Vibration Control Analysis of a Smart Flexible Cantilever Beam Using Smart Material

Abstract

This paper features the modeling and design of a pole placement and output Feedback control technique for the Active Vibration Control (AVC) of a smart flexible cantilever beam for a Single Input Single Output (SISO) case. Measurements and actuation actions done by using patches of piezoelectric layer, it is bonded to the master structure as sensor/actuator at a certain position of the cantilever beam. The smart structure is modeled based on the concept of piezoelectric theory, Bernoulli -Euler beam theory, using Finite Element Method (FEM) and the state space techniques. The number of modes is reduced using the controllability and observability grammians retaining the first three dominant vibratory modes, and for the reduced system, a control law is designed using pole placement and output feedback techniques. The analyzed case studies concern the vibration reduction of a cantilever beam with a collocated symmetric piezoelectric sensor/actuator pair bonded on the surface. The transverse displacement time history, for an initial displacement field at the free end, is evaluated. Results are compared with other works, and the control design shows that Pole Placement method is an effective method for vibration suppression of the beam and settling time reduction.

Keywords

• vibration, active vibration control, smart material, cantilever beam