A novel modulated single Fourier series time function for mathematical modelling and simulation of natural sampled pulse width modulation in high performance brushless motor drives

Pulsewidth modulation (PWM) is widely used as an efficient power transfer mechanism in switch mode power supply dc to dc conversion, uninterruptible power supplies (UPS), Class D audio power amplification, and in speed and torque control of industrial machine drives. For this reason very accurate and efficient simulation models of these industrial devices based on a power dispatch PWM kernel, which is a non linear process, are required during the computer aided design phase for performance related prediction and evaluation before hardware prototyping and large scale production begins. This is particularly important in the integrated circuit design of high fidelity Class D audio amplifiers and in embedded high performance industrial motor drives systems for robotic applications. In this paper a new mathematical model for PWM simulation and analysis is presented which is based on a novel concept of a modulated single Fourier series (MFS) time function. The validity of this analytical Fourier model is first proven and the accuracy is then checked by simulating the action of a classical natural sampled PWM analog comparator modulator fed with a triangular carrier and a variety of arbitrary non periodic signals. Results are presented to establish the accuracy of the MFS strategy in high performance industrial brushless motor drive (BLMD) simulation, instead of classical iterative solutions of analog comparator modulator operation for PWM representation, with experimental test data.