Adaptive‐Like Vibration Control in Mechanical Systems with Unknown Paramenters and Signals

Abstract

AbstractThis paper describes the application of an on‐line algebraic identification methodology for parameter and signal estimation in vibrating mechanical systems. An important property of the algebraic identification is that the parameter identification is not asymptotic but algebraic, that is, the parameters are computed as fast as the system dynamics are being excited by some external input or by changes in the initial conditions. The algebraic identification is then employed to estimate mass, stiffness, and viscous damping in simple mechanical systems using only position measurements. This approach is also used in the identification of frequency, phase, and amplitude of exogenous vibrations affecting a mechanical system. The algebraic identification is then combined with a certainty equivalence controller to asymptotically stabilize the system response and, simultaneously, cancel harmonic vibrations. The proposed adaptive‐like control scheme is fast and robust against unknown parameters and frequency variations. Some numerical and experimental results illustrate the dynamic and robust performance of the algebraic identification and the active vibration controller.