Modeling of low frequency dynamics of a smart system and its state feedback based active control

Major physical systems/structures suffer from unwanted vibrations. For efficient working of such systems, these vibrations have to be controlled. In this paper, mathematical modeling of an aluminum cantilever beam with bonded multiple piezoelectric patches which act as the disturbance generator, sensor as well as control actuator has been presented. This piezoelectric laminate cantilever beam is assumed to be vibrating in a single degree of freedom i.e. in the flexural mode only and the corresponding state space models have been derived analytically using the finite element technique. Dominant modes of flexural vibration are identified from the frequency response of the developed model of the system and finally a state feedback controller based on pole placement technique is designed to actively suppress the vibrations. Through numerous simulations as well as experimental validation, the effectiveness of the active controller in damping the vibrations at various excitation frequencies as well as frequency ranges along the flexural mode is established.