Question about PI control constants 1

[eeprom]

Hello,
I am working on a PI controller for a pump system, and I am trying to figure out how to relate the gain and integration time to the physical system. The system set point is 60 psi. If the system is in manual mode, sitting at 40 psi, and I give a step input of 20 psi, it takes about 15 seconds to reach the set point of 60 psi. As I
remember from controls class (way back when), the 15 seconds represent four time constants for the system. And so the system time constant is around 3.67 seconds. How can I use this information to set the integration time? And, what is the integration time with respect to the physical system? I would assume that I could set the gain to 1 and adjust in the field. Is there a method of system testing which would give me an initial ball park estimate for gain?

thanks for your help.

Andy

 

[ScottyUK]

Google [blue]"Ziegler-Nichols" loop tuning[/blue] and report back. This is 'the' classical loop tuning method taught in college. It usually gives fairly good results on most processes, hence its popularity. There is far more information out there on the net than we could ever hope to write in a text-only forum. The link below is one which caught my eye out of hundreds - chapter 6 in particular, but the others might be a useful refresher:

http://www.learncontrol.com/tutorial/index.html

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Sometimes I only open my mouth to swap feet...

 

[sreid]

You could try this.

1)Make smaller steps to avoid saturating the control loop (say 2 PSI steps).

2)Turn off (or minimize) the integral gain).

3)Increase the proportional gain until you have some overshoot then decrease it until the system is over damped.

4) Make certain the integral windup limit (if there is one) is turned on.

5) Increase the integral gain until there is some overshoot. Then decrease it until the response is over damped. If the setteling time is not important, you may want to decrease this a lot.

6)Make big steps to make certain that the system is stable for saturated control conditions.

 

[PNachtwey]

ZN is not the right tuning method for this application. eeprom has done half the work by computing the plant time constant. All he needs to do now is compute the plant gain. This is easily done by figuing out what percent of the output was required to maintain 20 psi and the percent output required to maintain 60 psi. Then one calculates the ratio for PSI/%output. Hopefully this is linear. Then one plugs this into the formulas found on

http://www.controlguru.com.

One can find the procedures for finding the gains on controlguru too. I would find out the change in the required output for each 10 psi and plot it to figure out if the system is linear.

The formulas, assuming no dead time, are:
Ti = Tp eeprom has calculated this already.
Kc = Tp/(Kp*Tc)
Kp is the gain in PSI/%.
Tc is the closed loop time constant. 1 second is a good number. If one assumes that the pressure increases 1 psi for 1% of output then then gains would be:
Kc=3.67
Tp=3.67

This will yield nice smooth responses that will reach the set point in 5 seconds ( 5 times the closed loop time constant ).

The is a similar solution on sci.engr.control. The gains are not that critical, a few percent here and there will be OK.

"1)Make smaller steps to avoid saturating the control loop (say 2 PSI steps)."
Not necessary. The controller should be able to handle saturation for short periods of time.

"2)Turn off (or minimize) the integral gain)."
the controller will never reach set point.

"3)Increase the proportional gain until you have some overshoot then decrease it until the system is over damped."
That works but the calculations will reduce the trial and error time.

"4) Make certain the integral windup limit (if there is one) is turned on."
A control controller always has integrator limits enabled.
This shouldn't be a problem on this type of system. ( type 0 ) See below.

"5) Increase the integral gain until there is some overshoot. Then decrease it until the response is over damped. If the setteling time is not important, you may want to decrease this a lot."
There really isn't any point in making the integrator time constant longer than the plant time constant of 3.67 seconds. If one calculates the formulas for the gain using direct synthesis then one can see that Ti=Tp. This will lead to a nice first order response.

"6)Make big steps to make certain that the system is stable for saturated control conditions." The system will saturate when given a step increase but only for a short amount of time. The closed loop time constant is 1 second so the output should be saturated for no more than a fraction of 5 closed loop time constants. If the control output is saturated longer than this then the pump cannot maintain the pressure and the pump is sized wrong or there is a leak. eeprom should know the limits of his system when he does his open loop tests.

 

[sreid]

1) We know almost nothing about the plant he is controlling.

2) We know almost nothing about the form of the PI controller he is using.

3)The 15 second time from 40 to 60 PSI looks like a slewing time, not a time constant.

 

[eeprom]

Here's some more information. I have a system settling time of around 15 seconds, an overshoot of around 17%. Using these bits of data, I have established that my system natural frequency is about 0.273 radians per second, and the system behaves (sort of) according to:

G(s) = 0.273
--------------------
s^2 + .539s + 0.273

This is based on a step input of 1/2 half the total range.

So, I am trying to build a PI compensator in the form of
K1 + K2/s, using a Siemens S7 PLC. My goal is to reduce the overshoot to less than 10%, and to keep the settling time between 12 and 14 seconds. I have never done a PI in the physical world before, and I would like to know what constants I will need to obtain, and how to I choose them. I am not looking for an answer as much as I am trying to understand how PIs work.

Thanks

 

[itsmoked]

P is proportional.
It simply applies more 'restoring' effort to the system the farther the system is from setpoint.

The only problem with this simple system is that as the system reaches setpoint, by definition, the restoring effort diminishes to nothing. This means that the system never exactly reaches setpoint. It just gets close.

We need something else to actually hit setpoint ALWAYS.

How can we alter things so that we actually reclaim some 'authority' near setpoint?

Hey! If we were to add up this final "offset error" over time it would actually start to accrue some respectable value. Hey! That is, by definition, what "taking an integral", or integrating is. The sum of the area under a curve.

Enter the 'I' part. It is just that. Over time the I part shifts the output in a manner to drive this 'error area' to zero.

Works great. Caveats; If the I part has too large a gain multiplying it, the system can chase its tail oscillating around the setpoint.

Alternatively if something happens to prevent the system from eliminating the error then over time that integral will get huge or "wind up". This causes wild system excursions and must be avoided.

Keith Cress
Flamin Systems, Inc.-

http://www.flaminsystems.com