What is PID Open Loop Estimation.vi doing?

[Lewis_G]

Hi,

I'm using the PID Autotuning Design VI to aide in PID tuning.  Most of the step response PID tuning methods work using the open loop step response of the system.  My system is an integrating process which means when the input signal is a step, the process variable will change at a constant rate.  So I can’t give it a step response in open loop.

In order to get a step response, I must be using this VI when the control loop is closed. When doing this, the VI  Autotuning Design VI estimates the open loop dynamics of the system using the PID Open Loop Estimation.vi

I want to know how this VI estimates the open loop dynamics based on the closed loop dynamics?

Both of these VIs are part of the PID toolkit.

There is a note on the BD of the VI saying “1^st order” so I’m guessing the inputs to the VI are fitted to some first order transfer function and then block diagram reduction is used to remove the feedback loop.

So how does this VI estimate open loop dynamics?

Cheers.

Lewis

[Barp]

At the moment, the closed-loop identification is only based on first-order model with delay. Which means that after obtaining the equivalent first order model using only a proportional controller, this VI will try to remove open-loop parameters based on the closed-loop response.

Does is make sense?

[Lewis_G]

Hi Barp,

Thank for you getting back to me.  I fully understand why this VI is needed and what it is doing but I want to know how it is doing it?

The true case is running the following equations to estimate the closed loop response:

Where are these equations from? How do they work?  What literature are they discussed in?

Thanks again, your help is much appreciated.

Lewis

[BenClark · Accepted solution]

Hi Lewis,

I'd thought I'd share the method of getting down to the Open Loop estimations:

Using first principles in control theory, we know that the closed loop gain is:

From here we need to get G(s) as the subject of the equation:

1. Make the numerator the subject of the equation.
2. Expand.
3. Rearrange to get G(s) on one side.
4. Factorise to get one set of G(s)
5. Rearrange to make G(s) the subject of the equation.

For calculating the time constant conversion, I feel that this website explains the calculations involved quite nicely:

http://www.facstaff.bucknell.edu/mastascu/econtrolhtml/Intro/IntroNotes/IntroNote_1OrdTimeConst.htm

In this page it describes a general principle for a first order proportional controller and describes an expression for the closed loop time constant based on this. At the bottom of the page  we have the same equation as the VI but with T_cl as the subject of the equation.