Time-delay control of a switchable stiffness system

This paper focuses on suppression of free vibration of single degree-of-freedom systems that possess time delay. The switchable stiffness (SS) control strategy is reviewed. The implication of time delay is examined. It shows that the system delay can cause malfunction of the direct SS control. To overcome this problem, the two time-delay control strategies are proposed. The first strategy named as half period delay SS control introduces an intentional delay such that the switch action takes place in a half of oscillation period later. The second strategy named as quarter period delay SS control is to add an intentional delay such that the switch action occurs in a quarter of oscillation period later. In this case, the SS control law is inverted. An apparatus consisting of an electromagnetic (EM) spring is developed to validate the proposed strategies. The stiffness models of the system are established. In computer simulation, three cases have been examined. In case A, the system is simplified as linear and the dynamics of the EMs is neglected. In case B, the stiffness models are used and the dynamics of the EMs is neglected. In case C, the stiffness models are used and the dynamics of the EMs is considered. An experimental study is conducted in real time. The results have validated the observations obtained from the computer simulations.