinear systems. The simulation results show their superior performance for nonlinear systems. In conclusion the main contents are as follows:
1) one kind of quickly constrained generalized predictive control algorithm is presented based on the T-S fuzzy model which is used to approach the SISO nonlinear systems, its computer load is not too large;
2) one kind of quickly constrained generalized predictive control algorithm is presented based on the T-S fuzzy model which is used to approach the MIMO nonlinear systems,it avoids the nonlinear search and need not to solve Diophantine functions by using a soft gene of input,so its computer load is not too large;
In the last section of this dissertation, a conclusion is presented, and some jobs needed to be done in the future are drawn.
引文
[1]王伟.广义预测控制理论及其应用.北京:科学出版社,1998,9
[2]王伟.一种广义预测自适应控制的直接方法.自动化学报,1996,22(3):270-277
[3]舒迪前,石中锁.隐式自适应广义预测控制及其全局收敛性.自动化学报,1995,21(5):545-554
[4]Clarke D W,Feng R Scattolini.Constrained receding-horizon predictive control.IEE Proc-D,1991,138(4):347-354
[5]Rossiter J A,Louvaritakis B.Constrained stable generalized predictive control.IEE Proc.-U.1993,140(4):243-254
[6]Lelic M A,Zarrop M P.Generalized pole placement self-tuning controller.Int.J.Control,1987,46(2):547-568
[7]顾兴源,毛志忠.一种基于广义预测控制的极点配置自适应控制算法.控制与决策,1992,7(3):221-224
[8]Corradini M L,Orlado G.A VSC algorithm based on generalized predictive control.Automatica,1997,33(5):927-929
[9]王轶,席裕庚.广义预测控制的并行算法.自动化学报,1996,22(1):74-78
[10]张智焕,王树青,荣冈.基于精确线性化的MIMO双线性系统预测函数控制.控制理论与应用,2003,20(3):477-480
[11]王伟.具有Hammerstein形式的非线性系统广义预测控制.控制理论与应用,1994,11(6):672-680
[12]Ping Lu.Nonlinear predictive controllers for continuous systems.Journal of Guid Cont and Dynamias,1995,17(3):553-560
[13]Sahjendra N.Singh,Marc Steinberg,Robert D.Digirolamo.Nonlinear predictive control of feedback linearizable systems and flight control system design.Journal ofGuid Cont and Dynamics,1995,18(5):1023-1028
[14]Badr A,Binder Z,Rey D.Application of tracking multi-model control to a nonlinear thermal process.Int.J.System Science,1990,21(9):1795-1803
[15]张泉灵,王树青.化学反应器温度跟踪预测函数控制的研究与应用.控制理论与应用,2001,18(4):559-563
[16]胡家升,潘红华,苏宏业,褚健.预测函数控制系统的闭环性能分析.控制理论与应用,2001,18(5):774-778
[17]Clarke D W,Mohtadi C.Properties of generalized predictive control.Automatica,1989,25(6):859-875
[18]胡品慧,袁璞.状态反馈预测控制干扰解耦的研究.控制与决策,2003,18(2):194-198
[19]孙青林,陈增强,袁著祉.基于频域β-GPC稳定性分析与设计及在中频电源控制中的应用.电工技术学报,2004 6,19(6):23-29
[20]张峻,席裕庚.广义预测控制系统的若干稳定性结果.控制理论与应用,1998,15(1):24-30
[21]Clarke D W,Mohtadi C,Tuffs P S.Generalized Predictive Control,Part 1 and Part 2.Automatica,1987,23(2):137-160
[22]Robinson B D,Clarke D W.Robustness effect of a prefilter in Generalized Predictive Control.IEE Proc-D.,1991,138(1):2-18
[23]张峻,席裕庚.带有噪声滤波器的GPC鲁棒性分析.控制与决策,1997,12(3):260-263
[24]刘兵,徐立鸿,冯纯伯.具有饱和输入的预测控制的稳定性分析.控制理论与应用,1997,14(2):178-183
[25]徐立鸿,冯纯伯.加权多步预报控制——鲁棒性的频率分析.自动化学报,1993,19(6):724-727
[26]席裕庚,耿晓军,陈虹.预测控制性能研究的新进展.控制理论与应用,2000,17(4):469-475
[27]Rossiter J A,Kouraritakis B,Dunnett R M.Application of generalized predictive control to a Boiler turbine unit for electricity generation,IEE Proc.-D.,1991,138(1):59-67
[28]Eduardo F C,Berenguel M.Application of generalized predictive control to a solar power plant.Oxford Vorkshop94,1994:483-490
[29]Tham M T,Vagi F,Morris A J,Wood R K.Multivariable and multirate self-tuning control:a distillon column case study.IEE Proc.-D.,1991,138(1):9-24
[30]陈福祥,金晖.模糊预测控制机理研究.武汉工业大学学报,1997,19(1):48-52
[31]谢克明,马小军.模糊预测控制的实现形式.太原理工大学学报,1999,30(6):575-579
[32]Pu Han,Hong-Jun Liu,Li-Min Meng,Na Wang,Research of grey predictive fuzzy controller for large time delay system,Machine Learning and Cybernetics,2005,proceedings of 2005 International Conference on,2005,2(18-21):829-833
[33]Culal Batur,et al.Predictive fuzzy expert controllers.Computers in Eng.,1991,20(2):199-209
[34]刘欣,尹绍清,削顺达.模糊自适应Smith预估控制器及其应用.控制理论与应用,1993,10(4):399-403
[35]达鹏飞.针对造纸过程大时延的模糊预测控制.第二届华人智能预测控制自动化大会论文集,1997:1794-1798
[36]李常贤,诸静.模糊预测控制与模糊控制技术在水泥工业中的应用.电气自动化,2003,25(2):1-3
[37]李常贤,诸静.双模模糊预测控制在水泥回转窑生料系统中的应用研究.石油化工自动化,2003,No.3:29-32
[38]王立新.自适应模糊系统与控制——设计与稳定性分析.北京:国防工业出版社,1995
[39]Takagi T,Sugeno M.Fuzzy identification of system identification to modeling and control.IEEETrans.On SMC,1985,15(1):116-132
[40]Jang-Hwan Kim.Generalized predictive control using fuzzy neural network model.Proc.of 1994 IEEE Conf.on Neural Network,1994:2596-2598
[41]Doris Saez,Aldo Cipriano.Design of fuzzy model based predictive controllers and its application to an inverted pendulum.IEEE Int.Conf.on Fuzzy Syst.,1997:915-918
[42]Sousa J M.Fuzzy predictive control applied to an air-conditioning system.Control Engineering Practice,1997,5(10):1395-1406
[43]Igor Skrjanc,Drago Matko.Predictive functional control based on fuzzy model for heat-exchanger pilot plant.IFAC 14th Triennial World Cong.,Beijing,P R China,1999:341-345
[44]王寅,荣冈,王树青.基于T-S模糊模型的非线性预测控制策略.控制理论与应用,2002,19(4):599-603
[45]Sousa J M,Setnes M,Kaymak U.Adaptive decision altematives in fuzzy predictive control.The 1998 IEEE Int.Conf.on Computational Intelligence,1998,1:698-703
[46]Sousa J M,et al.Model predictive algorithms based on fuzzy discrete alternatives,IEEE Int.Fuzzy Syst.Conf.Proc.,Seoul,Kores,August 1999:228-233
[47]Kaymak U,et al.A comparative study of fuzzy and conventional criteria in model-based predictive control.Fuzzy-IEEE' 97,Barcelona,Spain,July 1997:907-914
[48]Joao Miguel da Costa Sousa,Uzay Kaymak,Model predictive control using fuzzy decision functions,IEEE Trans.Syst.,Man,Cybern.B,2001,31(1):54-65
[49]Goodrich M A,et al.Model predictive satisfying fuzzy logic control.IEEE Trans.Fuzzy Syst.,1999,7:319-332
[50]Zammarreno J H,Vega P.Neural predictive control:application to a highly nonlinear system.Proc.ACC,Seatle,1995:2250-2256
[51]吴庆洪,张纪会,徐心和.一种有效的进化规划算法.系统仿真学报,1999,11(6):409-411
[52]Shin S C,Park S B.GA-based predictive control for nonlinear processes.Electronics Letters,1st.Oct.1998,34(20):1980-1981
[53]Ramirez D R,et al.Nonlinear MBPC for mobile robot navigation using genetic algorithms.Proc.of IEEE Int.Conf.on Robotics & Automation,Detroit,Michigan,May 1999:2452-2457
[54]Zadeh LA.Fuzzy sets.Information and Control,1965,8:338-353
[55]李少远,王群仙等.Sugeno模糊模型的辨识与控制.自动化学报,1999,25(4),488-492
[56]Chen Zengqiang,Zhao Tianhang,Yuan Zhuzhi.Multivariable PI type generalized predictive control.Journal of Systems Engineering and Electronics,1998,9(2):8-13
[57]徐映富.系统工程计算基础.重庆大学出版社,1994
[58]李为民,黄田.数控铣削过程有约束广义预测控制解析算法.自动化学报,1999,25(6):796-799
[59]李柠,李少远,席裕庚.MISO系统的多模型预测控制.自动化学报,2003,29(4):616-523
[60]金元郁.一种广义预测控制的快速算法.自动化技术与应用,2005,24(3):3-5
[61]杜晓宁,席裕庚,李少远,约束预测控制的一种快速算法[J],上海交通大学学报,2001,35(11):1624-1627
[62]Zhang Xinghui,Chen Zengqiang,Yuan Zhuzhi.Global convergence of adaptive predictive controller based on least squares algorithm.Journal of Systems Engineering and Electronics,2003,14(4):70-73
[2]王伟.一种广义预测自适应控制的直接方法.自动化学报,1996,22(3):270-277
[3]舒迪前,石中锁.隐式自适应广义预测控制及其全局收敛性.自动化学报,1995,21(5):545-554
[4]Clarke D W,Feng R Scattolini.Constrained receding-horizon predictive control.IEE Proc-D,1991,138(4):347-354
[5]Rossiter J A,Louvaritakis B.Constrained stable generalized predictive control.IEE Proc.-U.1993,140(4):243-254
[6]Lelic M A,Zarrop M P.Generalized pole placement self-tuning controller.Int.J.Control,1987,46(2):547-568
[7]顾兴源,毛志忠.一种基于广义预测控制的极点配置自适应控制算法.控制与决策,1992,7(3):221-224
[8]Corradini M L,Orlado G.A VSC algorithm based on generalized predictive control.Automatica,1997,33(5):927-929
[9]王轶,席裕庚.广义预测控制的并行算法.自动化学报,1996,22(1):74-78
[10]张智焕,王树青,荣冈.基于精确线性化的MIMO双线性系统预测函数控制.控制理论与应用,2003,20(3):477-480
[11]王伟.具有Hammerstein形式的非线性系统广义预测控制.控制理论与应用,1994,11(6):672-680
[12]Ping Lu.Nonlinear predictive controllers for continuous systems.Journal of Guid Cont and Dynamias,1995,17(3):553-560
[13]Sahjendra N.Singh,Marc Steinberg,Robert D.Digirolamo.Nonlinear predictive control of feedback linearizable systems and flight control system design.Journal ofGuid Cont and Dynamics,1995,18(5):1023-1028
[14]Badr A,Binder Z,Rey D.Application of tracking multi-model control to a nonlinear thermal process.Int.J.System Science,1990,21(9):1795-1803
[15]张泉灵,王树青.化学反应器温度跟踪预测函数控制的研究与应用.控制理论与应用,2001,18(4):559-563
[16]胡家升,潘红华,苏宏业,褚健.预测函数控制系统的闭环性能分析.控制理论与应用,2001,18(5):774-778
[17]Clarke D W,Mohtadi C.Properties of generalized predictive control.Automatica,1989,25(6):859-875
[18]胡品慧,袁璞.状态反馈预测控制干扰解耦的研究.控制与决策,2003,18(2):194-198
[19]孙青林,陈增强,袁著祉.基于频域β-GPC稳定性分析与设计及在中频电源控制中的应用.电工技术学报,2004 6,19(6):23-29
[20]张峻,席裕庚.广义预测控制系统的若干稳定性结果.控制理论与应用,1998,15(1):24-30
[21]Clarke D W,Mohtadi C,Tuffs P S.Generalized Predictive Control,Part 1 and Part 2.Automatica,1987,23(2):137-160
[22]Robinson B D,Clarke D W.Robustness effect of a prefilter in Generalized Predictive Control.IEE Proc-D.,1991,138(1):2-18
[23]张峻,席裕庚.带有噪声滤波器的GPC鲁棒性分析.控制与决策,1997,12(3):260-263
[24]刘兵,徐立鸿,冯纯伯.具有饱和输入的预测控制的稳定性分析.控制理论与应用,1997,14(2):178-183
[25]徐立鸿,冯纯伯.加权多步预报控制——鲁棒性的频率分析.自动化学报,1993,19(6):724-727
[26]席裕庚,耿晓军,陈虹.预测控制性能研究的新进展.控制理论与应用,2000,17(4):469-475
[27]Rossiter J A,Kouraritakis B,Dunnett R M.Application of generalized predictive control to a Boiler turbine unit for electricity generation,IEE Proc.-D.,1991,138(1):59-67
[28]Eduardo F C,Berenguel M.Application of generalized predictive control to a solar power plant.Oxford Vorkshop94,1994:483-490
[29]Tham M T,Vagi F,Morris A J,Wood R K.Multivariable and multirate self-tuning control:a distillon column case study.IEE Proc.-D.,1991,138(1):9-24
[30]陈福祥,金晖.模糊预测控制机理研究.武汉工业大学学报,1997,19(1):48-52
[31]谢克明,马小军.模糊预测控制的实现形式.太原理工大学学报,1999,30(6):575-579
[32]Pu Han,Hong-Jun Liu,Li-Min Meng,Na Wang,Research of grey predictive fuzzy controller for large time delay system,Machine Learning and Cybernetics,2005,proceedings of 2005 International Conference on,2005,2(18-21):829-833
[33]Culal Batur,et al.Predictive fuzzy expert controllers.Computers in Eng.,1991,20(2):199-209
[34]刘欣,尹绍清,削顺达.模糊自适应Smith预估控制器及其应用.控制理论与应用,1993,10(4):399-403
[35]达鹏飞.针对造纸过程大时延的模糊预测控制.第二届华人智能预测控制自动化大会论文集,1997:1794-1798
[36]李常贤,诸静.模糊预测控制与模糊控制技术在水泥工业中的应用.电气自动化,2003,25(2):1-3
[37]李常贤,诸静.双模模糊预测控制在水泥回转窑生料系统中的应用研究.石油化工自动化,2003,No.3:29-32
[38]王立新.自适应模糊系统与控制——设计与稳定性分析.北京:国防工业出版社,1995
[39]Takagi T,Sugeno M.Fuzzy identification of system identification to modeling and control.IEEETrans.On SMC,1985,15(1):116-132
[40]Jang-Hwan Kim.Generalized predictive control using fuzzy neural network model.Proc.of 1994 IEEE Conf.on Neural Network,1994:2596-2598
[41]Doris Saez,Aldo Cipriano.Design of fuzzy model based predictive controllers and its application to an inverted pendulum.IEEE Int.Conf.on Fuzzy Syst.,1997:915-918
[42]Sousa J M.Fuzzy predictive control applied to an air-conditioning system.Control Engineering Practice,1997,5(10):1395-1406
[43]Igor Skrjanc,Drago Matko.Predictive functional control based on fuzzy model for heat-exchanger pilot plant.IFAC 14th Triennial World Cong.,Beijing,P R China,1999:341-345
[44]王寅,荣冈,王树青.基于T-S模糊模型的非线性预测控制策略.控制理论与应用,2002,19(4):599-603
[45]Sousa J M,Setnes M,Kaymak U.Adaptive decision altematives in fuzzy predictive control.The 1998 IEEE Int.Conf.on Computational Intelligence,1998,1:698-703
[46]Sousa J M,et al.Model predictive algorithms based on fuzzy discrete alternatives,IEEE Int.Fuzzy Syst.Conf.Proc.,Seoul,Kores,August 1999:228-233
[47]Kaymak U,et al.A comparative study of fuzzy and conventional criteria in model-based predictive control.Fuzzy-IEEE' 97,Barcelona,Spain,July 1997:907-914
[48]Joao Miguel da Costa Sousa,Uzay Kaymak,Model predictive control using fuzzy decision functions,IEEE Trans.Syst.,Man,Cybern.B,2001,31(1):54-65
[49]Goodrich M A,et al.Model predictive satisfying fuzzy logic control.IEEE Trans.Fuzzy Syst.,1999,7:319-332
[50]Zammarreno J H,Vega P.Neural predictive control:application to a highly nonlinear system.Proc.ACC,Seatle,1995:2250-2256
[51]吴庆洪,张纪会,徐心和.一种有效的进化规划算法.系统仿真学报,1999,11(6):409-411
[52]Shin S C,Park S B.GA-based predictive control for nonlinear processes.Electronics Letters,1st.Oct.1998,34(20):1980-1981
[53]Ramirez D R,et al.Nonlinear MBPC for mobile robot navigation using genetic algorithms.Proc.of IEEE Int.Conf.on Robotics & Automation,Detroit,Michigan,May 1999:2452-2457
[54]Zadeh LA.Fuzzy sets.Information and Control,1965,8:338-353
[55]李少远,王群仙等.Sugeno模糊模型的辨识与控制.自动化学报,1999,25(4),488-492
[56]Chen Zengqiang,Zhao Tianhang,Yuan Zhuzhi.Multivariable PI type generalized predictive control.Journal of Systems Engineering and Electronics,1998,9(2):8-13
[57]徐映富.系统工程计算基础.重庆大学出版社,1994
[58]李为民,黄田.数控铣削过程有约束广义预测控制解析算法.自动化学报,1999,25(6):796-799
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[60]金元郁.一种广义预测控制的快速算法.自动化技术与应用,2005,24(3):3-5
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