Reference model decomposition in direct adaptive control

This paper introduces the method of ‘reference model decomposition’ as a way to improve the robustness of model reference adaptive control systems (MRACs) with respect to unmodelled dynamics with a known structure. Such unmodelled dynamics occur when some of the nominal plant dynamics are purposely neglected in the controller design with the aim of keeping the controller order low. One of the effects of such ‘undermodelling’ of the controller is a violation of the perfect model-matching condition of the primary controller. The decomposition can be seen as a way to adjust the reference model output (and hence the control goal) to the actual model-matching capabilities. It is shown that the decomposition alleviates the negative effects unmodelled dynamics have on the error equation. Simulation examples illustrate the decomposition design steps and show the obtained improvements.