## 6 Conclusions  
Adaptive algorithms usually have a complex nature, which demands a need for knowledge of statistics, mathematics, signal processing, and computing tools. This work sought to collaborate by presenting a discussion about these algorithms and a sequence of scientific tests that would allow their application in problems of mechanical, electronic, computing, and biomedical engineering. Computational modeling and simulations have been used in several areas, especially biomedical engineering to support product development and evaluation of strategies [41]. This type of approach allows methods to be evaluated prior to experiments on humans.  
The bibliographic review allowed the construction and survey of the necessary concepts for the application of adaptive filtering techniques in order to actively control vibration. In addition, information about the problem to be solved and knowledge of the vibratory patterns are mentioned here. This search was based on mathematical models, avoiding the need for the invasive data collection on patients.  
From the obtained results, it was noticed a great sensitivity to the model, the family of algorithms, and the parameters used. Active control of physiological and Parkinsonian tremors was presented using algorithms from the adaptive LMS family. The Fx-LMS-NLMS algorithm showed the best response among the algorithms used in this research. Its difference from the others, Fx-LMS and Fx-NLMS, is only in the number of iterations. The algorithm that obtained the slowest response was the result of non-normalization in the primary mesh, where the plant of the system is initially recognized. The Fx-LMS algorithm is traditionally used in strokes, and can, in a way, serve as a parameter in relation to its variations, per hour used in the control of physiological tremors.  
To provide active control of Parkinsonian tremors, the Fsinx-LMS algorithm was presented. Derived from Fx-LMS, this algorithm has only one additional block for the non-linearization of generated random signals, producing a random phase sinusoid. This was necessary so that the non-linearities of the model could be mapped by the adaptive system. It shows that there is a way to control deterministic and non-linear tremors, such as the tremor of [PERSON]'s disease, through LMS-type algorithms, provided that the generated signals are non-linear.  
This study can be extended to other types of algorithms, especially for Parkinsonian tremors. In this case, kernelized algorithms can produce better results in systems with non-linear characteristics present in models that replicate this type of pathology. These algorithms have been applied by the scientific community and produced good results. Other approaches for estimating nonlinear systems can yet be considered, such as [37; 38; 42; 43; 44].  
In addition, an implementation in embedded devices, DSP boards (digital signal processor) can improve the understanding of the behavior of these algorithms in a practical scenario, which would later serve as a basis for the development of an electronic prototype with the embedded technology composed of a sensor and actuator to provide active control.  
Conceptualization, R.S.A.A., W.D.P. and R.C.B.; methodology, R.S.A.A. and W.D.P.; analysis, R.S.A.A., J.C.T., W.D.P. and R.C.B.; writing--original draft preparation, R.S.A.A., W.D.P., R.C.B. and J.C.T.; writing--review and editing, R.S.A.A., V.R.Q.L., W.D.P., J.F.D.P.S. and R.C.B. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Fundacao para a Ciencia e a Tecnologia, I.P. (Portuguese Foundation for Science and Technology) by the project UIDB/05064/2020 (VALORIZA--Research Centre for Endogenous Resource 764 Valorization), and Project UIDB/04111/2020, ILIND--Instituto Lusofono de Investigacao e Desenvolvimento, under project COFAC/ILIND/ COPELABS/3/2020.