Boundary control of vibration and noise in distributed parameter systems: An overview

In this paper, we present a technical overview of the design and analysis of active boundary controllers for distributed parameter (vibration and noise) systems. This presentation is done in the context of Lyapunov control design and stability analysis tools, which are commonly applied to non-linear finite dimensional systems. The main purpose of this presentation is to shed more light on this powerful control design philosophy for distributed parameter systems. The Lyapunov-based boundary control framework will be illustrated through three example systems-the transverse vibrating string, the acoustic noise duct, and the flexible rotor-each with an increasing level of complexity. To complement the theoretical content of the paper, the experimental implementation of the flexible rotor controller is also presented.