Derivation of a new drive/coast motor driver model for real-time brushed DC motor control, and validation on a MIP robot

Brushed DC motors are usually driven with PWM forcing in one of two modes: drive/brake or drive/coast. That is, at the low state of the PWM forcing profile, the motor driver will either “brake” the motor with its own back EMF, or allow the motor to “coast” (i.e., spin freely). Drive/brake motor drivers, which are by far the most common, may be represented by a Multilevel Four-Quadrant DC Chopper model, while drive/coast motor drivers may be represented by two independent Bipolar Two-Quadrant DC Chopper models. Conveniently, when averaged over the PWM duty cycle, drive/brake motor drivers are accurately modeled as linear systems over their entire operational range. On the other hand, drive/coast motor drivers, when averaged over the PWM duty cycle, exhibit significant nonlinear behaviors that are dependent on factors such as inductance, PWM frequency, and rotor speed. Though there are some existing partial derivations of drive/coast motor driver models, no comprehensive, experimentally-validated modeling approaches appropriate for feedback control applications over the full dynamic range of the motor could be readily found in the literature. In this paper, we derive a practical nonlinear model of a drive/coast motor driver, validate this model using a motor dynamometer, and demonstrate a real-time implementation of this model on a Mobile Inverted Pendulum (MIP) robot.