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

Abstract

Absrracf -Pulsewidth Modulation (PWM) is widely used as an efficient power transfer mechanism in switch mode power supply dc to dc conversion, unintemptable 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 bared 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 camer and a variety of arbitrary non periodic signals. Results are presented to establish the accuracy of the MFS stratcgy 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. 1. INTRODUCTION PWM is the de facto industrial standard [I], as an energy saving strategy, for high efficiency power dispatch in a variety of high performance applications. These applications encompass embedded motive power systems with adjustable speed drives and torque actuatom [I], Class D power amplifiers in Hi-Fi audio applications [2], dc to ac inverters for UPS [3] and dc to dc converters for switch mode power supplies [4]. Power dispatch is accomplished in the last case [ 5 ] by means of a PWM switching regulator in the power conversion stage (PCS) while continuous variable voltage and frequency control of induction motor and BLMD systems is achieved by means of a sinusoidal reference PWM controlled inverter power amplifier stage. Wide bandwidth current loop control in high performance motor drives [6] relies on the asynchronous natural sampling mode for sinusoidal PWM as the preferred form of carrier modulation because of its inherent simplicity and ease of implementation using analog circuitry. In this instance a fixed high frequency triangulariramp camer sampling waveform along with a variable frequency and amplitude sinusoidal reference signal are fed to the inputs (iip) of a comparator modulator for each phase. The analog comparison at the intersection points of the two waveforms shown in Fig. 1 results in a two level width modulated pulse switching sequence which is used to control the inverter power amplifier output (oip) duty cycle. The camer frequency, for asynchronous operation, is chosen sufficiently high for harmon...