Analysis, Simulation, and Control of Vibration in SMA Consisiting Systems

The procedure of modeling+of shape memory alloy (SMA) dynamics and the corresponding computerized algorithm are described extensively in this paper. In shape memory alloys, due to the existence of the Martensite and Austenite phases in the microscopic structure of the alloy and also conversion between the phases, the elasticity modulus of the material shows a time varying behavior, while the structures of the equations describing the dynamics of the system remain similar to the ones with constant elasticity modulus. To evaluate the effect of conversion between phases on the elasticity modulus, the Martensite to Austenite volume fraction is of the main concern. Therefore, the mentioned elasticity modulus can be modeled as an oscillating spring-damper-mass system with variable parameters. Then, a new chattering alleviation algorithm for sliding mode control (SMC) of non-linear systems is presented. In the new method, a mathematical function for regulating parameter is introduced. Due to the initial choice of this parameter by designer, the state vector of the system approaches the sliding surface with any arbitrary speed and enters the boundary layer surrounding the sliding surface, while the state vector does not include fast behaviors through the boundary layer. To show the abilities and the merits of the aforementioned regulating routine on the vibration control of a SMA system, simulations are carried out within Simulink environment. The results show that our proposed algorithm has positive effects on the control system performance, while the 5% uncertainity in the elasticity module has no effect on it.