广义连续系统与广义离散系统的鲁棒控制
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摘要
广义系统由于其深刻的实际背景已引起广泛的关注,许多正常系统的有关结论被相继成功的推广到了广义系统。本文针对当前广义系统理论的研究现状,在深入研究广义系统理论的基础上,系统的研究了广义系统的鲁棒控制理论,提出了一些新的解决问题的办法。本文的主要内容如下:
(一)针对广义连续系统,研究了其鲁棒控制和鲁棒H_∞控制问题。利用了“广义二次稳定”及“广义二次可镇定”的概念,得到了所考虑系统鲁棒镇定的输出反馈控制律;设计了鲁棒H_∞状态反馈控制律,分析表明,对所有容许的不确定性,所设计的鲁棒H_∞状态反馈控制律保证闭环系统正则、无脉冲、稳定且满足一定的H_∞性能指标。
(二)针对广义离散系统,研究了其鲁棒控制和鲁棒H_∞控制问题。利用线性矩阵不等式的方法,得到了该系统鲁棒镇定的状态反馈控制律;设计了鲁棒H_∞状态反馈控制律,分析表明,对所有容许的不确定性,所设计的鲁棒H_∞状态反馈控制律保证闭环系统正则、因果、稳定且满足一定的H_∞性能指标。
(三)应用MATLAB软件,对所研究系统的数学模型进行仿真,通过仿真证明了本文中所得结果的正确性。
During the past years a great deal of interest has been devoted to the study of generalized systems due to their applications in representing and resolving problems concerning many naturally occurring systems. A great number of results and notions in state-space systems have been extended to generalized systems. In the light of recent work in the theory of generalized systems and that of robust control for generalized systems, this dissertation provides a systematic study on the theory of robust control for generalized systems. Some new results of robust control for state-space systems have been extended to generalized systems.
The main contents and results in this dissertation are as follows:
1)The problems of robust control and robust H_∞control for generalized continuous systems are studied. A robust output feedback controller of generalized systems is derived via the notion of generalized quadratic stability and generalized quadratic stabilizability. We also develop a robust state feedback H_∞control design, which guarantees that for all admissible uncertainties the generalized system is stable, regular, impulse-free and satisfying H_∞norm constraint.
2)The problems of robust control and robust H_∞control for generalized discrete systems are studied. A robust state feedback controller is derived via matrix inequalities. We also design a robust state feedback H_∞controllor, which guarantees that for all admissible uncertainties the generalized system is stable, regular, causal and satisfying H_∞norm constraint.
3)Finally,some examples are given to illustrate the design procedures and the simulation results have shown the nice control or observation performance.
(一)针对广义连续系统,研究了其鲁棒控制和鲁棒H_∞控制问题。利用了“广义二次稳定”及“广义二次可镇定”的概念,得到了所考虑系统鲁棒镇定的输出反馈控制律;设计了鲁棒H_∞状态反馈控制律,分析表明,对所有容许的不确定性,所设计的鲁棒H_∞状态反馈控制律保证闭环系统正则、无脉冲、稳定且满足一定的H_∞性能指标。
(二)针对广义离散系统,研究了其鲁棒控制和鲁棒H_∞控制问题。利用线性矩阵不等式的方法,得到了该系统鲁棒镇定的状态反馈控制律;设计了鲁棒H_∞状态反馈控制律,分析表明,对所有容许的不确定性,所设计的鲁棒H_∞状态反馈控制律保证闭环系统正则、因果、稳定且满足一定的H_∞性能指标。
(三)应用MATLAB软件,对所研究系统的数学模型进行仿真,通过仿真证明了本文中所得结果的正确性。
During the past years a great deal of interest has been devoted to the study of generalized systems due to their applications in representing and resolving problems concerning many naturally occurring systems. A great number of results and notions in state-space systems have been extended to generalized systems. In the light of recent work in the theory of generalized systems and that of robust control for generalized systems, this dissertation provides a systematic study on the theory of robust control for generalized systems. Some new results of robust control for state-space systems have been extended to generalized systems.
The main contents and results in this dissertation are as follows:
1)The problems of robust control and robust H_∞control for generalized continuous systems are studied. A robust output feedback controller of generalized systems is derived via the notion of generalized quadratic stability and generalized quadratic stabilizability. We also develop a robust state feedback H_∞control design, which guarantees that for all admissible uncertainties the generalized system is stable, regular, impulse-free and satisfying H_∞norm constraint.
2)The problems of robust control and robust H_∞control for generalized discrete systems are studied. A robust state feedback controller is derived via matrix inequalities. We also design a robust state feedback H_∞controllor, which guarantees that for all admissible uncertainties the generalized system is stable, regular, causal and satisfying H_∞norm constraint.
3)Finally,some examples are given to illustrate the design procedures and the simulation results have shown the nice control or observation performance.
引文
[1] S. L. Campbell ,Singular systems of differential equations , London , Pitman, 1982.
[2] H. H. Rosenbrock, Sructure properties of linear dynamial systems , int. J of Contr,1974,20(2):191-202
[3] D. G. Luenberger, Singular dynamical leontief systems,Econometrica, 1977,45(4):991-995
[4] 赵新良,动态投入产出模型,辽宁人民出版社,1991
[5] 张金水,广义系统经济控制论,清华大学出版社,1990
[6] Lewis,F. L. ,A tutorial on the geometric analysis of linear time-invariant implicit systems.Automatica,1992,28(1):119-137
[7] Cobb , J. D. ,Fundamental properties of the manifold of singular and regular linear systems. J. Math.Anal.Appl.,1986,120:328-353
[8] Newcomb R W. The semistate description of nonlinear time variable circuits ,IEEE Trans Circuits and Systems ,1981,CAS-28(1):62-71
[9] 张庆灵,广义大系统的分散控制与鲁棒控制,西安:西北工业大学出版社,1997
[10] Dai L, singular control systems,Springer,Berlin,1989
[11] R. W. Newcomb and B. Dziurla, Some ccircuit and systems applications of semistate theory, Circuits Syst. Signal Process,vol.8,pp.235-260,1989
[12] 张庆灵,杨冬梅,不确定广义系统的分析与综合,沈阳,东北大学出版社,2003
[13] 梅生伟,现代鲁棒控制理论与应用,北京,清华大学出版社,2003
[14] Black H S, Stabilized feedback amplifiers,U.S ,Patent No.2,102,671,1927
[15] Davison E J , The output control of linear time invariant multivariable systems with unmeasurable arbitrary disturbances,IEEE Transaction on Automatic Control,AC-17:621-630,1971
[16] Pearson J B,Staats P W Jr,Robust controllers for linear regulators,IEEE Transaction on Automatic Control,AC-19:231-234,1974
[17] Mertzios , B. G. , On the sensitivity analysis of linear time-invariant singular systems , IEEE Trans , Circuits and Systems,1984,31:978-982
[18] Nichols,N. K. ,Robust control system design for generalized state-space system.Proc.of 25th IEEE CDC,1986,538-540
[19] Syrmos,V.L. and Lews,F.L.,Robust eigenvalue assignment in generalized systems.Proc.of 30th IEEE CDC,1991,1433-1434
[20] Fang,c. and Chang. F., Analysis of stability robustness for generalized state-space systems with structured perturbations. Syst. Contr. Lett, 1993, 21(2):109-114
[21] Lin,J.L and Chen,S. J .,Robust stabiliy analysis of generalized interval systems using a structured singular value. Int. J. Syst. Sci., 1998, 29 (2): 199-206
[22] 王朝珠,戴立意,贾新春,一类广义不确定线性系统的稳定控制,控制理论与应用,1990,7(2):18-25
[23] Su. Q.and Synnos,V. L.,Robust stabilization of singular systems with H ∞-bounded uncertainty - Circ.Syst.Sig.Process , 1998 ,17(6):737-755
[24] 温香彩,刘永清,广义不确定线性系统的稳定化控制器设计。自动化学报,1996,22(3):263-269
[25] 高志伟,李光泉,郑丕谔,带前馈的广义分散控制系统固定模,天津大学学报, vol.26, no.2, pp.21-29, 1993.
[26] 高志伟,王先来,李光泉,互质因子摄动系统的敏感性分析,系统工程理论与实践,vol.17, no.12, pp.34-38, 1997.
[27] Zhiwei Gao, Analysis for performance sensitivity of systems with structured uncertainty,'' Control & Intelligent Systems, vol.26, no.3, pp.73-76, ACTA Press, 1998.
[28] 高志伟,王先来,李光泉, 真镇定广义系统分散正常动态补偿器的设计, 系统工程理论与实践, vol.19, no.1, pp.1-8, 1999.
[29] 高志伟, 广义系统降阶正常观测--控制器与双互质分解, 自动化学报,vol.26, no.1, pp. 24-31, 2000.
[30] 高志伟,王先来, 结构不确定性系统的敏感性分析, 自动化学报, vol.26, no.3, pp. 360-364, 2000.
[31] Zhiwei Gao, and F. Y. Wang, New results on doubly coprime fractional representations of generalized dynamical systems, IEEE Transactions on Automatic Control, vol.48, no.2, pp.299-303, 2003
[32] Zhiwei Gao. and Ho, D. W. C., Proportional multiple-integral observer design for descriptor systems with measurement output disturbances, IEE Proc. - Control Theory Appl., vol.151, no.3, pp.279-288, 2004.
[33] Zhiwei Gao and Ho, D. W. C., State/noise estimator for descriptor systems with application to sensor fault diagnosis,'' IEEE Transactions on Signal Processing, regular paper, vol.54, no.4, pp. 1316-1326, 2006.
[34] Zhiwei Gao and H. Wang, Descriptor observer approaches for multivariable systems with measurement noise and application in fault detection and diagnosis, Systems and Control Letters,vol.55, no.4, pp.304-313, 2006.
[35] Fang. C., Lee. L.and Chang.F.,Robust control analysis and design for discrete-time singular systems,Automatica,1994,30(11):1741-1750
[36] 张庆灵,徐心和,离散广义系统稳定性分析与控制的 Lyapunov 方法,自动化学报,1998,vol.24,No.5:622-629
[37] Chen,S. J,Lin. J. L ,Robust Stability analysis of uncertain singular systems,Proc of SICE Annual Conference,Tokushima,1997
[38] 徐胜元,杨成梧,离散广义系统的鲁棒稳定性,自动化学报,2001,27(1):89-92.
[39] Zhang. G. M,Jia Y.M New results on discrete-time bounder real lemma for singular systems :strict matrix inequality conditions,Proc of ACC, Anchorage, 2002
[40] Lin J.L.,Chen S.J.,Robustness analysis of uncertain linear singular systems with output feedback control ,IEEE Transactions on Automatic Control , 1999,vol.44,No.10:1924-1929
[41] 姚波、王福忠,离散广义系统的渐进稳定性分析与控制,东北大学学报,2002,vol.23,No.4:315-317
[42] 谢湘生,胡刚,带有外干扰的离散广义系统鲁棒 H ∞控制器的设计,控制理论与应用,2002,vol.19,No.6:937-939]
[43] Masubuchi I,Kamitane Y,Ohara A and Suda N. H ∞control for descriptor systems:A matrix inequalities approach, Automatica, 1997, 33(4): 669-673
[44] 杨战民,广义系统的控制问题,[硕士学位论文],西北轻工业学院,2002
[45] 胡刚,参数不确定广义系统的鲁棒 H ∞控制,同济大学学报, 2003,31(3):334-338
[46] 戴立意,离散广义系统的求解和能控、能观性,数学物理学报,1989,9(2):129-138.
[47] 胡刚,孙继涛,时变广义系统稳定性分析,同济大学学报,2003,31(4):481-485
[48] 徐胜元,齐延信,杨成梧,结构不确定性广义系统的鲁棒控制,南京理工大学学报,1999,23(4):349-352。
[49] 吴健荣,广义系统族的二次稳定与二次镇定,物理学报,2004,53(2):325-330
[50] Xu S Y,Yang C W. An algebraic approach to the robust stability analysis and robust stabilization of uncertain singular systems ,Int J Systems Science,2000,31(1):55-61
[51] Khargonekar,P.P.,Petersen,I.R.,and Zhou,K.Robust stabilization of uncertain linear systems:quadratic stabilizability and H ∞ control theory.IEEE Trans.Automat Contr.,1990,35(3):356-361.
[52] Petersen I R.A stabilization algorithm for a class of uncertainlinear systems,Syst Contr Lett,1987,7(8):351-357.
[53] Khargonckar P P,Petersen L R,Zhou K. Robust stabilization of uncertain linear systems:quadratic stabilization of uncertain linear systems:quadratic stabilization and H ∞ control theory , IEEE Trans Automat Contr,1990,35(3):356-361.
[54] 李秀英,刑伟,不确定广义系统的鲁棒 H ∞控制 ,哈尔滨师范大学学报自然科学版,2003,19(5):7-9.
[55] 胡刚,孙继涛,参数不确定广义系统的鲁棒 H ∞控制 , 同济大学学报,2003,31(3):334-338.
[56] 徐胜元,杨成梧, 广义不确定系统鲁棒稳定性及鲁棒镇定的矩阵不等式方法,自动化学报,2000,26(3):132-135
[57] 徐胜元,牛玉刚,杨成梧,不确定离散广义系统的鲁棒 H ∞控制,自动化学报,2000,26(5):656-659.
[58] Fu,M. and Barmish,B,R. , Maximal unidirectional perturbation bounds for stability of polynominals and matrices.Syst.Contr.Lett.1988,11:173-179.
[59] Lancaster,P and Tismenetsky,M.,The theory of matrices,2nd edition,Academic Press,NY,1985.
[60] Xu S Y,Yang C W. Stabilization of discrete time singula systems: a matrix inequalities approach,Automatica 1999,35(9):1613-1617.
[61] Liqian Zhang and Biao Huang, LMI Synthesis of H 2 and Mixed H 2 /H∞ Controllers for Singular Systems, IEEE Transactions on Circuits and Systems, Part 2, vol. 50, No.9, 2003
[2] H. H. Rosenbrock, Sructure properties of linear dynamial systems , int. J of Contr,1974,20(2):191-202
[3] D. G. Luenberger, Singular dynamical leontief systems,Econometrica, 1977,45(4):991-995
[4] 赵新良,动态投入产出模型,辽宁人民出版社,1991
[5] 张金水,广义系统经济控制论,清华大学出版社,1990
[6] Lewis,F. L. ,A tutorial on the geometric analysis of linear time-invariant implicit systems.Automatica,1992,28(1):119-137
[7] Cobb , J. D. ,Fundamental properties of the manifold of singular and regular linear systems. J. Math.Anal.Appl.,1986,120:328-353
[8] Newcomb R W. The semistate description of nonlinear time variable circuits ,IEEE Trans Circuits and Systems ,1981,CAS-28(1):62-71
[9] 张庆灵,广义大系统的分散控制与鲁棒控制,西安:西北工业大学出版社,1997
[10] Dai L, singular control systems,Springer,Berlin,1989
[11] R. W. Newcomb and B. Dziurla, Some ccircuit and systems applications of semistate theory, Circuits Syst. Signal Process,vol.8,pp.235-260,1989
[12] 张庆灵,杨冬梅,不确定广义系统的分析与综合,沈阳,东北大学出版社,2003
[13] 梅生伟,现代鲁棒控制理论与应用,北京,清华大学出版社,2003
[14] Black H S, Stabilized feedback amplifiers,U.S ,Patent No.2,102,671,1927
[15] Davison E J , The output control of linear time invariant multivariable systems with unmeasurable arbitrary disturbances,IEEE Transaction on Automatic Control,AC-17:621-630,1971
[16] Pearson J B,Staats P W Jr,Robust controllers for linear regulators,IEEE Transaction on Automatic Control,AC-19:231-234,1974
[17] Mertzios , B. G. , On the sensitivity analysis of linear time-invariant singular systems , IEEE Trans , Circuits and Systems,1984,31:978-982
[18] Nichols,N. K. ,Robust control system design for generalized state-space system.Proc.of 25th IEEE CDC,1986,538-540
[19] Syrmos,V.L. and Lews,F.L.,Robust eigenvalue assignment in generalized systems.Proc.of 30th IEEE CDC,1991,1433-1434
[20] Fang,c. and Chang. F., Analysis of stability robustness for generalized state-space systems with structured perturbations. Syst. Contr. Lett, 1993, 21(2):109-114
[21] Lin,J.L and Chen,S. J .,Robust stabiliy analysis of generalized interval systems using a structured singular value. Int. J. Syst. Sci., 1998, 29 (2): 199-206
[22] 王朝珠,戴立意,贾新春,一类广义不确定线性系统的稳定控制,控制理论与应用,1990,7(2):18-25
[23] Su. Q.and Synnos,V. L.,Robust stabilization of singular systems with H ∞-bounded uncertainty - Circ.Syst.Sig.Process , 1998 ,17(6):737-755
[24] 温香彩,刘永清,广义不确定线性系统的稳定化控制器设计。自动化学报,1996,22(3):263-269
[25] 高志伟,李光泉,郑丕谔,带前馈的广义分散控制系统固定模,天津大学学报, vol.26, no.2, pp.21-29, 1993.
[26] 高志伟,王先来,李光泉,互质因子摄动系统的敏感性分析,系统工程理论与实践,vol.17, no.12, pp.34-38, 1997.
[27] Zhiwei Gao, Analysis for performance sensitivity of systems with structured uncertainty,'' Control & Intelligent Systems, vol.26, no.3, pp.73-76, ACTA Press, 1998.
[28] 高志伟,王先来,李光泉, 真镇定广义系统分散正常动态补偿器的设计, 系统工程理论与实践, vol.19, no.1, pp.1-8, 1999.
[29] 高志伟, 广义系统降阶正常观测--控制器与双互质分解, 自动化学报,vol.26, no.1, pp. 24-31, 2000.
[30] 高志伟,王先来, 结构不确定性系统的敏感性分析, 自动化学报, vol.26, no.3, pp. 360-364, 2000.
[31] Zhiwei Gao, and F. Y. Wang, New results on doubly coprime fractional representations of generalized dynamical systems, IEEE Transactions on Automatic Control, vol.48, no.2, pp.299-303, 2003
[32] Zhiwei Gao. and Ho, D. W. C., Proportional multiple-integral observer design for descriptor systems with measurement output disturbances, IEE Proc. - Control Theory Appl., vol.151, no.3, pp.279-288, 2004.
[33] Zhiwei Gao and Ho, D. W. C., State/noise estimator for descriptor systems with application to sensor fault diagnosis,'' IEEE Transactions on Signal Processing, regular paper, vol.54, no.4, pp. 1316-1326, 2006.
[34] Zhiwei Gao and H. Wang, Descriptor observer approaches for multivariable systems with measurement noise and application in fault detection and diagnosis, Systems and Control Letters,vol.55, no.4, pp.304-313, 2006.
[35] Fang. C., Lee. L.and Chang.F.,Robust control analysis and design for discrete-time singular systems,Automatica,1994,30(11):1741-1750
[36] 张庆灵,徐心和,离散广义系统稳定性分析与控制的 Lyapunov 方法,自动化学报,1998,vol.24,No.5:622-629
[37] Chen,S. J,Lin. J. L ,Robust Stability analysis of uncertain singular systems,Proc of SICE Annual Conference,Tokushima,1997
[38] 徐胜元,杨成梧,离散广义系统的鲁棒稳定性,自动化学报,2001,27(1):89-92.
[39] Zhang. G. M,Jia Y.M New results on discrete-time bounder real lemma for singular systems :strict matrix inequality conditions,Proc of ACC, Anchorage, 2002
[40] Lin J.L.,Chen S.J.,Robustness analysis of uncertain linear singular systems with output feedback control ,IEEE Transactions on Automatic Control , 1999,vol.44,No.10:1924-1929
[41] 姚波、王福忠,离散广义系统的渐进稳定性分析与控制,东北大学学报,2002,vol.23,No.4:315-317
[42] 谢湘生,胡刚,带有外干扰的离散广义系统鲁棒 H ∞控制器的设计,控制理论与应用,2002,vol.19,No.6:937-939]
[43] Masubuchi I,Kamitane Y,Ohara A and Suda N. H ∞control for descriptor systems:A matrix inequalities approach, Automatica, 1997, 33(4): 669-673
[44] 杨战民,广义系统的控制问题,[硕士学位论文],西北轻工业学院,2002
[45] 胡刚,参数不确定广义系统的鲁棒 H ∞控制,同济大学学报, 2003,31(3):334-338
[46] 戴立意,离散广义系统的求解和能控、能观性,数学物理学报,1989,9(2):129-138.
[47] 胡刚,孙继涛,时变广义系统稳定性分析,同济大学学报,2003,31(4):481-485
[48] 徐胜元,齐延信,杨成梧,结构不确定性广义系统的鲁棒控制,南京理工大学学报,1999,23(4):349-352。
[49] 吴健荣,广义系统族的二次稳定与二次镇定,物理学报,2004,53(2):325-330
[50] Xu S Y,Yang C W. An algebraic approach to the robust stability analysis and robust stabilization of uncertain singular systems ,Int J Systems Science,2000,31(1):55-61
[51] Khargonekar,P.P.,Petersen,I.R.,and Zhou,K.Robust stabilization of uncertain linear systems:quadratic stabilizability and H ∞ control theory.IEEE Trans.Automat Contr.,1990,35(3):356-361.
[52] Petersen I R.A stabilization algorithm for a class of uncertainlinear systems,Syst Contr Lett,1987,7(8):351-357.
[53] Khargonckar P P,Petersen L R,Zhou K. Robust stabilization of uncertain linear systems:quadratic stabilization of uncertain linear systems:quadratic stabilization and H ∞ control theory , IEEE Trans Automat Contr,1990,35(3):356-361.
[54] 李秀英,刑伟,不确定广义系统的鲁棒 H ∞控制 ,哈尔滨师范大学学报自然科学版,2003,19(5):7-9.
[55] 胡刚,孙继涛,参数不确定广义系统的鲁棒 H ∞控制 , 同济大学学报,2003,31(3):334-338.
[56] 徐胜元,杨成梧, 广义不确定系统鲁棒稳定性及鲁棒镇定的矩阵不等式方法,自动化学报,2000,26(3):132-135
[57] 徐胜元,牛玉刚,杨成梧,不确定离散广义系统的鲁棒 H ∞控制,自动化学报,2000,26(5):656-659.
[58] Fu,M. and Barmish,B,R. , Maximal unidirectional perturbation bounds for stability of polynominals and matrices.Syst.Contr.Lett.1988,11:173-179.
[59] Lancaster,P and Tismenetsky,M.,The theory of matrices,2nd edition,Academic Press,NY,1985.
[60] Xu S Y,Yang C W. Stabilization of discrete time singula systems: a matrix inequalities approach,Automatica 1999,35(9):1613-1617.
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