Optimal control and H∞ filter for control of Timoshenko beam vibrations using piezoelectric material

Optimal control and H_∞ robust filter design for the beam vibration problem using smart material as actuators and sensors are studied. The Timoshenko beam (TB) is employed as the structural model. To stabilize the vibration of flexible beams, active control using piezoelectric (PZT) material as actuator is introduced. The distributed sensor using PZT material is considered to work as an estimator for the system state variables. The TB represented by the partial differential equation (PDE) is discretized using the central difference scheme to generate a finite dimensional model. This procedure provides the practical ability to implement the distributed sensing and actuation terms into the design. The optimal control theory is employed to determine the control voltages of the actuator such that the dynamic motion of the beams under Gaussian disturbance is stabilized. Furthermore, considering the unknown noise and errors existing in the measurement process, the state estimator is realized by the robust H_∞ filter. The effectiveness of this strategy is illustrated by a simulation example