非线性系统的干扰解耦与干扰抑制控制研究
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摘要
非线性控制系统是当今一个热点研究领域,同时控制系统消除或削减外部干扰的影响一直是受学者关注的问题。因此,深入研究非线性系统干扰解耦与抑制问题有着重要的理论意义和应用价值。本文分别基于微分几何理论和模糊双曲正切模型,针对一般非线性系统、时滞非线性系统、参数不确定常时滞和时变时滞非线性系统以及具有混合不确定时滞非线性系统等,对干扰解耦与抑制问题做进一步研究,取得了如下成果。
1.针对一类连续非线性MIMO系统讨论了稳定干扰解耦控制问题,应用非线性微分几何理论,提出了系统关于干扰的向量相对阶,基于相对阶概念给出了静态状态反馈控制器存在的充分必要条件。控制器可确保闭环系统不但是完全干扰解耦的,而且是输入输出解耦和线性化的,对感应电机控制系统进行仿真。
2.针对一类连续非线性时滞MIMO系统讨论了稳定干扰解耦控制问题,应用非线性微分几何理论,分别给出了无记忆和有记忆状态反馈控制器存在的充分必要条件。控制器可确保闭环系统输出不受干扰影响且与时滞无关,同时控制系统也是输入输出解耦和线性化的。
3.针对一类含有参数不确定项的连续多时滞非线性系统提出了鲁棒H∞干扰抑制控制方法,基于模糊双曲正切系统(FHM)给出了非线性系统的FHM建模方法及状态反馈控制器的设计方法,应用新的Lyapunov-Krasovskii泛函和线性矩阵不等式技术,设计了一类鲁棒H∞干扰抑制控制器,该控制器可确保闭环系统是渐近稳定且具有指定的干扰抑制水平。所得结果与已有结果比较有以下优点：该条件是时滞依赖的且考虑了更多系统信息,使得控制器具有更好的控制性能,大大降低了结果的保守性。
4.针对一类含有参数不确定项的连续时变时滞非线性系统,基于FHM模型设计鲁棒H∞干扰抑制控制器。在两种不同的条件下,应用Lyapunov-Krasovskii泛函和线性矩阵不等式技术,得到了一类鲁棒H∞干扰抑制控制器存在时滞依赖的充分条件,控制器保证闭环系统是渐近稳定的且具有指定的干扰抑制水平。
5.讨论了一类同时具有参数和结构不确定的连续时变时滞非线性系统的鲁棒H∞干扰抑制控制器设计问题。假设结构上未知非线性的具有时滞状态摄动是范数有界但增益是未知的,基于FHM模型利用Lyapunov-Krasovskii泛函和线性矩阵不等式技术,得到状态反馈自适应鲁棒控制器存在的充分条件。采用新自适应律和对未知参数估计方法,来消除结构不确定项对控制系统的影响。控制器可保证闭环系统鲁棒渐近稳定且具有指定干扰抑制能力。所得结果更具有普遍性和实际意义。
The nonlinear control systems have attracted more and more attention in the cur-rent research fields.Simultaneously, the problem to avoid or attenuate the influence of external disturbance is also considered by researchers for the control system. Therefore, the further research on disturbance decoupling and attenuation for nonlinear systems is of significance on academic and practical aspects. In this dissertation,based on differ-ential geometry theory and fuzzy hyperbolic model(FHM),the research on disturbance decoupling and attenuation of nonlinear systems is developed and explored, for general nonlinear system,time-delay nonlinear system, parameter uncertain time-delay nonlinear system,and structure uncertain time-delay nonlinear system, etc. The main research work is as follows:
1.The disturbance decoupling control problem is considered for a class of MIMO continuous nonlinear systems. Based on differential geometry theory, the relative degree vector with respect to disturbance is proposed. A nonlinear state feedback control law is constructed,which can ensure that outputs of the closed-loop system are unaffected by disturbances. Sufficient and necessary condition is derived for the existence of such feedback control law.The resulting closed-loop system is also input-output decoupled and linearized.Moreover,the stable condition is discussed briefly. A simulation to a practical system of induction motor is provided to illustrate the effectiveness of the presented method.
2.The disturbance decoupling control problem is considered for a class of time-delay continuous nonlinear systems. Under some assumptions and based on differential geometry theory, sufficient and necessary conditions are proposed for the existence of memorial and memoryless state feedback control law.The controllers can guarantee outputs the resulting closed-loop systems are unaffected by disturbances and independent of time-delays.Moreover, the overall decoupled systems are input-output decoupled and linearized.
3.The robust H∞disturbance attenuation control scheme based on fuzzy hyperbolic model(FHM)is proposed for a class of continuous time nonlinear systems with parametric uncertainties and multiple delays.FHM modeling method for time-delay nonlinear sys-tems is presented.By using a novel Lyapunov-Krasovskii functional and LMI technology, delay-dependent sufficient condition for the existence of a kind of state feedback controller is proposed in terms of linear matrix inequalities(LMIs).The controller can guarantee that the resulting closed-loop system is robustly asymptotically stable with a prescribed H∞performance level for all admissible uncertainties and time-delays.Compared with the existing results of our earlier work, the proposed result has the following advantages: the condition of the existence of controller is delay-dependent and dependent on more system parameter information.It can guarantee the designed controller reaches better performance. So, the conservativeness of result is reduced largely.
4.The robust H∞disturbance attenuation control scheme based on FHM is pro-posed for a class of continuous time nonlinear systems with parametric uncertainties and time-varying delay. By using Lyapunov-Krasovskii approach and LMI technology, delay-dependent sufficient condition for the existence of a kind of state feedback controller is proposed in terms of linear matrix inequalities.The controller can guarantee that the resulting closed-loop system is robustly asymptotically stable with a prescribed H∞performance level for all admissible uncertainties and time-delay. The condition is also dependent on more system parameter information,and the controller is also based on FHM.
5.For a class of continuous time nonlinear systems with parametric and structural uncertainties and time-varying delay, the robust adaptive H∞disturbance attenuation control scheme based on fuzzy hyperbolic model is proposed.it is assumed that nonlinear perturbations in system structure are normObounded and the gains are unknown.Based on FHM and using Lyapunov-Krasovskii approach and LMI technology, delay-dependent sufficient condition for the existence of a kind of state feedback robust adaptive controller is given in terms of linear matrix inequalities.The novel adaptive law and estimation method for unknown parameters are used to eliminate the influence of the structural uncertainties.The presented controller can guarantee resulting closed-loop system robustly asymptotically stable with a prescribed H∞performance level. The result is more all-pervading and significant.
1.针对一类连续非线性MIMO系统讨论了稳定干扰解耦控制问题,应用非线性微分几何理论,提出了系统关于干扰的向量相对阶,基于相对阶概念给出了静态状态反馈控制器存在的充分必要条件。控制器可确保闭环系统不但是完全干扰解耦的,而且是输入输出解耦和线性化的,对感应电机控制系统进行仿真。
2.针对一类连续非线性时滞MIMO系统讨论了稳定干扰解耦控制问题,应用非线性微分几何理论,分别给出了无记忆和有记忆状态反馈控制器存在的充分必要条件。控制器可确保闭环系统输出不受干扰影响且与时滞无关,同时控制系统也是输入输出解耦和线性化的。
3.针对一类含有参数不确定项的连续多时滞非线性系统提出了鲁棒H∞干扰抑制控制方法,基于模糊双曲正切系统(FHM)给出了非线性系统的FHM建模方法及状态反馈控制器的设计方法,应用新的Lyapunov-Krasovskii泛函和线性矩阵不等式技术,设计了一类鲁棒H∞干扰抑制控制器,该控制器可确保闭环系统是渐近稳定且具有指定的干扰抑制水平。所得结果与已有结果比较有以下优点：该条件是时滞依赖的且考虑了更多系统信息,使得控制器具有更好的控制性能,大大降低了结果的保守性。
4.针对一类含有参数不确定项的连续时变时滞非线性系统,基于FHM模型设计鲁棒H∞干扰抑制控制器。在两种不同的条件下,应用Lyapunov-Krasovskii泛函和线性矩阵不等式技术,得到了一类鲁棒H∞干扰抑制控制器存在时滞依赖的充分条件,控制器保证闭环系统是渐近稳定的且具有指定的干扰抑制水平。
5.讨论了一类同时具有参数和结构不确定的连续时变时滞非线性系统的鲁棒H∞干扰抑制控制器设计问题。假设结构上未知非线性的具有时滞状态摄动是范数有界但增益是未知的,基于FHM模型利用Lyapunov-Krasovskii泛函和线性矩阵不等式技术,得到状态反馈自适应鲁棒控制器存在的充分条件。采用新自适应律和对未知参数估计方法,来消除结构不确定项对控制系统的影响。控制器可保证闭环系统鲁棒渐近稳定且具有指定干扰抑制能力。所得结果更具有普遍性和实际意义。
The nonlinear control systems have attracted more and more attention in the cur-rent research fields.Simultaneously, the problem to avoid or attenuate the influence of external disturbance is also considered by researchers for the control system. Therefore, the further research on disturbance decoupling and attenuation for nonlinear systems is of significance on academic and practical aspects. In this dissertation,based on differ-ential geometry theory and fuzzy hyperbolic model(FHM),the research on disturbance decoupling and attenuation of nonlinear systems is developed and explored, for general nonlinear system,time-delay nonlinear system, parameter uncertain time-delay nonlinear system,and structure uncertain time-delay nonlinear system, etc. The main research work is as follows:
1.The disturbance decoupling control problem is considered for a class of MIMO continuous nonlinear systems. Based on differential geometry theory, the relative degree vector with respect to disturbance is proposed. A nonlinear state feedback control law is constructed,which can ensure that outputs of the closed-loop system are unaffected by disturbances. Sufficient and necessary condition is derived for the existence of such feedback control law.The resulting closed-loop system is also input-output decoupled and linearized.Moreover,the stable condition is discussed briefly. A simulation to a practical system of induction motor is provided to illustrate the effectiveness of the presented method.
2.The disturbance decoupling control problem is considered for a class of time-delay continuous nonlinear systems. Under some assumptions and based on differential geometry theory, sufficient and necessary conditions are proposed for the existence of memorial and memoryless state feedback control law.The controllers can guarantee outputs the resulting closed-loop systems are unaffected by disturbances and independent of time-delays.Moreover, the overall decoupled systems are input-output decoupled and linearized.
3.The robust H∞disturbance attenuation control scheme based on fuzzy hyperbolic model(FHM)is proposed for a class of continuous time nonlinear systems with parametric uncertainties and multiple delays.FHM modeling method for time-delay nonlinear sys-tems is presented.By using a novel Lyapunov-Krasovskii functional and LMI technology, delay-dependent sufficient condition for the existence of a kind of state feedback controller is proposed in terms of linear matrix inequalities(LMIs).The controller can guarantee that the resulting closed-loop system is robustly asymptotically stable with a prescribed H∞performance level for all admissible uncertainties and time-delays.Compared with the existing results of our earlier work, the proposed result has the following advantages: the condition of the existence of controller is delay-dependent and dependent on more system parameter information.It can guarantee the designed controller reaches better performance. So, the conservativeness of result is reduced largely.
4.The robust H∞disturbance attenuation control scheme based on FHM is pro-posed for a class of continuous time nonlinear systems with parametric uncertainties and time-varying delay. By using Lyapunov-Krasovskii approach and LMI technology, delay-dependent sufficient condition for the existence of a kind of state feedback controller is proposed in terms of linear matrix inequalities.The controller can guarantee that the resulting closed-loop system is robustly asymptotically stable with a prescribed H∞performance level for all admissible uncertainties and time-delay. The condition is also dependent on more system parameter information,and the controller is also based on FHM.
5.For a class of continuous time nonlinear systems with parametric and structural uncertainties and time-varying delay, the robust adaptive H∞disturbance attenuation control scheme based on fuzzy hyperbolic model is proposed.it is assumed that nonlinear perturbations in system structure are normObounded and the gains are unknown.Based on FHM and using Lyapunov-Krasovskii approach and LMI technology, delay-dependent sufficient condition for the existence of a kind of state feedback robust adaptive controller is given in terms of linear matrix inequalities.The novel adaptive law and estimation method for unknown parameters are used to eliminate the influence of the structural uncertainties.The presented controller can guarantee resulting closed-loop system robustly asymptotically stable with a prescribed H∞performance level. The result is more all-pervading and significant.
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