I was interested to know others opinions on tuning of loops with large process time constants and small dead time's.
These cause the Tp/Td ratio to be quite large, hence causing very large Kc when using the Z-N method's.

Ok, here is the loop data (after an open loop step response and subsequent FOPDT modeling):

Process Type: Pressure Control
Step Direction: CV Open, thus Pressure Inc.
Change in Control Valve (dCV): 0.72%
Change in Process Variable (dPV): 0.71%
Process Gain (Kp): approx 1
Process Time Constant (Tp): 65sec
Dead Time (Td): 2sec

I plotted the data to a FOPDT model to accuratly determine the Process Time Constant (Tp).

From Z-N equations (both the Process Gain & Reaction Rate methods produce the same results), I calculated:
Controller Gain (Kc): 29.67
Integral Time (Ti): 6.6sec

Please tell me if these were calculated worng, but it appears like Z-N is grossly incorrect when the loop has a large Tp with respect to its Td.

I have tried with an Aggressive IMC method and this also gave the values of:
Controller Gain (Kc): 7.76
Integral Time (Ti): 65sec.
Closed Loop Time Constant (Tc): 6.5sec

Moderate IMC gave more expected values of:
Controller Gain (Kc): 0.98
Integral Time (Ti): 65sec.
Closed Loop Time Constant (Tc): 65sec

If anyone out there can offer some much needed advice as to how I should approach this, I would be very grateful.

Thanks,
Glenn

 

To do a sanity check on your results, look at what happens on a Bode diagram.

With a FOPDT process, the cycle period if it should manage to go into continuous oscillation is 4 times the dead time = 8 seconds in your case. The cycle frequency is then 1/8 = .125 Hz. The -3dB frequency of the time constant is 1/(2 x pi x T) = .00245 Hz. The ratio of the -3 dB frequency to the cycle frequency is .00245/.125 = .0196 so the process dynamic gain at this frequency is .0196 if process DC gain is 1.

For quarter-amplitude damping, the loop gain at the cycling frequency is 0.5, so KC x .0196 = 0.5, so Kc = 25 for purely proportional control. So your first result is not too far out, based on an ideal FOPDT process. But your actual process will be a lot more complicated than that, and this is why (as has been stated here on many occasions in the past) Z-N and other methods can provide only an estimate of suitable controller settings.

- quarter-amplitude damping may not be the best response for your particular process
- detailed dynamics and nonlinearities make the actual process response much more complex than the model
- etc.

So you need at some stage to go on line and tune using a systematic adjustment procedure. The one I have used most successfully with relatively fast processes is a variation on the Ultimate Cycle method:

- start off with a low gain ("low" in this context being about 1/10 the "typical" value for your particular controlled variable)
- set integral time to 0/reset rate to infinity
- increase gain (about 2:1 steps initially till there are signs of overshoot, then 1.5:1) till a suitable response is obtained.
- adjust the gain to about 0.8 of that value, and integral time to about the cycle time observed.
- adjust integral time to give an acceptable response.

Regardless of what the books say, at some stage you will have to go live and see what happens - with a process such as the one you have described, you are likely to find the acceptable controller settings determined by process noise and the acceptable gain will be found by increasing controller gain until the valve starts to move an unacceptable amount in response to process noise.

Bruce

 

Bruce,

Thanks for your prompt reply. I ended up using a similar method to the one you outlined above. After using about 80% of the inverse of Kp (for the Kc parameter), and 4 x Td for the Ti, I made the necessary adjustments from observations (SP bumps up and down).

Turns out the loop was much more complex than initially thought. The Temperature Control sprays had quite a considerable impact on the Downstream pressure, so the Pressure loop and Temperature loop would continually over correct each other... happy days trying to fnd that 'happy place' where they could get along.

Your reply has really prompted me to learn more about the Frequency Analysis of loops. My practical knowledge in this area is quite restricted, however I do know what it is and the theories governing it all.

Is it possible that you can point me in the right direction as to the 'real life' use of Frequency Analysis (any useful website would be beneficial).
I started to think about this after observing oscillations in a loop about 4 weeks ago, and it made me ponder what the impact the Integral Action has on the oscillations, etc.

Additionally, considering how information from a bode plot could help me determine what impacts noisy flow measurements have on feed forward loops that require a high gain setting in order to make the necessary CV adjustment (due to disturbance).

 

Aha - you have an interactive process. Temperature is usually very slow and noise-free, so can often be decoupled from other loops by making it much slower than the interacting loop. One method is to tune the faster loop first, then tune the slow loop with the fast loop in operation. But you may find that the whole thing turns to custard if the slow loop is switched to manual or the operating conditions change significantly. If interaction is significant, the standard single-loop methods may not work under all circumstances... I very rarely use frequency analysis as a serious tool - it is handy to give a quick visualisation if things don't go to plan, but so many real-world factors (control valve characteristics, process noise, outside influences etc) come into play that it takes a lot of time to get a satisfactory transfer function.

Cheers,
Bruce

 

Why didn't you stick with the IMC gains? They will work. I didn't reply before because I thought you had the answer (IMC). ZN is not the answer. The formulas for the IMC gains can be derived. They are not estimates like the ZN method. The ZN gains will always provide an under-damped with a lot of overshoot. The IMC gains will provide something that looks like a critically damped response with little if any overshoot.

Your plant dead time is not very long compared to the plant time constant so I don't see a problem with the dead time.

Visit http://www.controlguru.com for examples of how to apply the IMC gains. You can be more aggressive. The formula for Kc is Tp/(Kp*(Tc+DT))
where Tc is the closed loop time constant. The conservative thing to do is to make Tc=Tp, which is what you did. You can make Tc smaller. Ti is still always equal to Tp for PI tuning of a FOPDT plant.

 

Thank you both for your input.

I did (and mostly do) stick with IMC. However, like most things, I was interested to know other people's approach and explanations of these problems/issues. It helps me to identify any misconceptions I may have, and also helps me to thing of issues from another angle.

Cheers,
Glenn

 

Experience has shown that all these various formulas just works well within a certain range. Therefore our own tool evaluates 25 different methods w.r.t. the user specification (SP or load tuning, fast or smooth action, or minimum use of the resource) and presents the three best results graphically. The integrated simulation environments allows to test these settings for various disturbances but also noise, sticking vales etc in shortest time. Final results are typically quite different from the single method approach.

Hans H. Eder
[email protected]
www.act-control.com