Adaptive Nonlinear Boundary Control of a Hybrid Euler–Bernoulli Beam with Coupled Rigid and Flexible Dynamics

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This paper establishes adaptive nonlinear boundary control of an Euler–Bernoulli beam with rigid and flexible hybrid motion in the plane. In the previous work, a nonlinear boundary control was designed based on partial differential equation model that stabilizes the beam vibration while regulating the rigid body position and orientation. Here, the control law in the previous work is redesigned to establish an adaptive boundary controller that is able to compensate for system parametric uncertainties. Lyapunov analysis shows that the proposed adaptive control achieves asymptotic stability for the hybrid beam system. Simulation results are used to illustrate the efficacy of the proposed controller.