Evaluation of (unstable) non-causal systems applied to iterative learning control

This paper presents a new approach towards the design of iterative learning control \cite{moore}. In linear motion control systems the design is often complicated by the inverse plant sensitivity being non-causal and even unstable. To overcome these problems the inverse system is split up in a causal and a non-causal part. We apply high-performance differentiating filters together with a mixed boundary value ODE solver to compute the control signal. This allows for an accurate approximation of the theoretical solutionand offers the advantage of control over the boundary conditions of the learnt signal. The advantages of this approach over the existing commonly-used ZPETCtechnique are demonstrated by two examples, respectively a non-minimum-phase system and an industrial H-drive.