Friday Math Quiz

[Eugen]

I don't understand the parabola as the "most efficient" motion profile, .

The answer is below:

but could see that a controlled jerk at the beginning at end of a smooth transition as easier on your equipment - the real goal of the post.

If "the jerk" is distributed through the all length of travel then the smothest possible transition (or efficency) is achived, hence PARABOLA.

Was there a PID given for a similar problem in the other (long time ago) post, or I'm mixing things up?

 

[surferb]

Thanks for the clarification!

I'm not sure that OP knew exactly what to ask. Perhaps you could best help him with the intent on his question by guiding him through optimizing the parameters to his problem.

Could there be one ideal solution or many with different characteristics?

The answer is below:
If "the jerk" is distributed through the all length of travel then the smothest possible transition (or efficency) is achived, hence PARABOLA.

Was there a PID given for a similar problem in the other (long time ago) post, or I'm mixing things up?

 

[kamenges]

Originally posted by surferb:

How are there "many combinations of the velocity,acceleration and time that will meet your needs"?

Given the constraints the OP made, there is only one solution. However, the costraints were somewhat arbitrary. Why 5"/sec² for acceleration rate? Why not 6, or 4 or 7? Why 4.77777 seconds to complete the move? Why not an even 5? And then, as you said, you can start tossing in jerk (and snap, crackle and pop as required). So there are a wide variety of possible combinations that would most likely solve the base problem given some flexibility.

Up until the end the thread was directly answering the OP; that is, given the constraints, how do I calculate the velocity required to match my old performance given the new acceleration rate. While this may not be the optimal solution it answered the question. I would have suggested that some jerk be added to the profile if beating on the system is a concern. But that may or may not be available to russmartin.

As for the parabolic velocity profile, I think it provides the best use of the available power. You accelerate hardest at zero speed, where most actuators have the best chance of accelerating hard. The accel tapers off as you increase in speed. My gut feeling is this is especially true in fluid power systems but it applies to motor driven systems also. However, as stated, you get a pretty nasty jolt at the beginning and the end of the move since the acceleration rate is very high at these points.

Keith

 

[OkiePC]

Why 4.77777 seconds to complete the move?

I think that was derived from the original cycle rate.

Nice thread, lots of useful formulae here!

Maybe we should add to the thread some s-curve math too, which may be more suitable than parabolic in some applications. I would have to google it though. . . or look in an old GML manual.

Then the OP can have his pick of solutions.

Paul

 

[kamenges]

Originally posted by OkiePC:

Quote:
Originally Posted by kamenges
Why 4.77777 seconds to complete the move?



I think that was derived from the original cycle rate.

That line was somewhat rhetorical. I know the time came from the original application. But in this case I doubt that it was a hard limit of any kind. I was trying to make the point that the values from the original post seemed pretty arbitrary and that being allowed to move them around some adds profile flexibility.

Originally posted by OkiePC:

Maybe we should add to the thread some s-curve math too, which may be more suitable than parabolic in some applications.

That would be reasonably entertaining. However, in practice, you would usually just move the numbers around until you get the performance you're happy with. You probably have a hard upper limit on accel rate based on the motor/load combination as well as an upper limit on speed based on the motor. In addition you have an upper limit on jerk based on the dominant system compliance. But outside of that you have quite a bit of freedom and can evaluate performance iteratively.

Keith

 

[russrmartin]

More OP info for clarification

All,

I'm definitely glad this post created as much interest as it has. For more clarification, the system is a servo axis on a highly cycled saw. Therefore, the old cycle time of 4.77 seconds is highly critical as far as production is concerned. This saw cycles about twice a minute, or 120 cycles. Being the saw axis is already the bottleneck, slowing this axis down further would have a largely negative effect on production.

This axis is a Kinetix6000 axis, and the move is executed via the MAM command in CLX. With the profile set to S curve in the move properties, I was allowed to alter the accel and decel rates, as well as the max velocity. I don't believe one has the ability to alter jerk rates with the move commands involved(if so, please feel free to elaborate.)

This info hopefully gets everyone on the same page as far as why the original post mentioned nothing about jerk rates or parabolic moves. My understanding is that the MAM set to S curve takes care of these calculations based on the info you give it, i.e. the variables I had asked about.

The 5 in/s^2 was based on calculations concerning the mass of the load, the distance from the plane of travel, and the torque rating of the guidearms the axis travels on.

Hope this gives everyone a clearer picture of the situation and why the original answers really did meet the requirements of the question, and where the "arbitrary" values came from. Peter's answer just prompted me to wonder what others out there do, as I've only been exposed to what I see here. Thanks again to all.

Russ

 

[kamenges]

Russ, the only reason I thought the limits were somewhat arbitrary was that they were simply the values from 'before'. I kind of figured you didn't want the move to take longer than 4.7777 sec. But why not shoot for 4.5 sec and give yourself some extra 'fluff' time?/

Originally posted by russmartin:

I don't believe one has the ability to alter jerk rates with the move commands involved(if so, please feel free to elaborate.)

If you are using the MAM command you should be able to specify the jerk value. The only thing they recommend you not do is change the jerk rate on an active move. If you really want to play with jerk you can use a tag as the jerk rate. This is possibly a firmware level dependent item. I am looking at CLX V15 and V16 and they allow changing jerk.

The thing about adding jerk is that the peak acceleration rate using jerk will be higher than the peak acceleration on a constant acceleration move, all other things being equal. However, the benefits of adding jerk to the profile tend to outweigh the increase in peak acceleration unless acceleration becomes a hard limit. In your case it sounde like it might be. The impact forces encountered in the drivetrain as the backlash comes out during a step accel move are usually much worse that the increased accel due to adding jerk.

Keith

 

[russrmartin]

Thanks Kieth for the tip. I'll have to take a closer look at this when I have some free time. This machine is still running V13, so if it is version dependent, it may not matter. But I had not noticed this feature in the newer versions either, and it would just be another tool for the box. Thanks again.

Russ