(i) A Nitinol wire actuator is constructed from a bundle of 10 wires each of 0.4 mm diameter and...

(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.