Modeling, simulation, and optimal control of a shape memory alloy actuator (original) (raw)
Shape memory alloys possess unique thermomechanical properties that make them the subject of many scientific research papers. Nickel Titanium, also known as Nitinol, the most frequently used shape memory alloy, responds to changes in the stress and temperature fields with remarkable mechanical properties, such as shape memory effect and super-elasticity, which can be used for sensing and actuation purposes. In this paper, mathematical models for the isothermal and non-isothermal conditions of a shape memory alloy actuator are developed by considering a single degree of freedom oscillator with a nonlinear spring acting as shape memory alloy. In the first part of the paper, we investigate the isothermal condition of the SMA actuator by choosing a constant temperature where the SMA exists either in a single phase. A model for the matensitic phase is developed based on Landau-Ginzburg-Devonshire theory that defines the free energy in a polynomial form enabling the description of the SMA shape memory effect (SME) and pseudoelasticity. The resulting model is then linearized, and a linear quadratic regulator (LQR) controller is used to stabilize the system around a stable equilibrium. In the second part, the non-isothermal condition of the SMA is investigated by constructing a thermo-mechanical model. Due to the complexity of the derived thermo-mechanical model, and the need to control its response, a reduced-order model based on the Galerkin method is derive and analyzed. A linear feedback control strategy for nonlinear systems is then implemented to design a controller for reference input tracking.
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