Nonlinear vibration suppression of cantilever beams using bi-moments induced by PZT actuators

Abstract

We investigate the use of PZT (lead zirconate titanate) patches as actuators and sensors and nonlinear saturation and internal resonance control methods to suppress steady-state and transient vibrations of a cantilever beam. The saturation control method uses the saturation phenomenon to suppress steady-state vibrations of a dynamical system with quadratic nonlinearities and 2:1 internal resonances. The internal resonance control method uses the energy exchange phenomenon due to internal resonances and added dampings to suppress transient vibrations. To test this nonlinear control technique in an efficient and systematic way, we built a digital control system that consists of SIMULINK modeling software and a dSPACE DS1102 controller in a pentium computer. The results show that the saturation control method is robust and efficient in suppression steadystate resonant vibrations. The internal resonance control method works but is inconvenient for use. We also investigate the linear position-feedback control of the same system. Results show that the linear position-feedback control of transient vibration is more robust and efficient than the internal resonance control method but there are some drawbacks.