Model Reference Adaptive Control with Proportional Integral Adaptation Law

In this contribution we extend the classical update law of the certainty equivalence based (indirect) model reference adaptive control (MRAC) with an additional feedthrough error term. We use a linear state-space representation of the parameter estimation error in order to construct a Lyapunov function. Without unstructured uncertainties, we can show asymptotic stability of the closed loop. Even for relatively high adaptation gains the algorithm can reduce the oscillations of the state variables. In case of unstructured input uncertainties, the additional term reduces the model following error drastically without increasing the control signal for low frequency unstructured uncertainties. For the simplified pure linear case we analyze the effect of the additional proportional error feedthrough in the adaptation law showing its similarity to a disturbance observer. As a simulation example the wing-rock dynamics are reconsidered.