# Novel Real-Time Acoustic Power Estimation for Dynamic Thermoacoustic Control
## 5 Conclusions  
This paper has introduced a novel methodology for the real-time estimation of acoustic power in thermoacoustic systems, overcoming the limitations of traditional methods based on temporal averaging. The approach focuses on continuously acquiring and adjusting measurements of acoustic wave pressure, enabling the instantaneous estimation of acoustic power. Two methods for estimating the power delivered to the load have been evaluated: (method 1) instantaneous power evaluation, which calculates the power consumed by the resistance in the RC load, and (method 2) one-period average power calculation using the well-established two-microphones method. These methods have been validated with both different synthetic signals and experimental measurements. The results reveal that the new method provides real-time accurate estimations of the power delivered to the acoustic load and, thus, has shown potential for control-based applications. The average power calculated by the proposed methods, compared with that obtained by the reference procedure [17], shows excellent concordance both with synthetic signals (see Table 2) and experimental measurements (Table 7). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Average Power (mW)** & **Error (\%)** \\ \hline Reference method & 116.962 & – \\ Instantaneous power & 115.735 & 1.295 \\ (method 1) & 121.236 & –3.654 \\ One-period average & 121.236 & –3.654 \\ (method 2) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of the results obtained using different methods (measured signals). Figure 21: Evolution of the estimated average power using measured signals. The sensitivity analysis performed against uniformly distributed noise (see Table 3), Gaussian noise (see Table 4) and harmonic noise (see Table 5) shows that the power estimation accuracy degrades as the noise level increases. Although method 2 shows better accuracy at low noise levels, method 1 shows better robustness when the noise increases. Another factor that has been studied is the influence of the sampling time on the average power calculated (see Table 6). The results degrade significantly when insufficient sampling (less than eight samples per cycle of the observed signals) is used. Although method 2 presents better accuracy with fine sampling, method 1 shows better robustness against coarser sampling. This methodology allows for adaptive adjustments during operation in terms of system design and control, enhancing the overall system efficiency. Furthermore, real-time power measurement facilitates the implementation of more precise control systems, improving system performance across a range of applications. The practical implications of this work are significant, as the methodology can be adapted for low-cost data acquisition systems, making it accessible for both commercial and research applications. The approach outlined here also offers a foundation for the development of advanced controllers in thermoacoustic engines and other similar systems, potentially paving the way for their use in sustainable energy applications. Conceptualization, J.G. and C.I. ; methodology, J.G., E.P.d.I.F. and M.A.S.R. ; software, J.G. and E.P.d.I.F. ; validation, M.A.S.R., E.P.d.I.F. and A.-I.V. ; formal analysis, M.A.S.R. and E.P.d.I.F. ; investigation, J.G., E.P.d.I.F., M.A.S.R., A.-I.V. and C.I. ; resources, J.G. and C.I. ; data curation, E.P.d.I.F. and M.A.S.R. ; writing--original draft preparation, E.P.d.I.F., M.A.S.R., A.-I.V. and C.I. ; writing--review and editing, E.P.d.I.F., M.A.S.R., A.-I.V. and C.I. ; visualization, E.P.d.I.F., M.A.S.R., A.-I.V. and C.I. ; supervision, J.G., E.P.d.I.F., M.A.S.R., A.-I.V. and C.I. ; project administration, C.I. ; funding acquisition, C.I. All authors have read and agreed to the published version of the manuscript. This research is part of the project PID2022-138700 OB-I00 funded by MICIU/AEI/10.13039/501100011033 and FEDER, UE. Not applicable.