Enhanced robustness for vibration control by means of piezo-actuators shunted to RL impedances

Semi-passive vibration attenuation by means of shunted piezo-actuators is gaining more and more interest in research and industry thanks to its capability to provide satisfactory performances without high costs. This is made possible by the absence of active controllers, which implies the use of expensive electronics. These semi-passive controllers rely on a properly designed electric impedance, which is then shunted to the actuators. The structure of the impedance depends on which kind of control is required (i.e. monomodal, multi-modal, broad-band). In case of mono-modal attenuation, the impedance is usually constituted by the series of a resistance R and an inductance L. The electrical system made up of R, L and the capacitance of the piezo-actuator constitutes a resonant circuit, whose eigenfrequency and damping must be tuned according to the characteristics of the mechanical system to be controlled. Thus, the transfer function between the disturbance and the structure vibration under controlled conditions depends on the values of R and L. Different formulations to tune R and L are available in the literature for an optimised choice of these values. Nevertheless, there is a big issue concerned with such a control strategy: the control RL impedance is fixed and thus this kind of control is not able to respond to possible changes of the mechanical system under control. As an example, a temperature change can cause an eigenfrequency shift and this can make the control ineffective. This paper investigates how to increase the robustness of RL controllers in order to extend their effectiveness to time-varying mechanical systems. This is achieved by building an analytical model, which is then used to test different strategies to choose the values of R and L. Numerical simulations are carried out to find the best algorithm to tune R and L to increase robustness. Finally, experimental tests are performed to validate the conclusion reckoned by simulations. The algorithm chosen in the end to extend RL control robustness can be used with any type of structure (e.g. beams, plates) and is capable to provide the values of R and L a priori (i.e. only knowing mechanical and electrical parameters of the structure and the actuator respectively) by means of analytical formulas.