Improved tracking performance of variable structure control using Fourier series based iterative learning

A new approach to reduce chattering of variable structure control and improve tracking accuracy is proposed, which is based on frequency domain iterative leaning. For a deterministic nonlinear uncertain dynamical system with limited bandwidth, the desired control input corresponding to the desired trajectory which lasts for a finite duration is invariant over every iteration and can be formulated as a Fourier linear combiner with constant harmonic magnitudes and limited number of elements. Since the elements of the basis of the Fourier space are orthogonal, an iterative learning scheme is proposed to individually force every component of the actual feedforward compensation converge to that of the desired control input. As a result, switching gains can be greatly reduced and chattering problem can be alleviated. It is proven that the scheme guarantees that system states are bounded for all trials and eventually stay on the switching surface for the whole iteration. Application example for a DC servomotor confirms the effectiveness the proposed scheme.