## 1 Introduction  
In the fields of aerospace, robotics, civil engineering and other industries, flexible structures are prevailing due to their advantages of lightweight and lower energy consumption. However, flexible structures are highly resonant systems and exhibit the inherent property of vibration in presence of external disturbances, which leads to a deterioration of positioning accuracy and efficiency. Thus, vibration suppression of those multi-mode structures becomes imperative [1]. In recent years, smart materials have been extensively used for vibration control of flexible structures. Those materials include shape memory alloys, piezoelectric transducers and so on [2]. Among them, piezoelectric materials have the advantages of small volume, fast response and can be easily integrated onto the host structures. As a result, active vibration control of smart structures utilizing piezoelectric materials has become more attractive [3]. To obtain a better performance for vibration suppression of flexible structures, both accurate dynamic modeling and suitable controller design are required. Controller design often relies on accurate modeling of the system dynamics [4]. In most previous studies, various efficient approaches have been proposed to establish the mathematical model of smart flexible structures. In general,dynamic behaviors of flexible structures can be obtained by analytical modeling based on partial differential equations (PDEs) [5]. However, it is difficult to simulate the properties of a relatively complicated system accurately. In some cases, it is intractable, even impossible, to find the system differential equations. In addition, the introduction of piezoelectric actuators/sensors adds complexity to the analytical modeling. Numerical approaches based on finite element method (FEM) are developed to obtain equivalent finite-dimensional models of smart structures, and yield fairly accurate results [6]. However, these approaches always require intensive mathematical derivations, which are usually labor intensive and time consuming. Meanwhile, these modeling techniques are sometimes hindered by factors such as the assumption of ideal boundary conditions, perfect bonding between the host and actuators/sensors, and so on [7]. An alternative modeling approach is system identification, which captures the input-output dynamics of smart structures using experimental data. Moreover, the issues of the sensor/actuator dynamics, signal conditioners and control unit are all included in the experimental model. Thus, the established model faithfully represents the dynamics of the flexible structures incorporated with smart materials, and the tangled mathematic calculations are also avoided. The identification process can be conducted in the frequency domain, or in the time domain. Among those time domain methods, [PERSON] et al. [8] presented an experimental model of a flexible beam system incorporated with piezoceramic actuators based on the ARMAX (auto-regressive moving average exogenous) model. [PERSON] et al. [9] derived a time-domain state space model of a flexible structure using the observer/Kalman filter identification method together with an eigensystem realization algorithm. [PERSON] et al. [10] employed the genetic algorithm (GA) to identify the model parameters of a linear difference equation for a rectangular flexible plate system. [PERSON] et al. [11] utilized a prediction error method to obtain the ARMAX model of a flexible beam bonded with piezoceramic actuator/sensor, and implemented a model reduction method to find the amenable reduced order. [PERSON] and [PERSON] [12] developed a nonlinear ARMAX model of a planar two-link flexible manipulator system, and designed a nonlinear adaptive controller based on the identified model. Flexible structures are distributed parameter systems, thus have multiple vibration modes, which display highly resonant behavior near to the structures' natural frequencies.