Vibration control of a smart structure using periodic output feedback technique

Active vibration control is an important problem in structures. One of the ways to tackle this problem is to make the structure smart, adaptive and self-controlling. The objective of active vibration control is to reduce the vibration of a system by automatic modification of the system's structural response. This work features the modeling and design of a Periodic Output Feedback (POF) control technique for the vibration control of a smart flexible cantilever beam system for a Single Input Single Output case. A POF controller is designed for the beam by bonding patches of piezoelectric layer as sensor/actuator to the master structure at different locations along the length of the beam. The entire structure is modeled in state space form using the Finite Element Method by dividing the structure into 3, 4, 5 elements, thus giving rise to three types of systems, viz., system I (beam divided into 3 finite elements), system 2 (4 finite elements), system 3 (5 finite elements). POF controllers are designed for the above three types of systems for different sensor/actuator locations along the length of the beam by retaining the first two vibratory modes. The smart cantilever beam model is developed using the concept of piezoelectric bonding and Euler-Bernouli theory principles. The effect of placing the sensor/actuator at various locations along the length of the beam for all the three types of systems considered 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 beam. The tip displacements with the controller is obtained. Performance of the system is also observed by retaining the first 3 vibratory modes and the conclusions are drawn.