(i) A Nitinol wire actuator is constructed from a bundle of 10 wires each of 0.4 mm diameter and length 200 mm. In a test, each wire is initially strained in the martensite phase by 2% at a...

(i) A Nitinol wire actuator is constructed from a bundle of 10 wires each of 0.4 mm diameter and length 200 mm. In a test, each wire is initially strained in the martensite phase by 2% at a temperature below Mf and rigidly fixed at the two ends. The wire is heated beyond the austenite finish temperature Af. Estimate the force generated. (ii) Each wire in the actuator is attached to a rigid body that is restrained by a stiff spring with a stiffness of 10 N/mm. Estimate the displacement of the rigid body as well as the strain and force developed in each wire. (iii) Ignoring all hysteresis and non-linear effects design a controller for the closed-loop control of the actuator. Assume the heating dynamics to be represented by a first-order lag. (iv) Introduce the hysteresis in the martensite fraction–temperature relationship and optimize the controller for closed-loop performance.