Hybrid System Stability and Capacitive Shunting of Piezoelectric Stiffness

Recent research demonstrated that an actively-switched capacitive shunt circuit across a piezoceramic stiffness element can provide the basis for a frequency-tunable solid state vibration absorber. From a theoretical standpoint, the stability characteristics of such a design are amenable to conventional mechanical systems analysis when the shunt circuit operates in quasi-steady manner. However, when active tracking of a disturbance is desired to enhance broadband disturbance attenuation, the conditions for closed loop stability of the electromechanical system are not clear. In the present research, a simplified mechanical model of a switch-shunted piezoceramic was first developed. This model was amenable to study as a hybrid or Witsenhausen switching system. Using the method of multiple Lyapunov functions, the simplified model was shown to be unstable for some switching strategies. Subsequently, a coupled electromechanical model was developed and used as the basis for numerical performance simulation. In this model, all switching strategies evaluated resulted in stable systems, although some exhibited considerably higher effective damping than others. These results indicate the importance of retaining electrical states in dynamical models of switched piezoelectric systems.