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

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:

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

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

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

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.

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.

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!

...

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

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.