Inductance of CIMs

[Joe Johnson]

Originally Posted by Rickertsen2

Do you have any other information on the interaction between the inductance of the coils, and the commutor and the PWM switching? I find this interesting.

Almost all my experience is from my former life in the auto industry.

There are 3 cases that are applicable to this discussion. Each of them involve cases where the normal behavior of motors did not behave as simple motor models would have us expect.

One was a small motor doing a very big job. We had to do a lot of work in a small amount of time and we only had a 280 series motor can to work with. We had peak current specs, actuation times and actuation forces competing for the design space. We almost had it but we could not meet the peak current spec because the brushes bridged commutators and cause very short, very high current spikes. We ended up getting relief on the specs for current.

The second was a largish motor (a Power Sliding Door motor). We were playing with PWM frequency to try to meet sound specs. PWM frequency can have a big effect on sound if you happen to be PWMing at or near a natural frequency of the body panels. As we varied PWM freq. we notice that as we increased the PWM frequency, we often had to increase the duty cycle of the motors (significantly at low duty cycles) in order to get the same performance of the motor. A simple analysis says that changing the PWM duty cycle is like changing the voltage on the motor. But this is not true, it is only a first order approximation. The approximation gets worse and worse as the PWM frequency grows. We believe that the main reason for this is that by increasing the PWM freq by a couple orders of magnitude, we started to get into the area where the inductance of the motor count not be neglected.

The third was a small motor driving a very lightly loaded actuator (it was lightly loaded most of the time, some times we need every inch-ounce the motor could provide). We were having impact problems at the end of the travel. "No problem," we thought. We had a plan: we could reduce the PWM duty cycle, this would be like reducing the voltage to the motor, which (we all know) reduces the free speed of the (almost unloaded) motor. This plan was based on our assumption that changing the PWM duty cycle is like changing the voltage on the motor -- not exactly true.

To our surprise, the free speed of the motor was basically flat as we reduced the duty cycle. Our tests were clear but our brains were fussy. What was going on?

As it turns out, not all PWMing is created equal.

Most PWMing (IFI's Victor included) switches between Vbatt and Open Circuit. This is what we were using. There are other types, but you can read my P.S. to learn about them.

In this case, it turned out that both the mechanical time constant and the electrical time constanst were fast with respect to our PWM period. What would happen is that in one PWM pulse (even at low duty cycles) the motor would accelerate to the Vbatt freespeed.* Once the motor was at Vbatt free speed, it would stop accelerating. When the PWM pulse ended it would cause an open circuit between the motor leads. But an open circuit motor that is lightly loaded will coast at basically the same speed. So it would coast, slowing down a little but not much, until... ...the next PWM pulse would come along and give the motor another kick, back up to the Vbatt freespeed.

It was not until the duty cycle got down to near the electrical or mechanical time constants of the motor that it slowed down at all. A very unexpected result, given our assumptions. By the way, other forms of PWM do not share this problem and are better for slow speed control of motors as a result.

So. That is that. Probably more than you wanted but you got anyway...

Joe J.

*FYI, back in the 70's when Permanent Magnet (PM) motors were new to the auto industry (and the world actually), GM did some tests on a 280 series lock unlock motor. An unloaded motor got up to its 12V free speed (12Krpm) from a dead start IN 1/4 TURN!!!!

P.S. There are at least 2 other methods of driving motors that are called PWMing.

Recall the first type is to switch between Vbatt and Open Circuit.

You can also switch between Vbatt and Shorting the motor leads (connecting both leads either to ground or to Vbatt, it makes little difference to the motor - it can make a lot of differenced to the voltage spikes the rest of the system sees -- but that is a different message). In my opinion, this is the type of PWMing we would like to use in almost all FIRST applications because it is easier to do control tasks that involve speed control using this method. The reasons are complicated, but there is a term in the equations of motion that help make the speed of the motor less sensitive to changes in load. This term is particularly effective at slow speeds so when you want to control something at slow speeds it helps you the most. Who has had fits and sleepless nights trying to get a FIRST robot arm to behave? Some of those lost winks could have been yours if IFI would implement a method to implement this type of motor driver.

You can also switch between Vbatt and -Vbatt (this kind of motor driver is sometimes called locked anti-phase -- see what Brother Barello has to say about it here). This sounds crazy because in order to get the motor to turn OFF you have to kick it half the time with Vbatt and half the time with -Vbatt. The reason I bring this up at all is that if it were not for inductive limitations on the current through the motor, OFF would essential be stalling the motor. I have never used this type of drive but the PWM frequency must be high enough to limit the current because people DO use this method. I should actually play with this method because it sort of seems too crazy to actually believe. The fact that people are not generally stupid (especial folks who build robots) and yet they use them must mean that they have something to offer (more than Barello's only 1 I/O pin required argument).


I just did some digging. I found this quote (here):

Locked anti-phase for the motor controller. Anti-phase is the easiest to hook up. For a discussion of the difference between locked anti-phase and sign magnitude (the two basic types) see National Semiconductor Note AN-694 (AN-694). When using locked anti-phase, the frequency of the PWM should be relatively high so that the motor coils can act as a filter to turn the pulses into an average DC output. Try to run the PWM at 19 kHz or higher when starting and then adjust to see how it works.

So there it is, high frequency is a must.

From the National Semiconductor app note referenced above:

If the ripple current through the load ever wants to reverse its
direction it is free to do so. This is due to the fact that two
switches are always driven ON and are always able to
conduct current of either polarity. Another benefit of this type
of control is that the voltage across the load is always
defined by the state of the switches, regardless of the direction
the load current wants to flow.
In applications where fast dynamic control of inertial loads
(i.e., the rapid reversal of the direction of rotation of a motor)
it is important that the “regeneration” of net average power
from the load back to the supply be able to take place. With
two switches ON there is always a path for this regenerative
energy.

So, it seems to me that perhaps dynamic control would be improved too. Hmmm.... much to think about... ...JJ

[Gdeaver]

Just saw this on the Globalspec web site.http://www.globalspec.com/MSKennedy/...eed_020802.pdf
It details the other speed controller Joe mentioned. These are used allot for brushless dc servo motors. The pulse width period can also have an effect on brush - commuter wear. Too long a period can cause wear.This link was posted in another thread this year. It may be of interest to reviewSpeed controller

[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)