Expanded Reference Models for Adaptive Control of Uncertain Systems with Actuator Dynamics

What is it about?

While addressing system uncertainties, the presence of unmodeled dynamics are often neglected in the design of model reference adaptive control laws. A practically unavoidable form of unmodeled dynamics is the actuator dynamics that is present in every physical system. In particular, if the bandwidths of each actuator channel are not sufficiently fast, then the closed-loop system trajectories may not behave close to the reference model trajectories and, importantly, the stability of the closed-loop system can be lost. The contribution of this paper is a new adaptive control architecture using expanded reference models for uncertain dynamical systems with actuator dynamics. The proposed approach allows the trajectories of an uncertain dynamical system to follow the trajectories of the expanded reference model. As compared to a well-known approach, it is shown that the expanded reference model trajectories remain predictably close to the trajectories of a given ideal reference model, which captures a desired closed-loop system performance. Furthermore, a command governor method is also developed along with the proposed expanded reference model to achieve asymptotic convergence of the expanded reference model trajectories to those of the ideal reference model such that the desired closed-loop system performance can be captured. For providing robustness against possible uncertainties in actuator bandwidths, in addition, an estimation of the actuator bandwidth is then incorporated to the proposed architecture.

Featured Image