时滞离散不确定系统的滑模控制研究
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摘要
随着计算机技术的飞速发展，离散控制系统的分析与设计已经成为控制理论的一个重要组成部分。另外，在航空航天、过程控制、网络控制系统中，由于信号传输及计算时间延迟，时滞现象普遍存在。时滞的存在严重降低了系统的性能，甚至使系统不稳定。另一方面，实际的控制系统通常都会受到各种外部扰动的影响，这些扰动不仅能使系统的工作点发生漂移，还会使系统的动态和稳态特性变坏，甚至使系统失稳，导致控制失败。因此，在具有时滞的离散不确定系统中，如何设计控制器消除或减小扰动对系统的影响，无论在理论上还是在实践中，都是很有意义的研究课题。
滑模控制由于算法简单、响应快速、鲁棒性好、易于工程实现等优点，近年来受到了控制界的广泛重视。本文以滑模控制理论为基础，结合多输出反馈技术、鲁棒控制、自适应控制、Lyapunov稳定性理论等，针对时滞离散不确定系统，给出了高性能镇定控制器和跟踪控制器的设计方法。本文的研究内容概括如下：
在前言中，回顾了变结构控制理论的发展，详细介绍了国内外关于连续系统的滑模变结构控制、不确定时滞系统的滑模变结构控制以及离散系统的滑模变结构控制理论的研究概况与现状，给出了本文的研究内容和研究意义。
第二章研究了利用变速趋近律实现离散系统的滑模控制问题。首先，对于无时滞的离散系统，构造了一种离散变速趋近律，证明了利用此趋近律设计的变结构控制器具有趋近速度快、抖振小的优良品质，并且证明了系统具有常值的滑模带以及系统运动最终趋于原点的性质；其次，对于有时滞的离散系统，利用极点配置法，给出了时滞离散变结构控制系统的滑模面方程，保证了系统滑模运动的渐近稳定性；并利用改进的离散趋近律给出了时滞离散变结构控制律以及系统滑模带的具体数学表达式。最后通过仿真实例，验证了本文提出的变结构控制器的设计方法能保证滑模最终趋于原点，且具有趋近速度快、抖动小的优良品质。
在第三章中，对于含有外部扰动的状态时滞系统，根据已知外部扰动条件的不同，设计了三种不同的控制策略用以消除或减弱扰动对系统的影响。一是对于外部扰动上、下界已知的时滞离散不确定系统，构造了一种新的近似变结构控制策略，证明了在此变结构控制器的控制下，系统具有准滑模带的存在性、有限可达性和趋近运动的全局稳定性。二是对于外部扰动变化率有界的时滞离散不确定系统，设计了新的对控制律实施在线补偿的扰动动态补偿器，解决了系统的不确定性问题。三是基于多输出反馈技术，结合趋近律方法，设计了能够物理实现的控制律，并证明了对于含有外部扰动的状态时滞系统此控制方法是有效的。最后，通过相同的仿真实例与其它控制策略进行了比较，体现了本文所提控制方法的优越性。
第四章研究了利用模型参考自适应滑模控制算法实现具有未知外部扰动的状态时滞系统的模型跟踪问题。本章提出了一种模型参考自适应滑模控制算法，通过构造离散的Lvapunov函数，证明了系统在所给控制的作用下具有渐近稳定性。另外，对于带有时滞关联项的离散大系统，本章提出了一种分散模型跟踪自适应滑摸控制算法，证明了误差系统在所给控制的作用下，系统的输出函数在准滑模带内步步穿越滑模面、跟踪误差最终趋于原点以及误差系统的趋近滑模带的运动是渐近稳定的等性质。最后给出了仿真实例，验证了所提方法的可行性。
在第五章中，研究了离散混沌系统的状态同步问题。首先，利用广义系统的概念给出了系数矩阵为能控标准型的滑模面方程，并利用极点配置定理给出了能使系统稳定的滑模面；其次，构造了含有自适应律的离散趋近律，设计了能够使系统达到同步的变结构控制器，并利用Lyapunov稳定性定理，证明了系统的趋近运动的稳定性。最后，通过对Duffing-Holmes系统的同步仿真，验证了该方法的可行性。另外，通过利用Terminal滑模控制技术设计了离散Terminal滑模控制器，构造了自适应趋近律，实现了离散系统的混沌同步；同时证明了误差系统在所给控制的作用下新设计的滑模面即为Terminal滑模面，并且系统运动具有步步穿越滑模面的性质。最后通过仿真说明了本章所提方法的有效性。
第六章在总结全文主要工作的基础上，对时滞离散不确定系统的滑模控制研究进行了展望。
With the development of computer techniques, the stability analysis and control algorithm design of discrete systems are important research subjects in control theory. Moreover, in aeronautics and astronautics, process control, and networked control systems, due to the delay in signal transmission and computation time, time delays are commonly encountered. The presence of time delays could seriously degrade performances of the control system, or even drives the system to instability. On the other hand, practical control systems are frequently subjected to various external disturbances. These disturbances can not only lead to working-position shift, but worsen the dynamic and stable characteristics of the system, or even destabilize the system and result in control failure. So it is of great significance to cancel or attenuate the effect of exogenous disturbances, both in theory and practice.
In recent years, sliding mode control receives wide attention because of its simplicity, quick response, robustness and easy realization. In this dissertation, the effective sliding mode controllers and trackers are designed based on sliding mode control theory, robust control, adaptive control and Lvapunov stable theory for discrete uncertain systems with time-delays. The contents of this dissertation are arranged as follows:
In the preface, an overview of the sliding mode control theory is given, and the relative studies on the methods of sliding mode control for continues systems, for the uncertain systems with time-delay and for discrete-time systems and their relevant control problems are reviewed. The research subject and significance of this dissertation are also shown.
Chapter 2 deals with the problem of how the discrete system is controlled effectively by using a variable rate reaching law. First, the dissertation constructs a new discrete variable rate reaching law based on the exponential reaching for discrete system without time-delay, and it is proved that the system with new controller designed by using this new reaching law not only can decrease system chattering and hold fast reaching speed, but also can fast approach to zero at last. Then, a discrete sliding mode surface is designed for discrete system with time-delay by using pole deployment method, and a new sliding mode controller is designed by using the new reaching law and the system is controlled stably. At last, an example is studied and its simulation results illustrate that the system not only can decrease chattering and have fast reaching speed, but also can quickly approach to zero by using the proposed scheme.
In chapter 3, three different methods to decrease or cancel the system chattering are proposed for uncertain discrete system with time-delay with different external disturbances. First, a discrete approximate sliding mode control method is adopted for the system with known boundary of external disturbances, and it is proved that the system can arrive the sliding mode layer in finite steps and the approaching movement is stable. Secondly, a novel discrete reaching law with dynamic disturbance compensator is presented for a class of uncertain systems with limited bounded in varying rate of external disturbance boundary, and the problem that the controller containing unrecognized states couldn't be actualized is solved. At last, a control law that can be actualized in physics based is designed based on multi-output feedback technique and the reaching law method, and it is proved that the controller can control the uncertain discrete system with time-delay effectively. The simulation results illustrate the proposed algorithms are more effective than the conventional methods.
The chapter 4 considers the problem how to design a model tracker by using model reference adaptive sliding mode control algorithm for uncertain system with time-delay. A novel model reference adaptive sliding mode control algorithm is presented, and the system can track the model reference system effectively by using the new controller where the boundary of external disturbance can not be known as usually. In addition, a decentralized model reference adaptive variable structure control algorithm for a class of perturbed large-scale discrete systems with varying time-delay interconnections is investigated, and a discrete robust adaptive quasi-sliding-mode tracking controller is presented. It is proved that by using the adaptive controller the output error decreases to zero and the trajectories of each subsystem traverse the sliding hyperplane in each step, and the globally asymptotically stability of the system is also proved based on the Lyapunov-Razumikhin stability theorem. Finally, an example is presented and its simulation results illustrate the efficiency of the proposed approach.
The chapter 5 considers the chaos synchrony problem for a class of discrete uncertain systems with time-delays. First, a switching function is designed to guarantee that the movement of the system is asymptotically stable in the switching manifold. And the equation of the switching surface is given based on pole assignment theorem; Then a discrete robust adaptive quasi-sliding-mode tracking controller is presented by constructing the two adaptive gains, and the globally asymptotically stability of the system is proved based on the Lyapunov-Razumikhin stability theorem. At last, the simulation examples illustrate that this algorithm is effective and robust with respect to some exogenous disturbances for Duffing-Holmes system. In addition, a discrete terminal sliding mode controller is proposed by applying terminal sliding mode control technique and selecting adaptive reaching law, and the chaos synchrony problem can be solved effectively by using this method. At the same time, it is proved that the designed sliding surface is a terminal sliding surface and the movement of the system controlled by given controller can traverse the sliding surface in each step. At last, an example is presented and its simulation results illustrate the efficiency of the proposed approach.
The last chapter summarizes the research work of this dissertation and gives an outlook on sliding mode control method for discrete uncertain system with time-delay.
滑模控制由于算法简单、响应快速、鲁棒性好、易于工程实现等优点，近年来受到了控制界的广泛重视。本文以滑模控制理论为基础，结合多输出反馈技术、鲁棒控制、自适应控制、Lyapunov稳定性理论等，针对时滞离散不确定系统，给出了高性能镇定控制器和跟踪控制器的设计方法。本文的研究内容概括如下：
在前言中，回顾了变结构控制理论的发展，详细介绍了国内外关于连续系统的滑模变结构控制、不确定时滞系统的滑模变结构控制以及离散系统的滑模变结构控制理论的研究概况与现状，给出了本文的研究内容和研究意义。
第二章研究了利用变速趋近律实现离散系统的滑模控制问题。首先，对于无时滞的离散系统，构造了一种离散变速趋近律，证明了利用此趋近律设计的变结构控制器具有趋近速度快、抖振小的优良品质，并且证明了系统具有常值的滑模带以及系统运动最终趋于原点的性质；其次，对于有时滞的离散系统，利用极点配置法，给出了时滞离散变结构控制系统的滑模面方程，保证了系统滑模运动的渐近稳定性；并利用改进的离散趋近律给出了时滞离散变结构控制律以及系统滑模带的具体数学表达式。最后通过仿真实例，验证了本文提出的变结构控制器的设计方法能保证滑模最终趋于原点，且具有趋近速度快、抖动小的优良品质。
在第三章中，对于含有外部扰动的状态时滞系统，根据已知外部扰动条件的不同，设计了三种不同的控制策略用以消除或减弱扰动对系统的影响。一是对于外部扰动上、下界已知的时滞离散不确定系统，构造了一种新的近似变结构控制策略，证明了在此变结构控制器的控制下，系统具有准滑模带的存在性、有限可达性和趋近运动的全局稳定性。二是对于外部扰动变化率有界的时滞离散不确定系统，设计了新的对控制律实施在线补偿的扰动动态补偿器，解决了系统的不确定性问题。三是基于多输出反馈技术，结合趋近律方法，设计了能够物理实现的控制律，并证明了对于含有外部扰动的状态时滞系统此控制方法是有效的。最后，通过相同的仿真实例与其它控制策略进行了比较，体现了本文所提控制方法的优越性。
第四章研究了利用模型参考自适应滑模控制算法实现具有未知外部扰动的状态时滞系统的模型跟踪问题。本章提出了一种模型参考自适应滑模控制算法，通过构造离散的Lvapunov函数，证明了系统在所给控制的作用下具有渐近稳定性。另外，对于带有时滞关联项的离散大系统，本章提出了一种分散模型跟踪自适应滑摸控制算法，证明了误差系统在所给控制的作用下，系统的输出函数在准滑模带内步步穿越滑模面、跟踪误差最终趋于原点以及误差系统的趋近滑模带的运动是渐近稳定的等性质。最后给出了仿真实例，验证了所提方法的可行性。
在第五章中，研究了离散混沌系统的状态同步问题。首先，利用广义系统的概念给出了系数矩阵为能控标准型的滑模面方程，并利用极点配置定理给出了能使系统稳定的滑模面；其次，构造了含有自适应律的离散趋近律，设计了能够使系统达到同步的变结构控制器，并利用Lyapunov稳定性定理，证明了系统的趋近运动的稳定性。最后，通过对Duffing-Holmes系统的同步仿真，验证了该方法的可行性。另外，通过利用Terminal滑模控制技术设计了离散Terminal滑模控制器，构造了自适应趋近律，实现了离散系统的混沌同步；同时证明了误差系统在所给控制的作用下新设计的滑模面即为Terminal滑模面，并且系统运动具有步步穿越滑模面的性质。最后通过仿真说明了本章所提方法的有效性。
第六章在总结全文主要工作的基础上，对时滞离散不确定系统的滑模控制研究进行了展望。
With the development of computer techniques, the stability analysis and control algorithm design of discrete systems are important research subjects in control theory. Moreover, in aeronautics and astronautics, process control, and networked control systems, due to the delay in signal transmission and computation time, time delays are commonly encountered. The presence of time delays could seriously degrade performances of the control system, or even drives the system to instability. On the other hand, practical control systems are frequently subjected to various external disturbances. These disturbances can not only lead to working-position shift, but worsen the dynamic and stable characteristics of the system, or even destabilize the system and result in control failure. So it is of great significance to cancel or attenuate the effect of exogenous disturbances, both in theory and practice.
In recent years, sliding mode control receives wide attention because of its simplicity, quick response, robustness and easy realization. In this dissertation, the effective sliding mode controllers and trackers are designed based on sliding mode control theory, robust control, adaptive control and Lvapunov stable theory for discrete uncertain systems with time-delays. The contents of this dissertation are arranged as follows:
In the preface, an overview of the sliding mode control theory is given, and the relative studies on the methods of sliding mode control for continues systems, for the uncertain systems with time-delay and for discrete-time systems and their relevant control problems are reviewed. The research subject and significance of this dissertation are also shown.
Chapter 2 deals with the problem of how the discrete system is controlled effectively by using a variable rate reaching law. First, the dissertation constructs a new discrete variable rate reaching law based on the exponential reaching for discrete system without time-delay, and it is proved that the system with new controller designed by using this new reaching law not only can decrease system chattering and hold fast reaching speed, but also can fast approach to zero at last. Then, a discrete sliding mode surface is designed for discrete system with time-delay by using pole deployment method, and a new sliding mode controller is designed by using the new reaching law and the system is controlled stably. At last, an example is studied and its simulation results illustrate that the system not only can decrease chattering and have fast reaching speed, but also can quickly approach to zero by using the proposed scheme.
In chapter 3, three different methods to decrease or cancel the system chattering are proposed for uncertain discrete system with time-delay with different external disturbances. First, a discrete approximate sliding mode control method is adopted for the system with known boundary of external disturbances, and it is proved that the system can arrive the sliding mode layer in finite steps and the approaching movement is stable. Secondly, a novel discrete reaching law with dynamic disturbance compensator is presented for a class of uncertain systems with limited bounded in varying rate of external disturbance boundary, and the problem that the controller containing unrecognized states couldn't be actualized is solved. At last, a control law that can be actualized in physics based is designed based on multi-output feedback technique and the reaching law method, and it is proved that the controller can control the uncertain discrete system with time-delay effectively. The simulation results illustrate the proposed algorithms are more effective than the conventional methods.
The chapter 4 considers the problem how to design a model tracker by using model reference adaptive sliding mode control algorithm for uncertain system with time-delay. A novel model reference adaptive sliding mode control algorithm is presented, and the system can track the model reference system effectively by using the new controller where the boundary of external disturbance can not be known as usually. In addition, a decentralized model reference adaptive variable structure control algorithm for a class of perturbed large-scale discrete systems with varying time-delay interconnections is investigated, and a discrete robust adaptive quasi-sliding-mode tracking controller is presented. It is proved that by using the adaptive controller the output error decreases to zero and the trajectories of each subsystem traverse the sliding hyperplane in each step, and the globally asymptotically stability of the system is also proved based on the Lyapunov-Razumikhin stability theorem. Finally, an example is presented and its simulation results illustrate the efficiency of the proposed approach.
The chapter 5 considers the chaos synchrony problem for a class of discrete uncertain systems with time-delays. First, a switching function is designed to guarantee that the movement of the system is asymptotically stable in the switching manifold. And the equation of the switching surface is given based on pole assignment theorem; Then a discrete robust adaptive quasi-sliding-mode tracking controller is presented by constructing the two adaptive gains, and the globally asymptotically stability of the system is proved based on the Lyapunov-Razumikhin stability theorem. At last, the simulation examples illustrate that this algorithm is effective and robust with respect to some exogenous disturbances for Duffing-Holmes system. In addition, a discrete terminal sliding mode controller is proposed by applying terminal sliding mode control technique and selecting adaptive reaching law, and the chaos synchrony problem can be solved effectively by using this method. At the same time, it is proved that the designed sliding surface is a terminal sliding surface and the movement of the system controlled by given controller can traverse the sliding surface in each step. At last, an example is presented and its simulation results illustrate the efficiency of the proposed approach.
The last chapter summarizes the research work of this dissertation and gives an outlook on sliding mode control method for discrete uncertain system with time-delay.
引文
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