This paper signifies the study of modeling and simulation of a single phase matrix converter for induction heating system. The working principle and the control method, using PID are revealing in detail. The performance of the system is carried out in MATLAB/Simulink environment with pulse width modulation switching strategy by varying the duty cycle. PID control is employed to obtain the better performance for a specified input supply for various output frequencies. The proposed control strategy of AC to AC converter has been discussed with a wide range of operating frequencies and results in low Total Harmonic Distortion.