Victors Non-linear!!!

[Rickertsen2]

Originally Posted by Al Skierkiewicz

Greg et al,
The reference in Kevin's post: http://www.enigmaindustries.com/links.htm lists the 884 as 120Hz and the 883 as 2kHz, hence my confusion. (being around for a long time does get in the way.) Greg, are you in a position to check rise time where you are right now?

Jim,
(I am confused and keep calling you Rick) You tell us that the motor is unloaded but it is connected to the FP gearbox. That is a load. The numbers in your table suggest the large amount of friction present at low speeds in that FP gearbox. At low speeds, a motor still must overcome internal losses due to friction, brush pressure and magnetic influences. On the FP motor in particular, there are only three commutator segments which means three windings. Depending on the duty cycle, energy may only be supplied to the motor for a small portion of the brush/commutator cycle at low speeds. If analyzed, you may find that current is only flowing to one winding at a time instead of two. (two gives better torque/output/higer current) In contrast, the drill motor has several windings/commutators and the spec sheets illustrate the difference in these two motors. Ironically, the graph you displayed in your earlier post is a typical charge current graph of an inductor. This may indicate the effect of the duty cycle vs. inductance or not.

Ok we have all come to the consensus that in order to figure out whether or not the victors are linear or not, we must measure duty cycle.

Exactly how do you calculate the reactance vs. time of an inductor with a square wave input. I know how to do this with a sine wave, but a square wave is much more complex. Would you model the first 10 or so sine components of the square wave? Is there a simpler way?

[MikeDubreuil]

Wouldn't you just add to the complexity of the test by adding a motor?

When I perform my test I plan on attaching the scope leads directly to the motor output on the Victor. With no other load other than the internal resistance of the scope. Is that a bad idea?

[Gdeaver]

The original poster was looking to measure the victor- motor system behavior by measuring voltage given by a volt ohm meter vs. rpm for a given setting of the robot controller. I submit that probably is not a good measure of our robot system. If you take the battery, power distribution wiring, RC, victors and motors and try to describe it, you'll end up with a complex system of equations with many independent variables. Not nice. The formulas in the ee books are simplifications with assumptions that for many apps are good enough to approximate the motor behavior. If you notice the Bosh motor curves we where given used a very tight linear power supply. That's not the case with our robot system. I think a better measure would be to take a Typical robot setup and the Fp motor. Apply a constant load to the motor.
Set the PWM variable and measure the RPM a second or 2 latter. Then increase the PWM variable by 1, measure the rpm. After the full PWM range has been measured, Increase the load by a fixed amount and measure for PWM range. Continue increasing the load by a fixed amount and measuring until the stall load is reached. The motor should be left to cool to eliminate the thermal effects. Then plot PWM setting, load , and rpm. The surface of the plot would give a visual representation of the motor - robot performance. With the same setup thermal performance could be measured by fixing the PWM variable and the load. Then measure and plot the rpm over time.
The some analysis could be made to see if those formulas and performance curves are valid. Comments?

[gc02]

Originally Posted by Al Skierkiewicz

Greg et al,
Greg, are you in a position to check rise time where you are right now?

I'd have to dig out a bunch of parts to do a test. I didn't measure the exact rise time, but when I ran the test before the motor's current was able to rise and fall completely between PWM pulses.

[gc02]

Originally Posted by MikeDubreuil

Wouldn't you just add to the complexity of the test by adding a motor?

When I perform my test I plan on attaching the scope leads directly to the motor output on the Victor. With no other load other than the internal resistance of the scope. Is that a bad idea?

If you just want to see the square PWM wave just connect the scope to the output terminals on the Victor. I think you'll get the same results whether or not the motor is connected. If you want to see the sawtooth wave generated by the rising and falling current in the motor you'll need to connect a current shunt in series with the motor and connect the scope to that.

[Kevin Sevcik]

Originally Posted by gc02

If you just want to see the square PWM wave just connect the scope to the output terminals on the Victor. I think you'll get the same results whether or not the motor is connected. If you want to see the sawtooth wave generated by the rising and falling current in the motor you'll need to connect a current shunt in series with the motor and connect the scope to that.

The voltage shouldn't be a simple square wave if there's motor in the system. DC motors generate back EMF and also present a fairly large inductance to the speed controller. All of this will have a definite effect on the voltage that you see on the scope with a motor connected.

[gc02]

Originally Posted by Kevin Sevcik

The voltage shouldn't be a simple square wave if there's motor in the system. DC motors generate back EMF and also present a fairly large inductance to the speed controller. All of this will have a definite effect on the voltage that you see on the scope with a motor connected.

You're right, I was thinking about the motor at stall and forgot about the back EMF. The cleanest PWM signal will be with no motor attached.

[gc02]

Originally Posted by Rickertsen2

Even if you assume that my pwm vs voltage graph is entirely bogus, that still doesn't explain the pwm vs speed graph which looks just like it.

What I'm suggesting does explain what you're seeing, sorry I can't explain it any better, there's a section in the Astroflight motor handbook about "lo-rate" speed controllers which covers exactly what you're seeing.

[Al Skierkiewicz]

Jim,
The best way to mathematically analyze this would be a single step function. From what Greg has written, it would seem that the inductance of a winding is small. A scope would verify that the inductance likely does not have an effect until pulse width is very small. I just had a thought...it is always possible that IFI has built in a power curve to compensate for the average motor response at low speeds. They are pretty smart guys. As I alluded to before, the actual current through the motor changes depending on how many windings are in the circuit. Since there is no sync between the PWM frequency and the motor speed, you should be able to observe steps in the waveform when a motor is connected. Another method is looking at the voltage drop across a series resistor. This is a simple solution since the wire acts a resistor. Attach your scope probe to battery negative and scope the "-" terminal of the speed controller input. You will be looking at the motor current through the controller but that has little effect on your data. (again you are looking for representative data, not absolute.) You should see step currents here as well as inductive response. You may need to play with horizontal sweep to see the edge of the rising pulse. Calculate current from the voltage you measure. A 12" piece of #10 is .001 ohm, so ad a few feet of #10 between the controller and the battery. (If measuring on a real robot, 24' of #6 is .001 ohm so fudge the series resistance.)
Back EMF will not be measurable, just it's effects. Remember that the impedance between the motor and controller are very low compared to other reactances within the motor. If you are measuring anywhere after the controller, DO NOT connect the ground lead of your probe to the controller output terminal. It is not at circuit common and is only near common when the controller is in the forward mode. Expect large amounts of noise at the motor terminals from brush arcing.
Finally, a plot of PMW to actual average voltage (from scope measurements of voltage and duty cycle) would be a very accurate way to look at linearity with and without motor.

[andy]

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

[gc02]

Originally Posted by andy

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

I disagree completly. I'll try and explain my theory a little better. The output of the speed controller, connected to a resistive load, gives us a nice square wave. With a square wave voltage/current are directly proportional to the duty cycle. Now if you throw an inductor in there, you no longer have a square wave, you have a funny sawtooth shaped wave and the output voltage/current are no longer linearly proportional to the duty cycle. They become related to the rise and fall times of the inductor and the length of the switching period. This non-linearity will become more pronounced at lower PWM frequiencies as the voltage/current have more time to rise and fall between the on and off switches. I'm sure you're right in that the duty cycle varies linearly, but I can definetly see how the voltage/current dont have to respond linearly.

[Rickertsen2]

Originally Posted by gc02

I disagree completly. I'll try and explain my theory a little better. The output of the speed controller, connected to a resistive load, gives us a nice square wave. With a square wave voltage/current are directly proportional to the duty cycle. Now if you throw an inductor in there, you no longer have a square wave, you have a funny sawtooth shaped wave and the output voltage/current are no longer linearly proportional to the duty cycle. They become related to the rise and fall times of the inductor and the length of the switching period. This non-linearity will become more pronounced at lower PWM frequiencies as the voltage/current have more time to rise and fall between the on and off switches. I'm sure you're right in that the duty cycle varies linearly, but I can definetly see how the voltage/current dont have to respond linearly.

So what you are saying is that you believe the reactance motor is varying with duty cycle? Do any of you know how to compute reactance over time of a square wave through an inductor? Would you break it up into sine waves and alanlyze the first 20 or so? Is there a simpler way? I can't even find the fourier series for anything but a truly square square wave.
BTW this is entirely possible as both tests had motors attached when they were performed. At this point we seem to have many theories and many untested hypotheses. I Think we will get a much clearer picture of what is going on onve someone measures duty cycle output vs. pwm input.

[gc02]

Originally Posted by Rickertsen2

So what you are saying is that you believe the reactance motor is varying with duty cycle? Do any of you know how to compute reactance over time of a square wave through an inductor? Would you break it up into sine waves and alanlyze the first 20 or so? Is there a simpler way? I can't even find the fourier series for anything but a truly square square wave.
BTW this is entirely possible as both tests had motors attached when they were performed. At this point we seem to have many theories and many untested hypotheses. I Think we will get a much clearer picture of what is going on onve someone measures duty cycle output vs. pwm input.

Take a look at the picture under the "Choosing a frequency based on motor characteristics" section of this website: http://homepages.which.net/~paul.hil...ntrollers.html
It shows the relationship between the PWM signal and the motor's current. If someone was to figure out the RMS current of that waveform at different duty cycles, I believe there would be a non-linear relationship between the RMS current and duty cycle.

Some information on inductor transient response is available here:
http://hyperphysics.phy-astr.gsu.edu...ic/indtra.html

[andy]

Originally Posted by gc02

I disagree completly.

That's ok

Originally Posted by gc02

Take a look at the picture under the "Choosing a frequency based on motor characteristics" section of this website: http://homepages.which.net/~paul.hil...ntrollers.html
It shows the relationship between the PWM signal and the motor's current. If someone was to figure out the RMS current of that waveform at different duty cycles, I believe there would be a non-linear relationship between the RMS current and duty cycle.

Really good website btw.

That is exactly what I began to think (I even drew pictures) but then I thought about what happens to voltage (emf) across an inductor. It gets really hairy because a back emf is produced when the current changes. This is an application of Faraday's Law which more or less says that if a change in current occurs, a change in the magnetic field will also occur that is exactly opposite and equivalent of the equivalent current.

This is given by the equation

emf = -Inductance * change in current / change in time

//Given the schematic (slightly modified so it has no whitespace) (why no whitespace Brandon? It makes it tougher for ASCII art ) Comments on schematic, switch represents half of the H-Bridge (in a way) resistor represents resistance of wire windings commutor etc. and inductor represents motor's inductance.

BATTERY____/ __C__^^^^__A__~~~__B___GROUND

//And the pulse produced by the switch (see schematic) potential difference between A and B

Voltage
12 | __
00 |_| |___ time
-12|


//With an inductor potential difference between A and B

Voltage
12 |
00 |_|\_ ___ time
-12|___|/

But what happens when I take into account the resistor? And try to measure voltage between C and B? Will it simply decrease the voltage by an increment (shift downward?) or will it cause a nonlinear response voltage change? I will try to puzzle that out when I am not so tired.

Also, for anyone who wishes to do circuit analysis, OrCad offers a free student copy of their product PSpice which I have yet to play with, however I am told that it can simulate this sort of thing rather nicely. The url is

http://www.orcad.com/downloads/demo/

Cool, goodnight

-Andy

[Al Skierkiewicz]

Ok James,
I thought I had it about seven or eight different times then I remembered I had a Johnson version of the FP motor sitting on a shelf so i took it out and looked at and did a little measuring and fudging some numbers and here is what I came up with.
The FP motor has three commutator segments and therefore three armature windings. If you draw out the equivalent circuit you will see that depending on what the brushes are contacting, you can have one of three conditions, 1) two windings in series, 2) one winding is parallel with two windings in series or 3) Two windings in parallel (the third is shorted by one of the brushes) Now doing some math making some assumptions and backing into the calculations, you can solve for L. At no load the specs are CEMF=2.35 volts I=1.1amps speed=15000RPM. Calculating for equivalent impedance from 1.1/(12-2.35)=.1 ohms. At 15000RPM shaft takes .004seconds/revolution or a commutator segment is engaged for 1.33mSec.(less than the "on"time of the speed controller at 50% duty cycle) Now making the assumption that a prudent designer would make the inductive reactance equal the series resistance at the highest frequency (1/1.33mSec=750Hz) then L would be 10 microhenries. The time constant for this inductance would be 0.2mSec. Hence, the current would would have a chance to rise (rather quickly) to full level at duty cycles down into the single digits. (about 2-3% duty cycle) As the motor RPM goes down, the inductance has less of an effect.
In analyzing the drill and chalupa which both have more windings, the inductance is likely far less per winding. (since there are more windings per armature, there is less wire/turns for each coil) In any case it does not seem that the controller switching at 120 Hz would have much effect on speed above 10% duty cycle.
In reading through Greg's linked article, the author referred to series wound DC motors (non permanent magnet) and controllers using kHz switching frequencies. Although a lot of his discussion and drawings are useful, the conclusions cannot fit our motor/controller combination. When looking at the voltage waveforms and sawtooth response, remember his switching frequency is very high and may (likely) be affected by controller output impedance. As the output impedance rises, the time constant stretches out and the resultant sawtooth response can be observed.
Now, if controllers are not introducing the error (deviation from linear) and inductance doesn't appear to have that effect than there is obviously something else. This is what I think it may be. At low RPM say 1000, the controller actually has time to turn on and off several times before a commutator segment will have turned past the brush. Total current will be a function of 1) speed at which the three winding conditions will switch vs. time 2) how many pulses can be delivered to a winding pair on average and 3) load. Since the test in question did have a load (Ok a small one) it is easy to see that these other factors would have an effect on motor performance.
At low speeds the meter should read more accurately (still flawed by rise time and frequency response) but cannot take into account the effect of rapidly changing load conditions as speed increases. The graph of controller output voltage, scope vs. meter should be an interesting thing to look at.