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摘要:为了对基于U模型的非线性控制系统进行研究,利用Super-Twisting控制算法,解决非仿射非线性系统的控制问题,对非线性函数进行神经网络逼近,运用Super-Twisting控制算法进行控制。选取恰当的Lyapunov函数,对Super-Twisting算法的收敛性进行了证明。为了验证该方法的可行性和有效性,利用Matlab软件进行仿真,结果表明在神经网络自适应Super-Twisting控制器的作用下,被控系统具有快速的跟踪性能和输出的有界性。
关键词:鲁棒控制;非线性系统;神经网络;U模型;Super-Twisting算法;自适应
中图分类号:TP273文献标志码:A
文章编号:1008-1542(2016)04-0376-06
Abstract:The Super-Twisting control algorithm is adopted to analyze the U model based nonlinear control system in order to solve the controller design problems of non-affine nonlinear systems. The non-affine nonlinear systems are studied, the neural network approximation of the nonlinear function is performed, and the Super-Twisting control algorithm is used to control. The convergence of the Super-Twisting algorithm is proved by selecting an appropriate Lyapunov function. The Matlab simulation is carried out to verify the feasibility and effectiveness of the described method. The result shows that the output of the controlled system can be tracked in a very short time by using the designed Super-Twisting controller, and the robustness of the controlled system is significantly improved as well.
Keywords:robust control; nonlinear system; neural network; U model; Super-Twisting algorithm; adaptive
非线性特性普遍存在于实际的生产中,非线性系统的控制问题一直以来是科学研究中需要解决的一个普遍性问题[1-3]。目前,有很多种设计工具和分析方法来研究非线性系统[4-6],线性化方法是最为普遍的方法。但是,线性化方法也有其弊端,在非线性程度强、控制精度要求高的情况下,难以得到良好的控制效果,而且大多数线性控制方法不能直接应用于非线性系统的设计[7-9]。因此,研究人员提出了多种关于非线性控制器的设计方法,有相平面法,Backstepping,Lyapunov函数法,描述函数法,反馈线性化等设计方法[10-12]。
建立一个通用、易于控制器设计并具有高精度的非线性模型是解决控制系统设计的关键。U模型的起源正是基于这样的认识演变而来的,自U模型被提出以来,已为非线性控制系统设计开创了一个新的研究领域[13-14]。朱全民等人提出了运用牛顿-拉夫逊迭代算法求解多项式,为U模型中非线性系统控制器的设计提供了基础[13]。U模型是表示一类平滑非线性对象的时变参数多项式函数,建立了一个简单的通用映射[14],可将平滑非线性离散时间输入-输出动态对象模型完全转换为线性控制可设计的结构。
滑模控制也称作变结构控制,本质上是一种控制不连续性的非线性控制[15-17]。相比于其他控制器,滑模控制的优点有:整体结构简单、快速响应、对内部参数和外部扰动均不灵敏、无需系统在线辨识等[18-20]。滑模控制与其他控制的区别在于系统本身并不固定,而是能够在动态过程中,根据系统当前的状态有目的性地不断变化,最终使系统按照预先设定的轨迹运动。但是,传统的滑模控制也有其弊端,由于自身的离散性存在了不可避免的抖震问题。高阶滑模(HOSM)的提出消除了传统滑模的弊端,并保留了传统滑模的优点。基于U模型的非线性系统控制可以实现很多系统的控制设计,特别是对于动态非线性对象进行极点配置,对前向自适应跟踪控制等控制问题。论文分析了基于U模型的三角结构非线性控制系统,运用了Lyapunov函数方法,对Super-Twisting算法的收敛性进行了证明,并对系统的状态和系统控制器的输出进行仿真,仿真结果证明所提出方法的正确性。
4结论
本文通过U模型的控制思路,将系统输出作为虚拟控制的输入,设计了非线性系统的Super-Twisting控制器,实现非仿射非线性系统的神经网络自适应控制,具有有限时间收敛的特点,能够更好地实现神经网络控制收敛时间的问题,完成了非线性系统的有限时间控制,最后通过仿真实验验证了算法的有效性。
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