Dal Borgo, Mattia
(2019)
Active vibration control using a nonlinear inertial actuator.
*University of Southampton, Doctoral Thesis*, 204pp.

## Abstract

This thesis presents a theoretical and experimental study of a stroke limited inertial actuator used in active vibration control. The active control system under investigation consists of an inertial actuator attached to a lightweight ﬂexible structure, a collocated vibration sensor and a velocity feedback controller (VFC). Since the control force is generated by accelerating the proof mass, controlling low frequency motions or large amplitude vibrations requires a very long stroke for the proof mass. One of the main limitations of inertial actuators is that the stroke length is ﬁnite, however. This not only limits the amount of force available from the actuator but also when the proof mass hits the end-stops it causes impulse-like excitations that are transmitted to the structure and may result in damage. Additionally, the shocks produced by the impacts between the proof mass and the end-stops are in phase with the velocity of the structure, leading to a reduction of the overall damping of the system, which can give rise to instability of the system and limit cycle oscillations.

This research examines the implementation of a nonlinear feedback controller to avoid collisions of the proof mass with the actuator’s end-stops, thus preventing this instability.

The nonlinear model of a stroke limited inertial actuator is ﬁrst identiﬁed using base and direct excitation experiments and a parameter estimation process. A nonlinear feedback control (NLFC) strategy is then presented, which actively increases the internal damping of the actuator when the proof mass approaches the end-stops. The experimental implementation of the NLFC is investigated for the control of a cantilever beam, and it is shown that the robustness of the VFC system to external perturbations is much improved with the NLFC. Finally, a virtual sensing approach based on an extended Kalman ﬁlter algorithm is discussed for the real-time estimation of the states of the proof mass that is used to calculate the feedback signal of the NLFC. It is shown experimentally that larger velocity feedback gains can be used without the system becoming unstable when the NLFC is adopted and the theoretical reasons for this increase in stability margin are explored.

**FINAL e-thesis for e-prints DAL BORGO 28169786 - Version of Record**

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