A methodology is developed for average modeling of discrete controllers for PWM power conversion systems. The method applies a section of a transmission line to emulate the basic delay inherent to the discrete sampling and control algorithms. It is shown how the simple delay line model can be used to build an average model of a zero order hold (ZOH) function that can be run on a general purpose circuit simulator. The model is compatible with DC, AC (small signal) and time domain (large signal) analyses. The method is further demonstrated by developing an average model of a digital PID controller for a boost converter and running large and small signal analyses of the closed loop system. Based on the proposed modeling and simulation approach, a procedure is suggested for the design of discrete controllers for switch mode systems.
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