Model Reference Adaptive Control of a Flexible Structure

In this paper, the model reference adaptive control for a flexible structure is investigated. Any mechanically flexible structures are inherently distributed parameter systems whose dynamics are described by partial, rather than ordinary, differential equations. Adaptation laws are derived by the Lyapunov redesign method on an infinite dimensional Hilbert space. Combined state and parameter estimator equations are constructed as an initial value problem of an infinite dimensional evolution equation in weak form. The well-posedness of the nonlinear closed loop system is shown. It is then shown through the Lyapunov redesign approach that the state error actually converges asymptotically to zero. With the additional persistence of excitation assumption, the parameter errors are shown to converge to zero as well.