Ripple instability in closed-loop pulse-modulation systems including invertor drives

Describing functions at subharmonic frequencies are established for a range of pulse modulators. These allow an analysis to be made of the phenomenon of ripple instability in closed-loop systems containing such modulators, wherein the loop may oscillate at a submultiple of the fundamental frequency of the ripple in the modulator output. This basically occurs because the gain of the modulator at these subharmonic frequencies can be greater than its d.c. value. The modulation processes studied are pulse-length, pulse-position, pulse-width and pulse-amplitude modulation. It is shown for these cases that the gain of the modulator is enhanced most at the ¿-order subharmonic, which, as a result, tends to be the dominant type of ripple instability. A particular application of these modulators in closed-loop systems which is of current interest is the thyristor invertor. In the second part of the paper the describing-function approach is developed to analyse the particular case of a d.c.-link invertor in a closed-loop system, e.g. a wide-bandwidth current-limit control in an invertor drive. It is shown to explain and predict the ripple-instability behaviour of the system, and good agreement is reached with analogue-computer results. The cases of fixed- and variable-frequency operation are investigated, together with the effects of utilising a thyristor amplifier in the loop to provide the d.c.-link voltage.