Downscaling of proof mass electrodynamic actuators for decentralized velocity feedback control on a panel

Abstract

This paper presents a simulation study on the downscaling of multiple electrodynamic proof mass actuators for the implementation of decentralized velocity feedback control loops on a thin panel. The system is conceived to reduce the panel response and sound radiation at low resonance frequencies. In the first part of the paper, the principal downscaling laws of a single proof mass actuator are revisited. In particular, the scaling laws are given for: (a) the fundamental natural frequency, (b) the damping factor, (c) the static displacement, (d) the maximum current that can be fed back to the actuator, (e) the maximum stroke of the proof mass and (f) the maximum control force that can be produced by the actuator. The second part of the paper presents a numerical study concerning the control performance produced by decentralized control systems with an increasing number of control units, which are scaled down in such a way as to keep the total base surface occupied by the actuators constant. This study shows that the control performance tends to rise as the number of control units is increased. However, this trend is reversed for large arrays of small scale actuators since the gain margin of the feedback loops tends to decrease with downscaling and incrementation of the actuators density.

Scaling of electromagnetic transducers for shunt damping and energy harvesting

“…The resistivity of the coil material does not depend of the scale of the transducer, but the volume of the coil clearly scales as the cube of characteristic length of the transducer, L, so that it scales as [L 3 ] in the notation used in reference [8][9][10], for example. The magnetic flux density is assumed to be saturated in a well-designed transducer, so this depends on the properties of the materials that the transducer is made from, but not its dimensions.…”

“…Another difference is that whereas an electromagnetic device, being velocity controlled, can add damping when short circuit, the piezoelectric device, being displacement controlled, is dominated by its stiffness when either open or short circuit and so requires a resistive element in the shunt to provide a damping impedance. Nevertheless, we can define an electromechanical coupling coefficient for this piezoelectric case, by taking the analogy between equation (A.6) and equation (10), as:…”

“…Gardonio et al [10], for example, show that the devices natural frequency, = / , scales as [L -1 ] and that the static displacement due to gravity, / , where is the acceleration due to gravity, scales as [L 2 ]. As the actuator gets larger, its natural frequency tends to fall, as expected, but of more concern is that its static displacement due to gravity will become large rather quickly.…”

Identification and analysis of nonlinear dynamics of inertial actuators

“…A velocity feedback controller consists of an actuator attached to a structure with a collocated sensor of vibration (usually an accelerometer) and a controller, which feeds back the velocity of the structure to the actuator [5]. The use of an electromagnetic inertial, or proof mass, actuator as the active forcing device in velocity feedback controllers has also been well documented [2,5,[7][8][9][10][11][12][13][14]. An inertial actuator consists of a magnetic proof mass, an electrical winding and a suspension, which connects the proof mass to a casing or base mass [7].…”

“…One of the harshest nonlinearity that affects the dynamic behaviour of an inertial actuator is stroke saturation. The displacement saturation phenomenon in inertial actuators has been investigated in [8,22,24,25,[30][31][32]. We investigate in detail the phenomenon of stroke saturation, and also show the results of the same methodology applied to several actuators with weaker and different kind of nonlinearities This paper investigates the nonlinear behaviour of inertial actuators and provides a methodology for detection, characterisation and identification of the nonlinear parameters.…”