please summarize the following: Introduction Proposed Strategy to detect resonant frequency/Problem Formulation This research proposes a novel method for the instantaneous tracking of the resonant frequency in induction heating systems and establishes a

### Summary This research paper presents a novel method for tracking the resonant frequency in induction heating systems, using a theoretical framework and a dynamic algorithm that allows for real-time measurement without requiring a frequency sweep. The focus is on a resonant RLC tank circuit, which comprises a resonant capacitor (C1) in parallel with a series resistor (R1) and inductor (L1). The study explores how variations in these components, influenced by changes in load characteristics (such as temperature and material properties), alter the resonant frequency. The proposed system for tracking resonant frequency consists of two main components: hardware and software. The hardware comprises a full-bridge resonant inverter paired with the RLC tank circuit and a microcontroller-based feedback system to measure and monitor the resonant frequency. The algorithm, implemented in the microcontroller, processes data from the hardware to determine the instantaneous resonant frequency and adjust the operational conditions accordingly. The hardware setup includes a zero-crossing detector (ZCD) that generates pulses when the output voltage crosses zero, measuring the time interval associated with these crossings to derive the resonant frequency. The microcontroller executes an algorithm that alternates the states of power transistors in the inverter, maintaining the oscillatory behavior of the RLC circuit while adapting to changes in load. The proposed algorithm allows the system to continuously synchronize the inverter's switching frequency with the resonant frequency of the RLC tank circuit, regardless of variable load conditions. This enhances the efficiency of the induction heating process by ensuring that the resonant circuit remains actively operational during fluctuations in load characteristics. As load characteristics change, the system detects the new resonant frequency and adjusts its operation dynamically, thus providing a robust solution for effective induction heating applications.