Model inverse based Iterative Learning Control using finite impulse response approximations

In Iterative Learning Control, the ideal learning filter is defined as the inverse of the system being learned. Model based learning filters designed from the inverse system transfer function can provide superior performance over single gain, P-type algorithms. These filters, however, can be excessively long if lightly damped zeros are inverted. In this paper, we propose a method for designing model based finite impulse response (FIR) learning filters. Based on the ILC injection point and discrete time system model, these filters are designed using the impulse responses of the inverse transfer function. We compare in simulation the ILC algorithms implemented at two different feedforward injection points and two different modeling methods. We show that the ILC algorithm injected at the reference signal and whose model is generated by discretizing the closed loop continuous time transfer function results in a learning filter with no lightly damped zeros. As a result, the learning filter has only two dominant filter taps much like the PD-type learning filter. We then implement these ILC algorithms on a wafer stage prototype. In this motion control application, we show that the model based ILC algorithm outperforms the P-type system in the plant injection architecture where longer FIR filters are needed for learning stability. We also show that the reference injection architecture provides superior performance to the plant injection for both model based and P-type ILC algorithms.