the resistance per unit length h is the coefficient of convection a u03c0d is the circumferential area of cooling d is the diameter of the wire t is the temperature and t a is the ambient temperature the coefficient h is assumed to have the characteristics of a second order polynomial to enhance the rate of convection at higher temperatures as observed in open loop results the constitutive equation relating changes in stress strain temperature and mole fraction is given by the following equation where u03c3 is the stress in the sma d is the average of the young 39 s moduli for the martensite and austenite phases u03b5 is the strain u03b8 t is the thermal expansion factor and u03c9 is the phase transformation contribution factor the model explains the hysteresis as well as the minor loops in the hysteresis as illustrated in fig7 the dynamic characteristics of the sma are completely defined by equation 4 or 5 heating or cooling together with equations 6 and 8 the u03c3 e is defined as the integral of the error i e where u03b5 is the strain of the sma actuator and u03b5 ref is the reference trajectory the dynamic equations of the sma along with equation 9 can be represented in the state space form and u is the input voltage to the sma wire the nonlinear equations are linearized about a set of operating points u03b5 0 t 0 u03be 0 u 0 on the reference trajectory to obtain the operating points u03b5 0 is chosen as the value of the reference strain at that instant of time t.