I was bored so..

I wrote a Excel spread sheet so that people could use to get experience at tuning PID for position control.

The reference position is a sine wave with a selectable amplitude and frequency.

The PID uses Tustin's approximation to convert an analog PID into a a digital PID. It also adds a low pass filter at 2/T radians where T is the sample period.

The system or plant is a simple single pole system with a gain and a time constant. The model is G/(ts+1) where G is the system gain in inches per second per volt,t is the time constant in seconds, and s is the Laplace operator.

position PID spread sheet.

If you get the tuning right you can get the actual position line to cover the target position line. When this happens you have the system perfectly tuned.

This system should be easy to tune because it has only one pole. However the output will saturate because the target velocity makes a step jump when starting.

Notice that it is more difficult to tune as the amplitude and the frequency become larger.

Click on the comments for more information.

Very informative, thank you

Note: For some reason the Graph has 126 pages and when you goto Print but only 1 has the Graph on it.

ditto..

I agree with Ron, it is a very interesting spreadsheet. Even though I don't do alot of motion control, it does help see the results of Proportioanl, Integral and Derivative control with respect to phase Lag and Lead compensation, being a newcomer to controls.

Thanks

Andrew

A more challenging system to tune.

The system model in the previous .zip file is a simple system that has only a gain and a time constant. The link below is a more realistic 3rd order system that will oscillate. Now the system has three parameters: a gain, natural frequency and a damping factor.

PID and 3rd Order System.

Just for fun I included a sum of errors squared display. Use this term to check if you are making an improvement after changing a gain. The goal is to minimize the sum of errors squared.

To make the system easier to tune:

Increase the natural frequency.
Change the damping factor so that it is closer to 1.
1 is critically damped.
>1 is over damped.
<1 is under damped and usually what one finds on real machines.

Enjoy. It is a challenge to tune the PID parameter to minimize the sum of errors squared, but the real good stuff is the equations.

kindly REPOST the Files

Dear,

Kindly upload once again these files and send us the link.


Regards,

Parsn

I will repost what I have.

The files will appear in this directory
http://www.deltamotion.com/peter/xls/
I will update this directory as I have time.

I don't do simulations using Excel anymore because the files get to be too big.

Thanks Peter this will help when I train other techs I work with

Did you notice how old this thread is?

You should know that I have a way of identifying systems.
There are type 0 ( non-integrating ) like temperature or velocity systems.
There are type 1 ( integrating ) like position and level.
For instance :
T1P1 means the the system is a integrating system ( position ). The P1 means the system has one real pole like the low pass filters.
T0P4 was made to be a challenge. It has four real poles and is non-integrating like a temperature system
The T1P1 systems should be good for practice tuning motion systems.
I don't know what the others are good for except to be a challenge.

lol no never noticed the age of the thread