Active Vibration Suppression of a Smart Beam via PID Control

In this study, a PID controller was designed for the active vibration suppression of a smart beam equipped with PZT (Lead-Zirconate-Titanate) patches. The smart beam is a cantilever aluminium beam having eight symmetrically located surface-bonded piezoelectric patches. In this particular application, a group of PZT patches closed to the root of the beam was used as actuators and from the remaining ones a patch was nominated as a sensor. All the actuators were used in bimorph configuration. PID controllers were known to provide better flexibility in adjusting the gain and phase characteristics than conventional integer-order PID controllers. The parameters of PID controllers are composed of the proportionality constant, integral constant, derivative constant, derivative order and integral order; hence its design is inevitably more complicated than that of a PID controller. First, the optimization problem of the regulator controller’s required parameters was established by using the transfer function of the smart beam. That transfer function was experimentally obtained by means of using aforementioned group of sensor/actuator piezoelectric patches. The PID controller was then considered by using a fourth degree approach of continued fraction expansion (CFE) method. Following this, the optimization problem of finding the PID controller’s parameters was solved by using both the MATLAB Optimization Toolbox and an optimization model, which has been developed in house by using MATLAB Simulink package program. The simulation results obtained in time domain demonstrated that the designed controller successfully suppressed the vibration levels of the smart beam for the first two flexural modes.