Modeling and analysis of flexible beams with surface-mounted PZT actuators

This paper examines a number of long-standing problems in high-fidelity modeling, precision positioning, vibration and disturbances attenuations, as well as tracking control problems for flexible beams. The mathematical models of beam are described by partial differential equations. The nonlinear PZT actuators dynamics is integrated to perform design and guarantee accurate performance analysis with outcomes prediction. Forces, developed by the PZT actuators, are applied to accurately position the beam, attenuate vibrations, and minimize disturbances. High-fidelity mathematical models of actuators must be studied and integrated because nonlinearities, hysteresis and other phenomena cannot be neglected. These nonlinear effects significantly degrade overall performance. Therefore, modeling, analysis, simulation and control problems must be solved. To guarantee the optimal performance, robust tracking control algorithms are designed using proportional-integral control laws with state feedback. In addition to the solution of tracking control problem, the parametric optimization problem needs to be examined. In particular, we research the closed-loop system performance by using different number of PZT actuators and optimizing their locations. The results reported are new and have not been reported in the literature. The proposed mathematical models, design procedures and optimization are verified through heterogeneous simulations and data-intensive analysis using the MATLAB environment.