###### Abstract
Some researchers have implemented adaptive controls applied to active bearings to compensate the forces due to rotor imbalance [13]. There are even methods [14] specialized in diagnosing and correcting imbalance online, which are based on a spectral analysis in the time and frequency domain. [PERSON] [15] proposed the development of controls for imbalance due to system synchronization that is based on spectral and phase analyses combined with speed control. The instantaneous estimation of the velocity and the phase angle complemented with FFT is still a current topic for researchers such as [PERSON] et al. [16] who carried out the diagnosis and correction of the imbalance by transforming the effects of the fluctuations of the angular velocity into the angular domain. Recently, non-contact techniques have been used for the diagnosis of imbalance, obtaining the location of the unbalanced mass in 3D through a stereo video system, synchronized with high-speed cameras [17]. Other authors [18] have applied speed gradient integral-differential algorithms to control phase variation between two rotors in the time series as an alternative to solve the synchronization problems caused by the imbalance that was diagnosed in the field. More recent studies consider the effect that overheating generated by extreme operating conditions has on the imbalance and apply structural, thermal, and spectral analyses, as well as Campbell diagrams [19]. In recent years, many groups have studied the effect of friction on rotating components. Some authors studied the dynamic behavior of a rotor subjected to the friction generated by the contact between the rotor and the stator. They analyzed the trajectories in the subspaces using [PERSON]'s theory [20] and showed that the points of contact between surfaces strongly influence the behavior. Other studies focused on improving the prediction of the remaining life in bearings by characterizing the nonlinear responses of lubrication [21]. [PERSON] et al. [22] conducted some research on the nonlinear friction effect on rotor systems and they analyzed the structural design of the rotor with Stribeck curves to diagnose vibration faults. An overhung rotor with two degrees of freedom was proposed to determine friction during contact between the rotor and the stator [23]. Some recent work studied the effect of a bolted disk joint on the motion stability of the rotor bearing system and the friction coefficient on rotor dynamics using the fourth-order Runge-Kutta method [24]. These authors have complemented their work with other typical methodologies as bifurcation diagrams, waterfall plots, times series, orbit trails, phase plane portraits, and Poincare maps to characterize the nonlinear friction effects. Further, the rotor-stator interaction phenomenon was investigated by finite element and Lagrange multiplier-based contact mechanics [25]. An elastic support/dry friction damper and a two-dimensional friction model-ball/plate model were used for active vibration control by [PERSON] et al. [26]. [PERSON] and [PERSON] [27] proposed some study examples for friction vibration and instabilities. Essential contributions on aircraft brake systems were made by including friction-induced vibration [28; 29]. [PERSON] et al. [30] analyzed systems with planar and rectilinear friction by studying the mode coupling instability and proposed a new shooting method to calculate the self-sustained vibrations of non-smooth contact dynamical systems for systems with planar friction [31]. Furthermore, friction and damping models, including the friction plane, were proposed by [PERSON] et al. [32] to obtain physical amplitudes in the nonlinear analysis of friction-induced vibrations of a rotor-stator. Additionally, [PERSON] et al. [33] applied deep learning to reduce energy losses due to vibration and friction in rotor bearing, to control the clearance in the bearings, the hydrodynamic force, and the trajectory of the rotor.