Analysis and control of nonlinear vibration in inertial actuators

Abstract

Proof-mass actuators are typically used to supply a secondary control force to a supporting structure for the purpose of improving its performance through active vibration control. These devices comprise a magnetic proof-mass that accelerates in response to an input current, and the resulting inertia provides a reaction force on the actuator casing and the structure itself. Due to design constraints and the need to prevent actuator damage, the displacement of the proof-mass is usually bounded by its stroke length, which is determined by the distance between the actuator end stops. If the proof-mass reaches the end of the stroke, it will collide with the end stops, thereby imparting large shocks to the supporting structure that may destabilise the closed-loop system. This phenomenon, known as stroke saturation, is strongly nonlinear and invalidates the linear Nyquist stability criterion, which significantly complicates the assessment of closed-loop stability. As an example, stroke saturation may occur when using proof-mass actuators in active car suspensions, due to large impulsive forces from the road.

The aim of this thesis is to examine the dynamical behaviour of several proof-mass actuators using experimental measurements, including the effects of stroke saturation and other nonlinearities. The experimental data is used to establish a Simulink model of an inertial actuator by applying nonlinear identifcation techniques. It is found that the actuator dynamics can be represented using a nonlinear single-degree-of-freedom system, where the actuator nonlinearities are modelled using various polynomial and piecewise terms. This is conformed by comparing the model results with the experimental data.

Using the Simulink model, it is shown that the actuator nonlinearities significantly reduce the closed-loop gain margin by exploiting regions of potential instability that are present in the underlying linear closed-loop system. Therefore, the relationship between the actuator nonlinearities and the closed-loop stability depends on the choice of underlying linear controller, as the actuator nonlinearities tend to accentuate underlying stability issues rather than induce instability by themselves.

To prevent stroke saturation from destabilising the closed-loop system, an on-off control law may be applied by implementing a knock detector and deactivating the control signal for a short time period once stroke saturation is detected. Provided that a suitable deactivation period is specified, the on-off control law is able to prevent stroke saturation from destabilising the closed-loop system, thereby increasing the closed-loop gain margin.

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