Analysis of DC motor armature copper losses in digital control and optimization of counter length used as phase comparator

The armature copper losses of an externally excited dc motor are analyzed for a digital control system comprising the motor, an amplifier, a reversible counter (used as phase comparator), and converters (D/A and A/D). The open- and closed-loop cases are analyzed, and the linear system gain is calculated for a given form factor. The minimal number of stages required for a given form factor and speed interval by use of nonlinear gain are also determined. The analysis is illustrated for a 10-kW motor, including the voltage and current waveforms (verified theoretically and experimentally) and the graphical relationship between the counter length (number of stages) and the form factor.