不确定系统的滑模控制理论及应用研究
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摘要
不确定系统的控制是目前控制理论研究的一个重要问题。目前针对不确定系统主要有鲁棒控制、自适应控制、滑模变结构控制与智能控制等方法。由于滑模控制系统的滑动模态对满足匹配条件的参数变化与外部扰动具有完全鲁棒性,因而受到了广泛重视。本文基于鲁棒控制、自适应控制以及模糊控制等理论,深入研究了不确定系统的滑模变结构控制问题。主要包括以下几个方面:
研究了一类不确定线性系统滑模控制器的设计问题。分析了一类不确定系统滑模面设计方法的本质,得到了设计滑模面的一种简单方法,可以利用不确定线性系统鲁棒控制的结论直接设计滑模面; 基于不确定滑模控制系统的实际滑动模态仅仅收敛于理想滑动模态周围一定区域的假设,提出了设计滑模面的一个充分条件,得到了不确定滑模控制系统的动态品质的一个估计式。
针对不确定时滞系统,提出了一种虚拟反馈控制与滑模控制相结合的控制策略,得到了设计时滞独立型的滑模面的一个充分条件,并设计了滑模控制器,确保了闭环系统的鲁棒稳定性。此外,将该方法进一步推广到一类不确定中立型时滞系统。由于虚拟反馈控制的使用,在不影响滑模控制器设计的前提下,简化了不确定中立型时滞系统的滑模面的设计,得到了设计时滞独立型的滑模面的一个充分条件。
基于全程滑模思想,结合自适应控制策略,设计了一种时滞依赖型的自适应滑模控制器。基于自由权时滞转换模型,把名义时滞系统时滞依赖稳定性的新结论,直接引入到不确定时滞滑模控制系统的设计中,简化了时滞依赖型的滑模控制器的设计问题,得到了设计时滞依赖型滑模面的一个充分条件,同时,减小了滑模面设计的保守性。
讨论了一类不确定非线性时滞系统的滑模控制问题。基于T-S 模糊模型,进一步推广了虚拟反馈控制与滑模控制相结合的思想,应用于不确定非线性时滞系统,设计了滑模控制器,导出了设计稳定滑模面的一个充分条件,确保了不确定非线性时滞系
Control of uncertain systems is an important research topic in automatic control field. At present, robust control, adaptive control, sliding mode control and intelligent control are main classes of control methods for uncertain systems. Sliding mode control theory is known to be an efficient alternative way to tackle uncertain system because ideal sliding mode is whole robust for matched parameter uncertainties and external disturbances. The aim of this dissertation is to study sliding mode control design approaches of feasibility for uncertain system by combining robust control, adaptive control, T-S fuzzy model control theory and sliding mode control theory. The following are main results:
Sliding mode control problem of a class of uncertain systems is discussed. The main character of design for a class sliding mode hyperplane is specified. Following this idea, it is shown that the design of robust sliding mode hyperplane is obtained easily from the corresponding conclusions of robust control for a class of linear systems with unmatched uncertainties. In addition, suppose the motions of practical sliding mode are only uniformly restricted to a certain region containing the original point. In this case, sliding mode dynamics deviated form ideal sliding mode motion is studied; and the estimate of the global closed-loop dynamics is given.
A novel sliding mode strategy with virtual state feedback control is presented for a class of uncertain time-delay system. A delay-independent sufficient condition for design of sliding mode hyperplane is developed. Simple sliding mode controller is constructed, and the global robust stability of the closed-loop system is guaranteed. In addition, this strategy is extended to a class of neutral time-delay system with unmatched uncertainties. The obtained sufficient condition for design of sliding mode hyperplane is considerable simple owing to the role of virtual feedback control.
Based on global sliding mode scheme, an adaptive sliding mode controller for a class of uncertain time-delay system is investigated. The main aim of adaptive sliding mode controller is to drive the system states to ideal sliding mode hyperplane. The design of sliding mode hyperplane is obtained through the delay-dependent robust stable conclusions
of nominal time-delay system based on state transformation model with free-weighting matrices, which leads less conservative for the design of sliding mode hyperplane. Fuzzy sliding mode controller for a class of nonlinear time-delay system in presence of both parameter uncertainties and external disturbance is discussed. The T-S fuzzy model is employed to represent the uncertain nonlinear time-delay system. Sufficient conditions for design of robust sliding mode hyperplane are given by using virtual state feedback control. The global asymptotic stability of the closed-loop control system is guaranteed. A novel discrete reaching law with dynamic disturbance compensator is presented for a class of uncertain systems. Measure of parameter uncertainties and external disturbances is obtained online through the deviations between the practical reaching law and the desired reaching law. The robust stability of the closed-loop system is guaranteed. System dynamics in the vicinity of the sliding mode hyperplane is examined in detail. It is shown that the dynamic features and robustness of the closed-loop system are improved effectively and all advantages of the reaching law are retained. The applications of sliding mode controller are discussed. The sliding mode controller for an inverted pendulum system on a cart is investigated based on virtual state feedback strategy, the experiment results are given in detail. Based on active control techniques, a active sliding mode control approach is presented for synchronization of two uncertain chaotic system. A fuzzy sliding mode controller is presented to stabilize uncertain Chen’s chaotic system based on T-S fuzzy model. The difficulty of constructing a robust sliding mode plane is alleviated by using virtual state feedback. Meanwhile, high gain to suppress the parameter uncertainties and external disturbances is avoided by tradeoff of T-S fuzzy control. In addition, discrete reaching law with dynamic disturbance compensator is applied to achieve accurate servo tracking to BLDC control system in the presence of load disturbance and plant parameter variations.
研究了一类不确定线性系统滑模控制器的设计问题。分析了一类不确定系统滑模面设计方法的本质,得到了设计滑模面的一种简单方法,可以利用不确定线性系统鲁棒控制的结论直接设计滑模面; 基于不确定滑模控制系统的实际滑动模态仅仅收敛于理想滑动模态周围一定区域的假设,提出了设计滑模面的一个充分条件,得到了不确定滑模控制系统的动态品质的一个估计式。
针对不确定时滞系统,提出了一种虚拟反馈控制与滑模控制相结合的控制策略,得到了设计时滞独立型的滑模面的一个充分条件,并设计了滑模控制器,确保了闭环系统的鲁棒稳定性。此外,将该方法进一步推广到一类不确定中立型时滞系统。由于虚拟反馈控制的使用,在不影响滑模控制器设计的前提下,简化了不确定中立型时滞系统的滑模面的设计,得到了设计时滞独立型的滑模面的一个充分条件。
基于全程滑模思想,结合自适应控制策略,设计了一种时滞依赖型的自适应滑模控制器。基于自由权时滞转换模型,把名义时滞系统时滞依赖稳定性的新结论,直接引入到不确定时滞滑模控制系统的设计中,简化了时滞依赖型的滑模控制器的设计问题,得到了设计时滞依赖型滑模面的一个充分条件,同时,减小了滑模面设计的保守性。
讨论了一类不确定非线性时滞系统的滑模控制问题。基于T-S 模糊模型,进一步推广了虚拟反馈控制与滑模控制相结合的思想,应用于不确定非线性时滞系统,设计了滑模控制器,导出了设计稳定滑模面的一个充分条件,确保了不确定非线性时滞系
Control of uncertain systems is an important research topic in automatic control field. At present, robust control, adaptive control, sliding mode control and intelligent control are main classes of control methods for uncertain systems. Sliding mode control theory is known to be an efficient alternative way to tackle uncertain system because ideal sliding mode is whole robust for matched parameter uncertainties and external disturbances. The aim of this dissertation is to study sliding mode control design approaches of feasibility for uncertain system by combining robust control, adaptive control, T-S fuzzy model control theory and sliding mode control theory. The following are main results:
Sliding mode control problem of a class of uncertain systems is discussed. The main character of design for a class sliding mode hyperplane is specified. Following this idea, it is shown that the design of robust sliding mode hyperplane is obtained easily from the corresponding conclusions of robust control for a class of linear systems with unmatched uncertainties. In addition, suppose the motions of practical sliding mode are only uniformly restricted to a certain region containing the original point. In this case, sliding mode dynamics deviated form ideal sliding mode motion is studied; and the estimate of the global closed-loop dynamics is given.
A novel sliding mode strategy with virtual state feedback control is presented for a class of uncertain time-delay system. A delay-independent sufficient condition for design of sliding mode hyperplane is developed. Simple sliding mode controller is constructed, and the global robust stability of the closed-loop system is guaranteed. In addition, this strategy is extended to a class of neutral time-delay system with unmatched uncertainties. The obtained sufficient condition for design of sliding mode hyperplane is considerable simple owing to the role of virtual feedback control.
Based on global sliding mode scheme, an adaptive sliding mode controller for a class of uncertain time-delay system is investigated. The main aim of adaptive sliding mode controller is to drive the system states to ideal sliding mode hyperplane. The design of sliding mode hyperplane is obtained through the delay-dependent robust stable conclusions
of nominal time-delay system based on state transformation model with free-weighting matrices, which leads less conservative for the design of sliding mode hyperplane. Fuzzy sliding mode controller for a class of nonlinear time-delay system in presence of both parameter uncertainties and external disturbance is discussed. The T-S fuzzy model is employed to represent the uncertain nonlinear time-delay system. Sufficient conditions for design of robust sliding mode hyperplane are given by using virtual state feedback control. The global asymptotic stability of the closed-loop control system is guaranteed. A novel discrete reaching law with dynamic disturbance compensator is presented for a class of uncertain systems. Measure of parameter uncertainties and external disturbances is obtained online through the deviations between the practical reaching law and the desired reaching law. The robust stability of the closed-loop system is guaranteed. System dynamics in the vicinity of the sliding mode hyperplane is examined in detail. It is shown that the dynamic features and robustness of the closed-loop system are improved effectively and all advantages of the reaching law are retained. The applications of sliding mode controller are discussed. The sliding mode controller for an inverted pendulum system on a cart is investigated based on virtual state feedback strategy, the experiment results are given in detail. Based on active control techniques, a active sliding mode control approach is presented for synchronization of two uncertain chaotic system. A fuzzy sliding mode controller is presented to stabilize uncertain Chen’s chaotic system based on T-S fuzzy model. The difficulty of constructing a robust sliding mode plane is alleviated by using virtual state feedback. Meanwhile, high gain to suppress the parameter uncertainties and external disturbances is avoided by tradeoff of T-S fuzzy control. In addition, discrete reaching law with dynamic disturbance compensator is applied to achieve accurate servo tracking to BLDC control system in the presence of load disturbance and plant parameter variations.
引文
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