Design of Adaptive Feedforward Algorithms Using Internal Model Equivalence

Certain types of adaptive algorithms used for repetitive control are input/output equivalent to linear time-invariant controllers. This paper concerns the consequences of this equivalence for analysis and design of these types of adaptive controllers. Specifically, the role of zero placement in the linear time-invariant equivalent is closely examined using root locus analysis, and a modification of one adaptive algorithm to include a feedthrough term is developed. Abstract The paper investigates the design of Adaptive Feedforward Cancellation (AFC) algorithms with sinusoidal regressors for repetitive control. Such adaptive algorithms are equivalent to linear controllers based on the Internal Model Principle (IMP). Using this equivalence and root locus rules, the phase advance of the regressor of the adaptive algorithm can be chosen to maximize the phase margin at low gains. A surprising result is that selecting the optimal phase advance is equivalent to placing a zero in the open right half-plane in certain cases. Complete design and analysis for the compensation of a single frequency periodic disturbance is done. A new variation of the AFC algorithm is also developed in which the adaptive portion acts in parallel with a feedthrough term. The IMP equivalent of this algorithm has two zeros instead of one. Analysis and simulation shows this method t have superior convergence and robustness properties when compared with the method ha feedthrough term. Discrete-time versions of the algorithms are briefly considered.