Dear Ron,
Since the system is thyristor control the closed loop control responds every AC cycle. The thyristors used are not GTOs so need to wait for the coming cycle. A sliding control method does give good results. Depending on the current consumption the system switches to constant voltage or constant current (foldback type) mode. The line voltage is also not constant. It it were a HF IGBT based system then PID control works great. As for sliding (call it a servo) control the system increases/decreases the firing angle to approach minimum error (deadband inserted). I have seen motor controllers which respond really quick (less than 6 cycles) to a motor start stop.
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