Adaptive Finite-time Synergetic Control of Delta Robot based on Radial basis Function Neural Networks

This paper proposes a novel robust proportional derivative adaptive non-singular synergetic control (PDATS) for the delta robot system. A proposal radial basis function approximation neural networks (RBF) compensates for external disturbances and uncertainty parameters. To counteract the chattering noise of the low-resolution encoder, a second-order sliding mode (SOSM) observer in the feedback loop showed the ability to obtain the angular velocity estimations. The stability of the PDATS approach is proven using the Lyapunov stability theory. Both the simulation and experiment result effectiveness and performances of the PDATS controller in trajectory; pick and place operations of a parallel delta robot. The characteristics of the controller demonstrate that the proposed method can effectively reduce external disturbance and uncertainty parameters of the robot by a convergent finite-time, and provide higher accuracy in comparison with finite-time synergetic control and PD control.

Numerical computation of the time non-linear fractional generalized equal width model arising in shallow water channel

The generalized equal width model is an important non-linear dispersive wave model which is naturally used to describe physical situations in a water channel. In this work, we implement the idea of the interpolation by radial basis function to obtain numerical solution of the non-linear time fractional generalized equal width model defined by Caputo sense. In this technique, firstly, a time discretization is accomplished via the finite difference approach and the non-linear term is linearized by a linearization method. Afterwards, with the help of the radial basis function approximation method is used to discretize the spatial derivative terms. The stability of the method is theoretically discussed using the von Neumann (Fourier series) method. Numerical results and comparisons are presented which illustrate the validity and accuracy of our proposed concepts.

Numerical computation of the time non-linear fractional generalized equal width model arising in shallow water channel

The generalized equal width model is an important non-linear dispersive wave model which is naturally used to describe physical situations in a water channel. In this work, we implement the idea of the interpolation by radial basis function to obtain numerical solution of the non-linear time fractional generalized equal width model defined by Caputo sense. In this technique, firstly, a time discretization is accomplished via the finite difference approach and the non-linear term is linearized by a linearization method. Afterwards, with the help of the radial basis function approximation method is used to discretize the spatial derivative terms. The stability of the method is theoretically discussed using the von Neumann (Fourier series) method. Numerical results and comparisons are presented which illustrate the validity and accuracy of our proposed concepts.