Model reference adaptive control of a flexible structure

In this paper. the model reference adaptive control (MRAC) of a flexible st ructure is investigated. Any mechanically flexible structure is inherently distributed parameter in nature, so that its dynamics are described by a pa rtial, rather than ordinary, differential equation. The MRAC problem is for mulated as an initial value problem of coupled partial and ordinary differe ntial equations in weak form. The well-posedness of the initial value probl em is proved. The control law is derived by using the Lyapunov redesign met hod on an infinite dimensional Hilbert space. Uniform asymptotic stability of the closed loop system is established, and asymptotic tracking, i. e., c onvergence of the state-error to zero, is obtained. With an additional pers istence of excitation condition for the reference model, parameter-error co nvergence to zero is also shown. Numerical simulations are provided.