## 2 Application to Flexible Structures
### Structural Vibration Control  
Studies on the application of SMA actuators for vibration control of various flexible structures with beams and plates have been continuously reported. [PERSON] and [PERSON] designed the H-inf controller based on the state space model governing the motion of SMA-beam structure and experimentally implemented the controller to effectively reduce unwanted vibrations in both transient and forced vibration cases [15]. [PERSON] et al. implemented several control algorithms associated with an SMA actuator to control unwanted vibrations of a flexible beam [16]. They formulated the online recursive square parameter estimator based on the auto-regressive model and evaluated control efficiency of an on-off controller; proportional and integral (PI) controller; and proportional, integral, and derivative (PID) controller. [PERSON] and [PERSON] proposed a passive control method by developing a composite structure reinforced with super-elastic shape memory wires and showed the increment of the tensile strength by activating SMA wires [17]. [PERSON] et al. carried out both vibration and position control of a flexible structure using two SMA springs that are integrated with the variable structure controller and the pulse width modulation method [18]. [PERSON] and [PERSON] introduced an elastic compensation system to resolve drawbacks of the SMA actuator: short stroke and inhomogeneity of useful force over the stroke in which a rocker-arm compensating mechanism was used as a proof-of-concept actuator [19]. [PERSON] et al. proposed a new method of operator-based nonlinear vibration control of a flexible arm using an SMA actuator in which the input is determined Lipschitz condition and robust right coprime factorization condition based on the Prandtl-Ishlinskii hysteresis model [20]. The configuration of the vibration control system of a representative flexible beam structure is shown in Figure 2.  
[PERSON] et al. presented the passive vibration control capability of SMA composite beams subjected to various blast pulses where the influence of temperature, place, prestrain, and thickness of SMA layers have been investigated through the transient response in time domain [21]. [PERSON] et al. proposed an SMA actuator with a helical coil spring shape for the vibration control of a single-degree-of-freedom system subjected to unbalanced excitement force in which the control of complex stiffness to reduce the resonance vibration has been emphasized [22]. [PERSON] and [PERSON] implemented a hybrid controller consisting of the inverse of the generalized Prandtl-Ishlinskii hysteresis model and PI controller for accurate deflection control by decreasing the steady state error of a large deformation structure [23]. [PERSON] et al. developed a variable stiffness fabric using  
Figure 1: The schematic location of SMA actuator for vibration control of flexible structures. (**a**) Beam external; (**b**) Plate/Composite embedded; (**c**) Film bonded to the surface. SMA covered with a shape memory polymer (SMP)-based thin film and its mechanical property showing the force versus deflection was investigated at different temperatures [24]. [PERSON] et al. manufactured an SMA beam by heat treatment after spray deposition to achieve high damping capacity quantified based on the concept of Hilbert transform [25]. [PERSON] and [PERSON] investigated the vibration control problem with broadband and nonrigid systems retaining periodic structures using a semi-two-dimensional model associated with SMA branches and non-SMA dual beams in which unwanted vibrations were attenuated in a broadband frequency by applying proper temperatures to SMA branches [26]. [PERSON] et al. proposed an active device for vibration control of the rotor dynamic system using SMA metal rubber where vibration amplitude was evaluated as a function of the critical speed [27].