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Adaptive Boundary Control of Flexible Manipulators with Parameter Uncertainty Based on RBF Neural Network
Shock and Vibration ( IF 1.6 ) Pub Date : 2020-11-16 , DOI: 10.1155/2020/8261423 Cang He 1, 2 , Fang Zhang 1, 2 , Jinhui Jiang 1, 2
Shock and Vibration ( IF 1.6 ) Pub Date : 2020-11-16 , DOI: 10.1155/2020/8261423 Cang He 1, 2 , Fang Zhang 1, 2 , Jinhui Jiang 1, 2
Affiliation
In this paper, nonlinear dynamical equations of the flexible manipulator with a lumped payload at the free end are derived from Hamilton's principle. The obtained model consists of both distributed parameters and lumped parameters, namely, partial differential equations (PDEs) governing the flexible motion of links and boundary conditions in the form of ordinary differential equations (ODEs). Considering the great nonlinear approximation ability of the radial basis function (RBF) neural network, we propose a combined control algorithm that includes two parts: one is a boundary controller to track the desired joint positions and suppress the vibration of flexible links; another is a RBF neural network designed to compensate for the parametric uncertainties. The iteration criterion of the RBF neural network weight matrix is derived from the extended Lyapunov function. Stabilization analysis is further carried out theoretically via LaSalle’s invariance principle. Finally, the results of the numerical simulation verify that the proposed control law can realize the asymptotic convergence of tracking error and suppression of the elastic vibration as well.
中文翻译:
基于RBF神经网络的参数不确定柔性机械臂的自适应边界控制。
本文基于汉密尔顿原理,推导了自由端集总有效载荷的柔性机械臂的非线性动力学方程。所获得的模型由分布参数和集总参数组成,即以常微分方程(ODE)的形式控制链节和边界条件的柔性运动的偏微分方程(PDE)。考虑到径向基函数(RBF)神经网络的强大的非线性逼近能力,我们提出了一种组合控制算法,该算法包括两部分:一个是边界控制器,用于跟踪所需的关节位置并抑制柔性连杆的振动;第二个是边界控制器。另一个是RBF神经网络,旨在补偿参数不确定性。RBF神经网络权重矩阵的迭代准则是从扩展的Lyapunov函数导出的。理论上,通过LaSalle的不变性原理可以进一步进行稳定性分析。最后,数值仿真结果验证了所提出的控制律能够实现跟踪误差的渐近收敛和弹性振动的抑制。
更新日期:2020-11-16
中文翻译:
基于RBF神经网络的参数不确定柔性机械臂的自适应边界控制。
本文基于汉密尔顿原理,推导了自由端集总有效载荷的柔性机械臂的非线性动力学方程。所获得的模型由分布参数和集总参数组成,即以常微分方程(ODE)的形式控制链节和边界条件的柔性运动的偏微分方程(PDE)。考虑到径向基函数(RBF)神经网络的强大的非线性逼近能力,我们提出了一种组合控制算法,该算法包括两部分:一个是边界控制器,用于跟踪所需的关节位置并抑制柔性连杆的振动;第二个是边界控制器。另一个是RBF神经网络,旨在补偿参数不确定性。RBF神经网络权重矩阵的迭代准则是从扩展的Lyapunov函数导出的。理论上,通过LaSalle的不变性原理可以进一步进行稳定性分析。最后,数值仿真结果验证了所提出的控制律能够实现跟踪误差的渐近收敛和弹性振动的抑制。