## 1 Introduction
These schemes include positive position feedback [21; 22], acceleration feedback [23; 24], full-state feedback [25], dynamic hysteresis compensators [26], pole placement control [27], and a hybrid of variable structure control and Lyapunov-based control [28]. Decoupled models were proposed to manage many degrees of freedom (DOF), and a backstepping method was introduced to design a robust controller with sliding mode and adaptive strategies [29]. To avoid the high computational burden of full-order controllers, a direct minimization method was introduced to design reduced-order H-infinity controllers and genetic algorithms [30]. The conventional approaches for active vibration control are often too complicated and thus difficult to implement. Furthermore, the control targets have to be determined, which limits the tracking, convergence, and stability performance. If a correct mathematical model of flexible structures can be derived, the structures can be regulated actively to isolate the structural vibration. However, several control schemes show performance degradation when the model is not precise enough and the structural dynamics varies with time due to structural modifications. To solve these issues, a simple and robust control algorithm should be developed without any correlation to the original structural dynamics and with low computational burden. This study uses an enhanced active vibration control method attenuate the vibration of a nonlinear elastic smart structure. A new control scheme called as the sliding mode least mean squares (SM-LMS) algorithm is proposed and validated both numerically and experimentally [31]. The control algorithm combines the optimal control characteristics of the least mean squares algorithm with the robustness of sliding mode control (SMC). It has been shown that SM-LMS can be successfully used for the displacement control of piezoelectric actuators [32]. However, no study has applied SM-LMS to the active vibration control of flexible structures. To validate the scheme, the controller was implemented on a smart structure constructed with an aluminum beam with two PZT actuators attached to form a bimorph structure and one PZT sensor. For the actual tests, we would not know the exact model of the system due to unknown changes in the operating environment, and the plant may vary over time. This changes the control parameters needed to achieve the best tracking performance. Thus, experiments of two different cases were prepared: (1) control for a baseline structure; and (2) control for a structure with additional dynamics that cannot be predicted. Additional impedance is added to the baseline structure to simulate a sudden change in the plant. The scope is limited to a single-input single-output system, and the first four peaks of the disturbance plant (the natural modes) are considered. Specific objectives of this research are described below. 1. Introduce the characteristics of the novel nonlinear control methodology (sliding mode least mean squares) and examine the performance on active vibration control through numerical simulations. 2. Identify the dynamic model of the active beam in the frequency domain with an impact hammer test. Estimate parameters of the linear beam model through a frequency domain identification method. 3. Conduct numerical validations with a conventional approach for attenuating vibration level of the structure under impulsive excitations and observe limitations. 4. Conduct experimental validations and examine the performance of the controller for the baseline structure and the modified structures in order to show the robustness of the new control technique.