Adaptive Robust Repetitive Control of A Class of Nonlinear Systems in Normal Form with Applications to Motion Control of Linear Motors

In this paper, the idea of adaptive robust control (ARC) is integrated with a repetitive control algorithm to construct a performance oriented control law for a class of nonlinear systems in the presence of both repeatable and non-repeatable uncertain nonlinearities. All the uncertainties are assumed to be bounded by certain known bounding functions. The repetitive control algorithm is used to learn and approximate the unknown repeatable nonlinearities, but with physically intuitive discontinuous projection modifications ensuring that all the function estimates are within the known bounds. Robust terms are constructed to attenuate the effect of various uncertainties including non-repeatable uncertainties effectively for a guaranteed transient performance and a guaranteed final tracking accuracy in general. Theoretically, in the presence of repeatable uncertainties only, asymptotic output tracking is also achieved without using an infinite fast switching control law or an infinite-gain feedback. The motion control of a linear motor drive system is used as an application example, and experimental results are presented to show the effectiveness of the scheme.