Shape Memory Alloy (SMA) actuators have hard nonlinearity such as backlash-like hysteresis. As well, the dynamics model is hard to obtain quantitatively. Therefore, when the conventional controllers such as the model based controllers and the proportional integral derivative (PID) controllers well not tuned are used for tracking, steady-state errors and limit cycle problems are able to be generated.
Prior to applying control schemes to an SMA actuator, dynamics for a rotary and bias-type SMA actuator was derived and thoroughly examined using the modified Liang's kinetics model, which is the model that modify the original Liang's model to guarantee the continuity of martensite fraction and to enforce additional occurrence conditions of the phase transformation. The modified Liang's model could keep martensite fraction continuous at the change of phase transformation process but the original model couldn't. As well, it could illustrate the actual hysteresis very well but the original model couldn't. In order to verify the derived dynamics including the modified Liang's model, cyclic hysteresis tests were also performed and those showed that the dynamics could describe the characteristic of the SMA actuator very effectively. This derived dynamics was also used for the prediction of control performance and the selection of gains for the time delay control (TDC).
The dynamics consisted of first order linear equation and second order nonlinear equation. Accordingly, control strategy was established as follows: Main controllers such as the TDC is designed for regulating the only second order nonlinear part for simplicity and the internal closed loop is designed for regulating the rest of them. As the main controllers, the TDC and the sliding mode control (SMC) were considered. The sliding mode control with time delay estimation (SMCTE) was proposed to apply the sliding mode control (SMC) to the SMA actuator and its gain tuning method was also investigated to display the same performance as the TDC. In addition, other controllers with time delay estimation mentioned in literature as well as the SMCTE were reviewed and compared mathematically.
Through control simulations and experiments, six controllers were evaluated as in the following: the PID control tuned by Ziegler-Nichols method, the TDC, the PID control based on the TDC, the SMCTE without boundary layer, the SMCTE with boundary layer (SMCTEBL), the relay control (RC). Prior to applying these controllers, the control strategy was examined from the point of view of influence of anti-windup scheme and high gain tuning on control performance. Anti-windup scheme was essential to protect windup phenomenon and high gain tuning was effective when a temperature disturbance existed. In the robustness test, the TDC with high gains showed robustness to inertia variation and temperature disturbance in comparison to the PID control with low gains. Finally, comparing six controllers, the TDC, the PID based on the TDC and the SMCTEBL showed good control performance with respect to the following criteria: the settling time, the error mean, the range of error and the range of error velocity.
