Analysis of friction-induced oscillation in negative stiffness control system

The effect of friction on a negative stiffness control system is investigated. The series combination of isolators of negative and positive stiffness of equal magnitude provides infinite stiffness as well as zero compliance of the vibration isolation table against direct static load. However the performance of negative stiffness control system is affected by friction adversely. In another word, nonlinear friction causes an adverse effect to the negative stiffness control system, such as limit cycle. In the present work, the friction induced limit cycle of the negative stiffness control system is identified by using describing function method. The intersection of linear and nonlinear part of the control system in the same complex plane reveals the existence of limit cycle which varies according to the control parameters. Hence the relationship between the stiffness of the negative stiffness control system and induced limit cycle (frequency and amplitude) is established theoretically. The induced limit cycle behavior is determined by the conditions of nonlinear part at the points of intersection. Finally the theoretical limit cycle for a specific set of control parameters in designing the controller is verified by experimental result under the same conditions.