[OT] Inflection point in step response (PID control)

Hi there, I am new here. I need some help for a problem in a PID control (for a project work). I'm doing a PID control and I'm using the so called "Nichols-Ziegler
method" to evaluate the parameters of it. I have the step response of my transfer function that I can view with MATLAB. My hard problem is that I am not able to find in the plot the inflection point in the step response. My question is: there is a graphic or analytical procedure (in MATLAB) to locate the inflection point of the step response? I try to find it in the point where the curve stops curving upwards and starts to curve downwards but I need an high precision. Heart thanks in advance!! P.S.Sorry for my english Kind Regards Giuseppe
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Welcome to the real world (even if viewed through the eye of Matlab).
What level of precision do you think you need? Remember that the original Z-N work was done for pneumatic controllers, where the setting accuracy for the tuning constants was about +/- 20%. The method is also applied successfully to responses obtained from noisy industrial processes with very small step changes (try to persuade an operator to bump a valve position signal on a running plant by more than about 5%)
Z-N methods give starting points for the tuning process, rather than allow you to calculate the exact values.
Anyone using Z-N for academic work should first of all read the original article to find out why the work was done and what their conclusions were based on - and it wasn't to obtain any sort of theoretical "optimal" control.
t1nt0r3r4 wrote:

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Bruce Durdle ha scritto:

Thank you for your answer Bruce.My real problem is that by the inspection I made on the plot to find the inflection point I get an approximation of it (I'm not sure that the location is right).I need more approximation than my solution by inspection (but not an industrial precision...the work that I'm doing is only an academic work for my university study). With the Z-N I have to obtain just starting points for the tuning process but I must draw a tangent through the inflection point to determine the process parameters (gain,deadtime,time constant).
I'm thinking to use the anti-Laplace: in work domain I should try the inflection point of the step response and then trasforming it in the frequency domain...what do you think about? Thanks for your help!! Greetings Giuseppe
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One thing to think about is the effect of any error in your determination of the gradient. If the gradient is too low, you will underestimate the rate of rise of the controlled variable, and also the pure delay element. Both of these will tend to give a controller gain from the formula that is on the high side. It is better to make your estimate steeper rather than flater, as this will give a more conservative initial setting with less risk of excessive gain. I'm not sure why you refer to "industrial precision" - the precision you ccan get in an industrial environment is actually very low. Think about 5% step changes in valve position and a signal with a noise component of 2 or 3%, and controllers where the accuracy of anjustment of the settings is +/- 20% - you don't get high precision (but thne, you don't really need it either).
t1nt0r3r4 wrote:

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We recently did work where a customer wanted to control a product property "spot-on 99% of the time" (an impossible feat, but yes, that was the "spec"). When I asked how accurate the instrument was for measuring the product's property in question, they said "+/- 0.5 out of 14.0" (+/- 12.5%) and repeatability was unknown.
Expectations and reality... often worlds apart.
Carl Cook BioComp Systems, Inc. http://www.biocompsystems.com
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Carl wrote:

I find that often the first service that I provide for a customer is helping them understand the reachability of their goals. Often I do this up front, and sometimes it's a deal killer, but at least they're not disappointed down the road!
--

Tim Wescott
Wescott Design Services
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Tim Wescott wrote:
...

Good man! (and good self defense too). It's very hard to explain to some people that one can specify the details to be performed or the results to be achieved, but not both.
Jerry
--
Engineering is the art of making what you want from things you can get.

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Agreed. We've killed a few deals this way as well. And it's for the better for all parties involved. It doesn't happen often because we take customers through a staged process whereby we do quick feasibility studies, then workshops with quantified results, then on to the project. We rarely get into these situations after multiple reviews of expectations and requirements, but sometimes a "blooper" gets into the RFP. Sometimes its a mis-wording or mis-understanding. For some, it is difficult to understand the difference between "99% accuracy" vs. "100% accurate 99% of the time".
Carl Cook BioComp Systems, Inc. http://www.biocompsystems.com
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t1nt0r3r4 wrote:

Giuseppe,
Finding a point of inflection by inspection is hard. One way to check a guessed inflection point is to draw a straight line between two points on the curve equally distant from the presumed point of inflection. If the straight line crosses the curve midway midway between the two points, you guessed well.
Desidero che il mio italiano era persino un quarto buon quanto il vostro inglese!
Jerry
--
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Jerry Avins ha scritto:

Thanks a lot for your help Jerry. I'll try this method...very good idea ;-) ! You are on the right way to talk with me in italian! :-) Greetings Giuseppe
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Jerry Avins wrote:

I was going to suggest numerical differentiation, but this should yield better results with noisy data. You could even use Matlab to automate this process if you needed to analyze a number of step responses from different systems.
You may also want to check out the Astrom-Hagglund method, which is a more recent refinement of the Z-N method.
--

Tim Wescott
Wescott Design Services
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