Seemingly Simple Kinematics Question

[jlatshaw]

Hello,

Perhaps I am overthinking this, but I am trying to find the acceleration of the 'pulse rate' in the below plot.
Every so many seconds there is a pulse (you can think of this as x displacement). The initial rate between pulses is 5 pulses/sec (you can think of this as velocity). I am attempting to find out what the acceleration of the pulses are.

At the far right of the plot the velocity becomes constant at 50 pulses/sec. The numbers at the bottom of the plot are simply counting the pulses. The red text above each pulse is the time in seconds between each pulse.

My problem is that when I use basic kinematic equation I can't determine the acceleration (it's almost like the acceleration is changing between pulses).

How do I determine the acceleration of the pulse rate?

Thank you for taking time to look at this. :)
-James

 

[berkeman]

Interesting display -- is that from an oscilloscope or logic analyzer or something? The numbers in the symbols are just a count of the symbols, right?

I just looks like a chirped waveform. And you are wanting to know the rate that the pulse frequency increases?

https://en.wikipedia.org/wiki/Chirp

 

[jlatshaw]

Hi Berkeman,

Yes, this is from a logic analyzer simulation that is counting steps from a stepper motor (each pulse is one step). And yes, the numbers on the bottom are keeping track of how many pulses have occurred. I should have mentioned that the horizontal axis is time.

Also yes, my goal is to determine what the the acceleration is (pulse/sec^2). The hardware that I am using has several inputs which are pulse velocity and pulse acceleration. In the above plot I have velocity set to 50 pulses/sec and acceleration set to 5. But, when I look at the above plot, it does not look like the acceleration is 5 pulses/sec^2 but I am trying to find out what units this acceleration value is into better understand what it is doing.

I will research more into the Chirp link that you provided. If this this is following a 'chirp profile' then that would explain why the acceleration appears to be changing.

Thanks again,
James

 

[berkeman]

The hardware that I am using has several inputs which are pulse velocity and pulse acceleration. In the above plot I have velocity set to 50 pulses/sec and acceleration set to 5.

Summary:: Referencing the below graph, how do I find the acceleration?

The initial rate between pulses is 5 pulses/sec (you can think of this as velocity). I am attempting to find out what the acceleration of the pulses are.

At the far right of the plot the velocity becomes constant at 50 pulses/sec.

I'm having trouble with the numbers you are mentioning. The plot looks like it starts at 5pps and chirps to higher pulse rates. But you say you are setting an initial value of 50pps with an "acceleration" of 5pps^2? Can you say what hardware you are using to do this generation?

 

[jlatshaw]

yes, those are the correct numbers. Here is a another plot showing when the pulses become constant and the total 'ramp up time'

As far as the physical hardware, this is actually a simulation of stepper driver module that is running on a Cyclone 10 FPGA which is sending the pulses to a stepper driver chip. But these are simulations. I am arbitraily choosing the input velocity (50 pps) and the input acceleration (5pps^2). But you are probably realizing the same thing that I did which is that the acceleration is not actually 5 pps^2.

I can re-run this simulation with different values if it helps?

Thank you very much for all of your help.

 

[berkeman]

Ah, thanks, that helps a lot. Is your goal to optimize the stepper motor acceleration profile for some application? Are you trying to balance maintaining high torque values as you increase the stepper rate? Or are you trying to generate the best profile for some machine movement (like a robot arm) where the stress on other mechanical parts plays a role in the optimization?

 

[jlatshaw]

The goal is to have a generic driving module that can have adjustable parameters (such as velocity and acceleration) to meet different profiles ( so I suppose the second option that you listed). But this driver won't be used for a robot arm, it will just be used for positioning (however, if you are about to offer some pros and cons between the two options that you mentioned, I'd love to hear them. I'm still pretty new to this and would love any input).

I suppose the main reason for this post was to attempt to discover meaningful units for the 'acceleration' input so that it can better used. But it looks to me like the 'acceleration' is more of a a chirped response which isn't exactly a 'linear chirp' or an 'exponential chirp.'

 

[berkeman]

BTW, I did a Google search on Stepper Motor Profiles and got some good hits. Different profiles (and their tradeoffs) are discussed in some of these hits:

https://www.google.com/search?client=firefox-b-1-d&q=stepper+motor+profiles