Passivity-based boundary control for vibration suppression of the shear beam

In this paper, the passivity-based boundary controller for the vibration suppression of the flexible beam is studied. The undamped shear beam model is used as a beam model. The beam is a parameter-distributed system represented by partial differential equations (PDEs). This technique uses the energy principle for control design by exploiting the passivity property of the beam. The storage or energy function of the beam is first introduced and then used to determine the passivity-based controller. The passivity of the system is proven using direct integration. The feedback system is proven in the sense of finite-gain L 2 stability. The proposed controller consists of the damping and elastic components applied at the beam end so that the domain (body) of the beam is not disturbed. The beam PDEs are treated directly without model reduction or truncation, so the control spillover problem is avoidable. The beam model PDEs are solved numerically by using the finite difference method. Numerical simulation results of the beam under control are presented to verify the performance of the control scheme.