## 5 Results
### Simulation Result of Physiological Tremors Control  
The results of this research are presented by comparing the algorithms Fx-LMS, Fx-NLMS, and LMS. In the first and second scenarios, the adaptive filters (Figure 1) were updated using the Fx-LMS and Fx-NLMS algorithms, respectively. In the third scenario, a hybrid condition was considered, in which the adaptive filter corresponding to the direct path is updated by the Fx-LMS algorithm and the filter in the secondary path is updated by the Fx-NLMS algorithm. The basic difference between the three scenarios is in the normalization of the error signal of the main and secondary loops. In Scenario 1, Fx-LMS, there is no normalization of the error signal data of the algorithm loops. In Scenario 2, Fx-NLMS, there is data normalization in both the main and secondary mesh. In Scenario 3, Fx-LMS-NLMS, the normalization is done only in the secondary path. * Scenario 1 (Fx-LMS): The behavior of the Fx-LMS algorithm (Scenario 1) in the active control of physiological tremor vibration is shown in Figure 6. The steady state is reached after approximately 4000 samples. Figure 7 presents the power spectral density (PSD) which quantifies the error distribution over the frequency spectrum. Figure 5: [PERSON]’s tremor signal in the frequency domain. * Scenario 2 (Fx-NLMS): The Fx-NLMS algorithm has normalized data in both the main and secondary loops, and its result for controlling the physiological tremor signal is illustrated by Figure 8. In this case, approximately 4500 samples are needed for the control signal to converge, following the reference values, and it is enough to minimize the tremors. In Figure 9, we present the power spectral density (PSD) to quantify the error distribution over the frequency spectrum. Figure 6: Control evaluation results produced by the Fx-LMS algorithm for 30 runs of a Monte Carlo simulation. Figure 7: Behavior of the power spectral density (PSD) of the error signal by Fx-LMS. * Scenario 3 (Fx-LMS&NLMS): In Scenario 3, the hybrid, the control structure uses the Fx-LMS-NLMS algorithms, which have normalized data in the secondary loop error. This arrangement of algorithms is a suggestion of this work regarding a change in the normalization of the secondary path only. This combination enables a gain in performance. Figure 10 shows the control result of the algorithm, where the steady state is reached with approximately 4000 samples. Figure 11 provides a clear and quantitative analysis of the frequency content of the error signal. Figure 8: Control evaluation results produced by the Fx-NLMS algorithm for 30 runs of a Monte Carlo simulation. Figure 9: Behavior of the power spectral density (PSD) of the error signal by Fx-NLMS. The Fx-LMS and Fx-NLMS algorithms, implemented in Scenarios 1 and 2, respectively, presented a similar mean squared error attenuation level. The most relevant difference in behavior occurred in the convergence times of each one of them. The Fx-LMS algorithm reached an error of \(-22\) dB in 4000 samples, 500 less than the time obtained in Scenario 2. The Fx-LMS-NLMS algorithm, implemented in Scenario 3, proved to be faster if compared to the NLMS algorithm, requiring 4000 samples to carry out the active control, a reduction of 30% compared to Scenarios 1 and 2. This result can be attributed to fast response due to normalized filtering in the modeling of the only plant of \(\mathbf{S}(z)\). This comparison can be seen in Figure 12.  
Figure 11: Behavior of the power spectral density (PSD) of the error signal by Fx-LMS–NLMS. Figure 10: Control evaluation by the Fx-LMS–NLMS algorithm for 30 runs of a Monte Carlo simulation. It is clear that an analysis in terms of computational complexity is necessary for a cost-benefit assessment. However, in a scenario where there is no complexity restriction, Ex-LMS-NLMS achieved faster convergence. Table 2 presents more clearly the final comparison of the results in terms of the number of iterations and the amplitude and attenuation of the tremors in terms of square mean errors.