Comparison of Control Laws for Vibration Suppression Based on Energy Consumption

Abstract

The research study presented here examines four conventional vibration suppression control laws and four hybrid modifications of these laws using a switching method. The motivation is to determine which of these eight controllers results in the least amount of power flow to the actuator to have the same settling time under free vibrations. The reason to look at reduced energy controllers is the idea that in some applications, very little energy is available for control, yet passive and semi-active methods cannot meet performance demands. In particular, the eventual goal is to reduce transient vibrations of smart structures using energy obtained from harvesting and/or low-power storage devices (batteries or super capacitors), as often desirable in aerospace systems. The four conventional active control systems compared in this study are Positive Position Feedback (PPF) control, Proportional Integral Derivative (PID) control, non-linear control, and Linear Quadratic Regulator (LQR) controls. A hybrid version of each controller is obtained by implementing a bang-bang control law (on-off control). The bang-bang control algorithm switches the control voltage between an external voltage supply and the feedback signal provided by the PPF, PID, non-linear, or LQR controllers. The purpose of combining the bang-bang control law with the aforementioned controllers is to reduce the power requirement for vibration suppression by providing an active controller with limited voltage input. Free vibrations of a thin cantilevered beam with a piezoceramic transducer are controlled by these eight controllers with a focus on the fundamental transverse vibration mode. Experimental results exhibit that the system with hybrid bang-bang-non-linear controller requires 67.3% less power than its conventional version. The hybrid versions require significantly less power flow compared to their conventional counterparts for the PPF, PID, and LQR controllers as well. Experiments also reveal the presence of substantial piezoelectric non-linearities in the transducer. The voltage-dependent behavior of the electromechanical coupling coefficient is identified empirically and represented by a curve-fit expression. A real-time adaptive control algorithm is developed to account for the voltage-dependent behavior of the coupling coefficient, enabling good agreement between the simulation and experimental results.