T.C. MANJUNATH and B. BANDYOPADHYAY : SMART CONTROL OF CANTILEVER STRUCTURES

This paper features the modelling and design of a type of multirate output feedback based controller (Fast Output Sampling Feedback FOS) to control the flexural vibrations of a smart flexible Timoshenko cantilever beam for a Single Input Single Output (SISO) case by retaining the first 2 dominant vibratory modes. Piezoelectric patches are bonded as sensor / actuator to the master structure at different finite element locations along the length of the beam. The beam structure is modelled in state space form using the concept of piezoelectric theory, the Timoshenko beam theory and the Finite Element Method (FEM) technique and by dividing the beam into 4 finite elements and placing the piezoelectric sensor / actuator at one discrete location as a collocated pair at a time, i.e., as surface mounted sensor / actuator, say, at FE position 1 or 2 or 3 or 4, thus giving rise to 4 SISO models of the same plant. FOS feedback controllers are designed for the above 4 models of the same plant. The piezo sensor / actuator pair is moved from the free end to the fixed end of the beam. The effect of placing the collocated sensor / actuator pair at various finite element locations along the length of the beam is observed and the conclusions are drawn for the best performance and for the smallest magnitude of the control input required to control the vibrations of the flexible beam.