Limit cycle analysis of a nonlinear controller for a proof-mass actuator

Proof-mass actuators have been proposed as actuators for vibration suppression in flexible structures. While these actuators have a favorable force-to-weight ratio, the finite travel of the proofmass, called the stroke length, imposes restrictions on the use of the actuator. The stroke length limits the amount of force available from the actuator. In addition, if the proof-mass runs against its stops, called here stroke saturation, shocks (high frequency disturbances) are imparted to the structure and damage may result. To increase the operating region for a given structure without increasing the mass of the proof-mass and/or the stroke length, several nonlinear control laws have been proposed to manage the proof-mass. The presence of a nonlinearity in the system, however, introduces the possibility of a limit cycle. Furthermore, we discuss the relationship between the various nonlinearities and the possible existence of limit cycles.