Model reference adaptive control of a flexible structure

Abstract

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

A new adaptive tracking control approach for uncertain flexible joint robot system

“…With this method, Zhang et al [11,12] considered adaptive dynamic surface control for nonlinear systems with uncertainties, Hou and Duan [13] studied how to design controller for integrated missile guidance and autopilot. Moreover, some other approaches such as model reference adaptive control [14,15] , robust adaptive control [16] and adaptive iterative learning control [17] are also useful to regulate such nonlinear systems. The adaptive tracking problem for FJR has been studied before.…”

Robust Adaptive Control of a Cantilevered Flexible Structure with Spatiotemporally Varying Coefficients and Bounded Disturbance

“…Compared to the finite dimensional case, the adaptive control of infinite dimensional systems is not well developed and has only recently been studied (5) - (10) . In this paper, a robust model reference adaptive control (MRAC) of a cantilevered flexible beam with unknown spatiotemporally varying coefficients and disturbance is developed.…”

Robust Mrac Of A Nonautonomous Parabolic System With Spatiotemporally Varying Coefficients And Bounded Disturbance

“…Distributed sensing and actuation are also assumed. Compared to the adaptive control/identification of finite dimensional systems, that of infinite dimensional systems is not well developed and has been recently studied [1][2][3][4][5][6][7][10][11][12][13][14][19][20]21,25,30,[32][33][34].…”