Please help, trouble in design PI controller (ZN FOPDT tuning)

t_n_k

Joined Mar 6, 2009
5,455
A further reflection on this 'saga' led me to take a second look at the simulations I've so far done on this problem.

Taking the steps outlined in my preceding post I obtain the first step response shown as an attachment.

Then I applied the Z-N heuristic approach of disabling the integral term in the PI block and 'winding up' the proportional gain until a steady-state oscillation is obtained.

Per the prescribed heuristic methodology I note the required gain to achieve oscillation [Ku] and the actual period of oscillation [Pu]

From these I derive the estimated values [per the literature] of

Kc=Ku/2.2=0.253/2.2=0.115

&

Ti=Pu/1.2=0.23/1.2=0.192 sec


Plugging these values into my simulation I obtain the second slightly less oscillatory response.

It's worth noting this distinction - I would suggest the Z-N method based on the second 'heuristic' approach produces a slightly 'better' response than the 'formula' method.
 

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Thread Starter

YukiWong

Joined Dec 5, 2011
27
A further reflection on this 'saga' led me to take a second look at the simulations I've so far done on this problem.

Taking the steps outlined in my preceding post I obtain the first step response shown as an attachment.

Then I applied the Z-N heuristic approach of disabling the integral term in the PI block and 'winding up' the proportional gain until a steady-state oscillation is obtained.

Per the prescribed heuristic methodology I note the required gain to achieve oscillation [Ku] and the actual period of oscillation [Pu]

From these I derive the estimated values [per the literature] of

Kc=Ku/2.2=0.253/2.2=0.115

&

Ti=Pu/1.2=0.23/1.2=0.192 sec


Plugging these values into my simulation I obtain the second slightly less oscillatory response.

It's worth noting this distinction - I would suggest the Z-N method based on the second 'heuristic' approach produces a slightly 'better' response than the 'formula' method.
Hi t_n_k, thank you very much on helping me until now :).

Ya, i had work out my transfer function and apply it with Skogestad's method and found that it had less overshoot compare to the Z-N.



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The pink color is the Z-N method and the yellow color is the Skogestad method.

Is it prove that skogestad is better than Z-N at this transfer function?
 
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steveb

Joined Jul 3, 2008
2,436
Since we are showing different methods, I thought I would post a solution using the gain and phase margin rule GM=12 dB and PM=45 deg. I just did a quick optimization which resulted int GM=11.8 dB and PM=48 deg. The end result is not too different than the Skogestad solution.

Personally, I try not to use methods developed by men whose names I can't pronounce :p

Seriously though, the gain/phase margin approach is quite good and even adaptable. More complex systems sometimes require further compensation techniques, but this often amounts to tweaking the open loop gain/phase response (adding either additional poles, zeros or pole/zero pairs) until the form is suitable for optimization with the phase/gain margin approach with a P or PI filter, as considered here. I've never had any issues using this approach, including the time I had to optimize the control of a system which had 14 poles and 13 zeros.

EDIT: I added a a Nichols plot and a Nyquist plot, (since I can pronounce their names :p) which are useful tools.
 

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Thread Starter

YukiWong

Joined Dec 5, 2011
27
Since we are showing different methods, I thought I would post a solution using the gain and phase margin rule GM=12 dB and PM=45 deg. I just did a quick optimization which resulted int GM=11.8 dB and PM=48 deg. The end result is not too different than the Skogestad solution.

Personally, I try not to use methods developed by men whose names I can't pronounce :p

Seriously though, the gain/phase margin approach is quite good and even adaptable. More complex systems sometimes require further compensation techniques, but this often amounts to tweaking the open loop gain/phase response (adding either additional poles, zeros or pole/zero pairs) until the form is suitable for optimization with the phase/gain margin approach with a P or PI filter, as considered here. I've never had any issues using this approach, including the time I had to optimize the control of a system which had 14 poles and 13 zeros.

EDIT: I added a a Nichols plot and a Nyquist plot, (since I can pronounce their names :p) which are useful tools.
thanks steve :) actually this is a model from DC Motor which connected through OP amp, Pre amp and servo amp.. anyway,why can't pronounce the name :p?
 
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