状态时滞线性参数变化系统控制研究
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摘要
实际的物理系统中存在着不同程度的非线性和时变特性,而线性参数变化系统能够解决非线性和时变问题,成为控制理论界关注的一个热点,其理论已经成功地应用于航空、航天、机器人和工业过程控制等领域。同时,广泛存在于系统中的滞后特性往往会影响系统的稳定性并使系统的性能指标变差,从而使得时滞线性参数变化系统的研究备受关注。本文在总结前人工作的基础上,采用参数线性矩阵不等式方法,系统、深入地研究了状态时滞线性参数变化系统的时滞相关稳定性、镇定、增益调度控制和模型降阶问题。
首先,针对具有时变状态时滞的线性参数变化系统,基于参数依赖Lyapunov-Krasovskii函数,就连续和离散两种情形,分别研究了参数相关和时滞相关稳定性条件,得到了多个稳定性准则。与已有的文献相比,本文得出的结果保守性有明显的降低。
其次,研究了具有时变状态时滞线性参数变化连续时间系统和离散时间系统的状态反馈镇定和H_∞控制问题。在前面得到的稳定性条件的基础上,设计了时滞相关增益调度镇定控制器和H_∞状态反馈增益调度控制器,并将控制器的存在条件转化为一组参数线性矩阵不等式的可行解问题。仿真结果进一步证明了所得到的设计方法具有较低的保守性。
然后,研究了基于状态观测器的输出反馈镇定和H_∞控制问题。针对具有时变时滞的连续系统和离散系统,分别给出了基于状态观测器的时滞相关增益调度控制器和H_∞控制器的设计方法,所设计的H_∞增益调度控制器和观测器能够保证闭环系统渐近稳定且具有期望的性能指标,数值仿真进一步证明了本文所提出方法的可行性与正确性。
最后,研究了状态时滞线性参数变化系统的H_∞模型降阶问题,基于参数依赖Lyapunov稳定思想,用矩阵的全等变换和变量替换方法,提出了状态时滞线性参数变化连续系统和离散系统满足H_∞误差性能要求的低阶模型的构造方法,数值仿真验证了所提出方法是可行的和正确的。
In physical systems,there exist various nonlinear and time-varying characteristics in different degree.And much attention has been paid to the study of linear parameter-varying (LPV) system because it can deal with the nonlinear and time-varying problems and its theory has been applied successfully in many fields such as aircraft,robot manipulators,and chemical process control.On the other hand,time delays,which are common in the number of industrial processes,will be a main source of bad performance or even instability for control systems.Therefore,it is noticed that the control problem of LPV systems with time delays has drawn increasing attention.The thesis,based on previous works of others, systematically and deeply investigates the problems of delay-dependent stability analysis, stabilization,gain-scheduled control and model reduction for LPV systems with state delays in terms of parameterized linear matrix inequalities(PLMIs).
Firstly,based on different parameter-dependent Lyapunov-Krasovskii functions,new parameter-dependent and delay-dependent stability criteria are proposed for LPV systems with a time-varying state delay in both continuous-and discrete-time cases.It shows that the stability conditions proposed in this thesis are much less conservative than the reported results.
Secondly,the problems of state feedback stabilization and H_∞control are addressed for LPV systems with a time-varying state delay in both continuous-and discrete-time cases. Based on the stability conditions obtained in this thesis,sufficient conditions are proposed for designing delay-dependent gain-scheduling stabilization controllers and H_∞state feedback gain-scheduling controllers,upon which can convert the existence condition of admissible controllers into the feasibility of convex problems subject to linear matrix inequalities.The numerical examples show that the proposed approach is less conservative.
Thirdly,the problems of state observer-based output-feedback stabilization and H_∞control are considered for LPV systems with a time-varying state delay in both continuous-and discrete-time systems.The observer-based delay-dependent gain-scheduling controllers and H_∞controller are designed respectively.The H_∞gain-scheduling controller and observer can guarantee that the resulting closed-loop system is asymptotically stable and has an adequate desired H_∞performance level.The efficiency and feasibility of the proposed technique are further demonstrated by numerical examples.
Finally,the problems of H_∞model reduction for time-delayed LPV continuous-and discrete-time systems are presented.Based on the parameter-dependent Lyapunov stability idea,the methods are presented for constructing a reduced-order time-delayed LPV system to approximate a given time-delayed LPV system with guaranteed H_∞error performance using congruence transformations and matrix variable changes.And numerical examples show the feasibility and applicability.
首先,针对具有时变状态时滞的线性参数变化系统,基于参数依赖Lyapunov-Krasovskii函数,就连续和离散两种情形,分别研究了参数相关和时滞相关稳定性条件,得到了多个稳定性准则。与已有的文献相比,本文得出的结果保守性有明显的降低。
其次,研究了具有时变状态时滞线性参数变化连续时间系统和离散时间系统的状态反馈镇定和H_∞控制问题。在前面得到的稳定性条件的基础上,设计了时滞相关增益调度镇定控制器和H_∞状态反馈增益调度控制器,并将控制器的存在条件转化为一组参数线性矩阵不等式的可行解问题。仿真结果进一步证明了所得到的设计方法具有较低的保守性。
然后,研究了基于状态观测器的输出反馈镇定和H_∞控制问题。针对具有时变时滞的连续系统和离散系统,分别给出了基于状态观测器的时滞相关增益调度控制器和H_∞控制器的设计方法,所设计的H_∞增益调度控制器和观测器能够保证闭环系统渐近稳定且具有期望的性能指标,数值仿真进一步证明了本文所提出方法的可行性与正确性。
最后,研究了状态时滞线性参数变化系统的H_∞模型降阶问题,基于参数依赖Lyapunov稳定思想,用矩阵的全等变换和变量替换方法,提出了状态时滞线性参数变化连续系统和离散系统满足H_∞误差性能要求的低阶模型的构造方法,数值仿真验证了所提出方法是可行的和正确的。
In physical systems,there exist various nonlinear and time-varying characteristics in different degree.And much attention has been paid to the study of linear parameter-varying (LPV) system because it can deal with the nonlinear and time-varying problems and its theory has been applied successfully in many fields such as aircraft,robot manipulators,and chemical process control.On the other hand,time delays,which are common in the number of industrial processes,will be a main source of bad performance or even instability for control systems.Therefore,it is noticed that the control problem of LPV systems with time delays has drawn increasing attention.The thesis,based on previous works of others, systematically and deeply investigates the problems of delay-dependent stability analysis, stabilization,gain-scheduled control and model reduction for LPV systems with state delays in terms of parameterized linear matrix inequalities(PLMIs).
Firstly,based on different parameter-dependent Lyapunov-Krasovskii functions,new parameter-dependent and delay-dependent stability criteria are proposed for LPV systems with a time-varying state delay in both continuous-and discrete-time cases.It shows that the stability conditions proposed in this thesis are much less conservative than the reported results.
Secondly,the problems of state feedback stabilization and H_∞control are addressed for LPV systems with a time-varying state delay in both continuous-and discrete-time cases. Based on the stability conditions obtained in this thesis,sufficient conditions are proposed for designing delay-dependent gain-scheduling stabilization controllers and H_∞state feedback gain-scheduling controllers,upon which can convert the existence condition of admissible controllers into the feasibility of convex problems subject to linear matrix inequalities.The numerical examples show that the proposed approach is less conservative.
Thirdly,the problems of state observer-based output-feedback stabilization and H_∞control are considered for LPV systems with a time-varying state delay in both continuous-and discrete-time systems.The observer-based delay-dependent gain-scheduling controllers and H_∞controller are designed respectively.The H_∞gain-scheduling controller and observer can guarantee that the resulting closed-loop system is asymptotically stable and has an adequate desired H_∞performance level.The efficiency and feasibility of the proposed technique are further demonstrated by numerical examples.
Finally,the problems of H_∞model reduction for time-delayed LPV continuous-and discrete-time systems are presented.Based on the parameter-dependent Lyapunov stability idea,the methods are presented for constructing a reduced-order time-delayed LPV system to approximate a given time-delayed LPV system with guaranteed H_∞error performance using congruence transformations and matrix variable changes.And numerical examples show the feasibility and applicability.
引文
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