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In this paper, a RISE (Robust Integral of the Sign Error) controller with adaptive feedforward compensation terms based on Associative Memory Neural Network (AMNN) type B-Spline is proposed to regulate the positioning of a Delta Parallel Robot (DPR) with three degrees of freedom. Parallel Kinematic Manipulators (PKMs) are highly nonlinear systems, so the design of a suitable control scheme represents a significant challenge given that these kinds of systems are continually dealing with parametric and non-parametric uncertainties and external disturbances. The main contribution of this work is the design of an adaptive feedforward compensation term using B-Spline Neural Networks (BSNNs). They make an on-line approximation of the DPR dynamics and integrates it into the control loop. The BSNNs' functions are bounded according to the extreme values of the desired joint space trajectories that are the BSNNs' inputs, and their weights are on-line adjusted by gradient descend rules. In order to evaluate the effectiveness of the proposed control scheme with respect to the standard RISE controller, numerical simulations for different case studies under different scenarios were performed.

In this paper a PD controller with intelligent compensation is used to solve the problem of tracking trajectories for a Delta Parallel Robot with three degrees of freedom. This controller uses an artificial B-Spline neural network as a feedforward compensation term. To evaluate the proposed controller performance some numerical simulations under two different scenarios have been carried out in order to know its effectiveness respect to a simple PD controller.

We have calculated the photonic band structure of a 2D photonic crystal whose empty cylinders are infiltrated by a liquid crystal; a D.C. electric field is applied in the direction parallel to the cylinders. The local dielectric constant within the cylinders is obtained by minimizing the free energy, which has elastic and electrostatic contributions. We have assumed strong anchoring of the molecules of the nematic liquid crystal at the cylinder boundaries and have averaged over the cross-sectional area of the cylinder. The resulting dielectric tensor is diagonal and depends on the applied field. Moreover, it has the same symmetry as a uniaxial material, so that the optical response of the H-modes and E-modes is given by different dielectric constants ("ordinary" and "extraordinary"). The photonic band structures exhibit a notable dependence on the applied field with shifts up to 6% of the bands. For the E-modes, with a careful choice of the filling fraction it is possible to design a complete photonic gap for a certain range of electric fields, and close the gap for other values of the field. Such behaviour could be applied to optical tuning, switching, and polarizing of light.