An integrated active-parametric control approach for active-passive hybrid piezoelectric network with variable resistance

Previous studies have shown that piezoelectric materials can be used to provide passive damping by shunting them with an electrical network, such as a series RL circuit. This same configuration can also be used in conjunction with an active voltage source as an active-passive hybrid vibration control method. This active-passive piezoelectric network (APPN) concept, which combines the advantages of passive damping and active control, has proven to be very effective for vibration suppression, especially in narrow-band applications. It has also been recognized that the resistor element in these devices, which is necessary to provide passive damping, can reduce the authority of the active control action by dissipating a portion of the control power. One possible method to improve upon this situation is to use a variable resistor in the shunt circuit and on-line adjust the resistance based on feedback. However, the concurrent design method previously synthesized for APPN systems becomes difficult to implement when such a state-dependent and time-varying resistor is used. In this research, an effective and simple active-parametric control law is developed for an APPN system with variable resistance. The active control law uses a simple but effective rate feedback law along with a feedback linearization technique to compensate for the dynamics of the variable resistor. The parametric control law is designed to turn the resistor off when the active source is supplying power to the actuator and turn the resistor on when necessary to dissipate power from the structure. With this variable resistance action it is possible to retain the passive damping abilities of the APPN circuit while minimizing the amount of control power that is dissipated in the circuit. A series of simulations are conducted in order to demonstrate the increased efficiency due to the variable resistance action. The effects of excitation bandwidth and controller gain on the performance of the system are also examined.