Adaptive tracking control by system inversion

This paper presents a discrete time adaptive inversion scheme for linear systems and its usage in adaptive feedforward and feedback controllers. Two parameter adaptation algorithms (PAA) were used in the proposed schemes. The first PAA applies the extended bias-eliminating least-squares (EBELS) algorithm for plant estimation to ensure convergence to a tuned model under colored noise and unmodeled dynamics. The second PAA applies EBELS or least mean squares (LMS), respectively for two adaptive inversion schemes, to estimate a finite impulse response (FIR) plant inverse filter. A feedforward and a repetitive feedback control algorithms are designed respectively by including the adaptive inverse filter.