Whooo buddy this is a funny thread!
First off, the original poster's name is James, not Rick or Jim, and he's on my team.
I figured I'd solve this dilemma the easy way (as I have no test equipment, victors or loads etc.) and call Innovation First and ask one of their techs. Their technician, Corey, said a couple of very valuable things.
-The victors are simply MOSFET H-Bridges controlled by a microprocessor which interprets the input PWM signal. So, given the input PWM high (on) time varies from 1ms (full reverse) to 2ms (full forward) where 1.5ms is neutral (off).The period of the input PWM signal is around 16-17ms or about 60Hz.
-The microprocessor controls the MOSFETs so that they output to the motors (and I quote) a "chopped pulse width modulated signal at 120 Hz"
-The processor controls the output duty cycle based on the input period of the PWM signal.
-Since they are true H-Bridges, they DO NOT vary (instantaneous) voltage, only (as he said) "on time" or duty cycle. (or average voltage, but we'll get to that later)
-When asked about linearity, he stressed that the devices are designed to be completely linear, there is no fancy PID or other control loop etc within the victors. This means, as PWM is linearly increased (outside the deadband), the percentage of "on time" (duty cycle) of the output signal is linearly correlated to the input PWM signal.
So, applying some simple physics and calculus, we can conclude that while voltage does not vary (and assuming the resistance and therefore current does not vary) since the time the voltage is applied varies, the power must vary by the following function:
To find the amount of power in a PWM signal where P(t) is the amount of power in terms of time we apply the average value theorem of calculus
power_average = 1/(T - T_0) * integral of P(t) from T to T_0 in terms of t
Where t is time and T - T_0 is the time interval the the average power was measured over
However, in James' defense, the same can be said for voltage. There is an average value function for voltage also which could be used to explain the values James recorded.
Where V(t) is the function of voltage in terms of time
voltage_ average = 1/(T-T_0) * integral of V(t) from T to T_0 in terms of t
Where t is time and T - T_0 is the time interval the the average voltage was measured over
BUT, weather or not this actually was the case depends on the characteristics of his meter. Suppose, his meter measures ten samples over a specified time interval then sums the samples and displays the value. Since the voltage changes with time, the meter COULD display erroneous values depending on WHEN those samples are collected. Say that the meter collects 5 samples while the signal is +12VDC and then another 5 samples when the signal is 0VDC. The meter would then sum those samples and display +6VDC. Here's the kicker, it is possible that the meter could display +6VDC at ANY DUTY CYCLE provided the right (or in this case, lucky) sampling rate. (google Nyquist sampling theorem for more information)
Remember that this all depends on the actual characteristics of the meter. Also, many more variables come into play when dealing with an inductive load (especially, in this case, a motor). Take for example, as the heat increases, the resistance (usually) also increases. We all know how hot the Fischer Price motors get. This is all not taking into account any rotational inertia, which is a another can of worms I don't want to open.
In summary, any nonlinearity you see in the duty cycle is caused by the input signal, in this case, the robot controller.
Good luck everyone!
-Andy
*disclaimer I am not an expert, and something above is probably wrong, I also have thick skin, have at it
