# Novel Real-Time Acoustic Power Estimation for Dynamic Thermoacoustic Control
## 1 Introduction
Additionally, experimental constraints imposed by working within the low-amplitude regime required by linear theory, such as the subtle pressure oscillations, demand high-precision sensors or signal amplification lock-in systems [27], which significantly impact the cost and complexity of the data acquisition setup. In this context, recent studies have demonstrated that low-cost systems, such as those based on the Arduino platform, can achieve promising results in dynamic applications, ensuring reliability at reasonably high sampling rates when a reduced number of sensors are used [28]. The development of a robust yet affordable acquisition system requires optimizing sampling frequency, data transmission, and error mitigation, as demonstrated by [PERSON] [29], who enhanced acquisition rates and minimized errors in Arduino-based platforms. Building on these findings, this study utilizes the previously validated low-cost Arduino-based acquisition system designed for thermoacoustic Stirling engines [30]. This system has been optimized to reduce noise-related errors and enhance dynamic response, ensuring both accurate real-time thermoacoustic power estimation and reliable measurements. This study presents a novel approach for the real-time estimation of instantaneous acoustic power in thermoacoustic engines, addressing the limitations of conventional time-averaged power estimation methods. The measurements are performed within a laminar regime, using the RC load-based method [30], where a resonator and a variable acoustic load are utilized to replicate the lossless acoustic behaviour of a piston in a linear alternator while accounting for parasitic losses due to piston motion. Unlike traditional methods that rely on time-averaged estimations, our procedure offers a way to measure instantaneous power by continuously acquiring and adjusting data on acoustic waves and system parameters. This allows real-time monitoring of the power dissipated in the RC load within the TA-SLiCE power extraction branch (see Figure 1), providing a more accurate and responsive approach for evaluating thermoacoustic power. Furthermore, the methodology is versatile and can be applied to various data acquisition systems, independent of their cost or complexity. The approach presented in this paper offers several advantages over traditional methods. A comparison between the real-time estimation technique and the widely used RC load-based method, which relies on averaged measurements, demonstrates that the proposed method provides accurate and timely results, even with a low-cost acquisition system. The effects of sampling rates and acquisition frequencies on measurement accuracy are also examined, showing that a higher resolution leads to reduced errors and greater precision in real-time applications. The obtained results emphasize the potential of real-time power measurement as a crucial tool for enhancing thermoacoustic engine performance, enabling new opportunities for control and optimization, such as the control algorithm developed by [PERSON] et al. [31], which improves efficiency and power density in thermoacoustic energy harvesters, making them more effective for practical applications in refrigeration and energy conversion. The paper is organized as follows: In Section 2, the theoretical background and methodology for real-time power estimation in thermoacoustic engines is outlined. Section 3 describes the experimental setup, measurements, and results. Section 4 includes the experimental validation of the estimation procedure, comparison with traditional approaches, and discussion. Section 5 provides the main conclusions of this work.