[Al Skierkiewicz]

Jim,
It is difficult to get a good read on the inductance of the motors when the brush assembly covers more than one winding most of the time. We can get an idea from backing into calculations if we make some assumptions. The worst case inductance stated so far is 230 micro henries. If we know that the switching frequency of the controller is about 2kHz and that there are 127 steps between full on and full off then (assuming no dead band) 1/2kHz=.5msec/127= 4 microseconds as the minimum "on" time for the controller. If we assume a stall current of 100 Amps (this makes the calculations easier) then the internal resistance = .12 ohms. Add to that a typical wiring/controller/connector/breaker loss of .03 ohms a typical robot will have a series resistance equivalent of .15 Ohms. Plug that into the charge equation for an inductor, I=(E*(1-e^^(-tR/L))/R or about .15 amps for the lowest speed PWM(if the controller is calibrated). An inductor (our motor winding) will reach about 90% of stall current (for this theoretical motor only) in approximately 2L/R or 0.07 msec or about at the 008 PWM value. It will reach full short circuit current in 6L/r or 0.2 msec or about 064 PWM value. Now all of this theory still does not account for the motor moving, different windings being switched in and out by the brushes or the mutual magnetic coupling taking place between windings. I think it is safe to say that we can reach full stall current on the motor (limited by the series resistance of all the losses) in a very short time. So for all but the most inquisitive, the effect of motor winding inductance does tend to be negligible for our use. Please note: that the motor will start to turn almost immediately unless stalled by an external force. It is there and it does effect the operation when viewed on test equipment but it does little for robot operation (with the motors we use) because of the human and electronic factors that come into play during a match. Let us not forget that full up on the throttle produces full DC where full stall current will be reached in 0.2 msec. or about 1/20 the reaction speed of the best driver.

As to discussion on some of the other topics. A "locked" motor is essentially a powered stall condition that requires precise choice of switching frequency to make the most efficient use of the specific motor in use. Please note that this method is the most costly in electrical terms since the load is always consuming full stall current when doing no work.
As to the two methods of motor drive... A dual polarity power supply does allow a simplification of the drive circuitry if you already have the power supplies in use in your system. A video recorder does use this drive system since it requires the dual supply for other analog circuitry. It also uses the antiphase locking feature in oder to produce a synchronous locked video still frame from tape. With the single supply, our motors and the systems in use, the speed controller running at 2Khz makes the most sense and takes into account all of the tradeoffs that need to be made in order to get a robot running.

P.S. Remember the controller output alternates between +12 and open circuit. It is not swinging to ground. That means that the when the power is removed, there is no circuit into which the inductor will discharge. Even though the magnetic field is collapsing, there is no where for the current to go. The controller only produces a load on the motor during a PWM 127 +/- the deadband and only when the jumper is in "brake" setting. While the motor is turning, a moving coil in a magnetic field will produce a current if there is a circuit for it to flow into. All of these events add up to the charachteristics you may see when using an oscilloscope to view these complex motor waveforms. Please remember when using the discharge equations for inductance that the resistance of the circuitry for a controller in "brake" no longer includes the supply side wiring (battery connectors, circuit breakers, supply side wiring and breaker panel). The only resistance is the wire and connectors between the motor and controller and the internal resistance of the controller. (as low as .0025 ohms)