Active control and stability analysis of flexible structures using nonlinear proof-mass actuators

Proof-mass actuators are highly advantageous for active control of structures, due to their large force-to-weight ratio and their ability to provide inertia without a ground reference. These devices comprise a proof-mass suspended in a magnetic field that is accelerated by an input voltage, in order to provide a reaction force on the actuator casing and the structure itself. However, if the input voltage is large, the proof-mass will hit the end-stops, thereby imparting large shocks to the structure that may destabilise the closed-loop system. To ensure that the closed-loop system is asymptotically stable, a control law that counteracts the destabilising effects of stroke saturation must be designed. First, a numerical study is conduced, where a dynamic model of a Micromega IA-01 proof-mass actuator is coupled to a flexible structure in a collocated pure-gain velocity-feedback closed-loop configuration. Using Lyapunov's direct method, it is shown that stroke saturation greatly reduces the closed-loop stability margin, due to large increases in the kinetic energy as the proof-mass moves from one end stop to the other. Finally, an alternative on-off feedback control strategy is briefly investigated, and its merits and drawbacks are discussed.