## 3 Vibration Active Control  
Firstly, it is necessary to characterize the vibrational properties of the structure, i.e., to know how the parts of the structure vibrate, to understand and control the vibration. Thus, we enable anticipating vibration levels or determining the actions to control vibration. While passive noise control has been the predominant method used in tremor control applications, the search for ultimate vibration control has advanced to the extent that the use of active forces would be preferable to neutralize vibration. In this vibration control technique, called active vibration control (AVC), the controller coefficients are constantly updated by an adaptive algorithm. The AVC scheme, as highlighted in Figure 1, basically consists of the plant system (coefficients that characterize the behavior of the dynamic system), actuators, sensors, and controllers. For the tests carried out, two random white Gaussian signals with zero mean and unit variance, uncorrelated, are generated. In Figure 1, they are represented by the noise generator blocks and \(x(n)\). The signal \(x(n)\) is used to recognize the plant coefficients of the main loop (direct path) \(W(z)\); on the other hand, the noise generator is an anti-signal generated in the loop (or secondary path) for recognizing the coefficients of the filter \(S(z)\). The response of the input signal into the second loop in a finite impulse response (FIR) filter is used to filter the \(\mathbf{x}(n)\) signal, which in turn feeds the adaptive algorithm, which acts to both recognize and estimate the coefficients of the main loop and to control the noise signal through the secondary loop. Active vibration control based on adaptive finite impulse response (FIR) filters typically introduces a conditional signal dispersion delay [21]. The reasons for these delays are geometric arrangements and computational time associated with the use of analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). Delays represent a phase shift in periodic signals. These delays prevent the instant feedback of signals from the least mean square (LMS) algorithm, for example. This can lead to instability and even divergence of the algorithms. Studies have presented a modification of the LMS algorithm, adjusting the underlying gradient descent algorithm [22; 23; 24; 25] to work around this problem. The result is that any delays that occur can be fully compensated for. Different strategies are proposed for the use of the LMS algorithm in controlling noise and vibrations, usually taking into account that the LMS alone is not capable of attenuating unpredictable signals, such as physiological tremors, for example. Active vibration control applications usually rely on the action of external elements, especially the analog-to-digital and digital-to-analog conversion processes, called here the secondary path. In the presence of those processes, traditional algorithms, such as LMS or RLS (recursive least square), should not be applied, being that the solution to this problem lies in filtering the input signal, using an estimation of the secondary path. The filtered-x least mean square (Fx-LMS) and its variations, which serve as the basis for this analysis, is an alternative proposed by [PERSON] et al. [26]. The strategy adopted also in [17] uses the internal model control method (IMC; the internal model control systems are characterized by a control device composed by the controller and by a simulation of the process, the internal model), together with the Fx-LMS algorithm to suppress noise and vibrations. Its results show the robustness and segment of reference values. Some variations of the Fx-LMS algorithm are widely explored in [27; 28], which may serve as a basis for comparing vibration control strategies in a future research. In this work, some adaptive algorithms based on the least mean squares for active control of variable vibration systems are evaluated. The framework also uses an auxiliary filter to improve the online estimation of the secondary path.