## 2 Application to Flexible Structures
### Other Structural Applications  
[PERSON] and [PERSON] designed a direct adaptive controller and applied it to an SMA actuator to reduce the measurement noise and estimate the system states by compensating the hysteresis behavior [67]. [PERSON] and [PERSON] presented a temperature feedback approach to control the radius of arc-shaped SMA wire using the pulse width modulation (PWM) \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **Control Type** & **Controller** & **Application** \\ \hline
[15] & & \
\begin{tabular}{c} Hoo controller based on the \\ state space model \\ \end{tabular} &
\begin{tabular}{c} vibration control of a \\ flexible beam \\ \end{tabular} \\ \hline
[28] & & \
\begin{tabular}{c} gain-scheduled Hoo \\ controller \\ \end{tabular} &
\begin{tabular}{c} vibration control of a \\ cantilever beam \\ \end{tabular} \\ \hline
[38] & Robust Control & \
\begin{tabular}{c} adaptive sliding mode \\ controller \\ \end{tabular} &
\begin{tabular}{c} vibration control of a \\ flexible needle \\ \end{tabular} \\ \hline
[51] & & \
\begin{tabular}{c} penalty-based sliding mode \\ control law \\ \end{tabular} &
\begin{tabular}{c} vibration control of a \\ flexible bar \\ \end{tabular} \\ \hline
[63] & & \
\begin{tabular}{c} adaptive sliding mode \\ controller \\ \end{tabular} &
\begin{tabular}{c} vibration control of a \\ two-link arm \\ \end{tabular} \\ \hline
[62] & Optimal Control & LQR controller &
\begin{tabular}{c} vibration control of a \\ one-link arm \\ \end{tabular} \\ \hline
[16] & & PI and PID controller &
\begin{tabular}{c} vibration control of a \\ flexible beam \\ \end{tabular} \\ \hline
[23] & PID Control & \
\begin{tabular}{c} hybrid control with PI \\ controller \\ \end{tabular} &
\begin{tabular}{c} control of large tip \\ deflection \\ \end{tabular} \\ \hline
[30] & & PID controller &
\begin{tabular}{c} vibration control of an \\ adaptive-passive beam \\ \end{tabular} \\ \hline
[18] & & \
\begin{tabular}{c} hybrid control based on \\ variable structure controller \\ \end{tabular} &
\begin{tabular}{c} position and stiffness \\ control of a flexible plate \\ \end{tabular} \\ \hline
[20] & & \
\begin{tabular}{c} operator-based controller \\ with hysteresis compensator \\ \end{tabular} &
\begin{tabular}{c} vibration control of a \\ flexible beam \\ \end{tabular} \\ \hline
[36] & & \
\begin{tabular}{c} interval type-2 fuzzy \\ controller \\ \end{tabular} &
\begin{tabular}{c} vibration control of a planar \\ structure \\ \end{tabular} \\ \hline
[64] & Others & \
\begin{tabular}{c} operator-based controller \\ \end{tabular} &
\begin{tabular}{c} vibration control of a \\ flexible arm \\ \end{tabular} \\ \hline
[65] & & \
\begin{tabular}{c} phase shift and neural \\ network controller \\ \end{tabular} &
\begin{tabular}{c} vibration control of rings \\ \end{tabular} \\ \hline
[66] & & \
\begin{tabular}{c} screw-type active controller \\ \end{tabular} &
\begin{tabular}{c} natural frequency control of \\ a cylindrical shell \\ \end{tabular} \\ \hline
[43] & & \
\begin{tabular}{c} passive control (stochastic \\ averaging method) \\ \end{tabular} &
\begin{tabular}{c} axial vibration control of \\ composite beam \\ \end{tabular} \\ \hline
[47] & Passive & \
\begin{tabular}{c} passive control \\ (self-regulation of the \\ stiffness) \\ \end{tabular} &
\begin{tabular}{c} vibration control of \\ fixed-fixed beam \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Control methods for flexible structures. method. The PWM-based nonlinear PID controller featuring a feedforward heat transfer model was realized to track the desired temperature trajectory [68]. [PERSON] et al. devised two antagonistic SMA wires and a mechanical joint coupled with a torsional spring to higher performance compared with the bias SMA actuator in which the differential SMA wire was used to increase the response speed, while the torsional spring was used to reduce the total stiffness of the SMA actuator itself [69].