Al,
I'm aware of everything you mentioned and I'm not sure that any of it contradicts what I'm saying.
I wish it was easy to draw pictures...
All I'm saying Al is that I believe the JAG linear transfer function that has been posted must have been taken in the BRAKE ON mode. Other xfer functions posted with Victors etc that are nonlinear were taken with the COAST ON mode.
Assume for discussion that the motor current is being driven positive during the PWM "on" phase.
In the brake mode, the "off" PWM phase places the low side FET's ON and essentially shorts the coil which provides a path for the current to drive toward -Vemf/R as a steady state and can reverse the current in the coil. In the coast mode, as you say, the low side FET's are OFF and the diodes are active. The diode will only conduct until the current drops to zero and then shuts off so Vemf cannot drive the current negative. So for most of the time , even though Vemf is there, it is not active in the calculation of current while in the "off" PWM phase for the coast mode. It is this that makes the difference. So my simple math model just assumes that Vemf is only present during the "on" PWM when operating in the coast mode but it does a great job of matching actual test data.
I am conjecturing that this is true for all the controllers we see in Vex and FRC. My experience with Vex motors tells me that they are coast mode since they have the same characteristic as the Victor nonlinear curve I posted earlier from Beach Bots. When I built the Vex Bbot inverse pendulum robot (
http://youtube.com/watch?v=4loT_Xfhvbk
), I spent a lot of time modeling the problem with MATLAB and was always disappointed when my optimal control theoretical gains did not match the gains actually needed. Most of the problem came from the nonlinear Vex motor gain and frictional dead zones anomalies. Ohhh how I wish I had a Vex motor with an H bridge in the brake mode. I am currently working on a Vex unibot that is stable in two axes and balances on one wheel and already have had numerous failures from sticky nonlinear motors.
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My suspicion is the motors were modeled and switching parameters set to optimize those motors. The manual goes on to say that other motor types may not behave the same and recommend the reader check the Brushed DC Motor Control Reference Design Kit (RDK) User’s Manual for more information on motor selection and use.
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I have spent some time with the RDK and it may be optimized for the CIM re matching the bridge dynamics , but I'm guessing that a transfer function run in the coast mode will be nonlinear. There might be some SW optimization but I suspect this is only for the current and encoder PID's. As I posted earlier to Joe Ross, the voltage control mode looks like a straight forward PWM motor controller that just puts out a PWM signal proportional to a voltage reference.