Open loop procedure of PID tuning

I recorded step response of temperature system. I would like to determent parameters of PI controller for that system.

I work in Matlab so I need hep on next topics:
1. recorded curve is not smooth, can I use LSQR function (or something else) to make it smooth. I recorded values of temperature in vector named "heat" and time in vector named "time". Dimensions of vectors are
1 x m.
2. How can I drown tangent for determining of time delay and time const
of system on base of step response. How to do it in Matlab.
3. I would like to make my function for determining of parameters for PI controller. Function should be based on step response of system in open loop. Give me advise what my function should look like, what should include, what useful matlab function should I use.
I'm electrical engineer and this days I'm working on my exam for post graduated studies, so any help would be useful.
Many thanks!
Looking forward to hearing from you. Best Regards. Open Loop Procedure
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Step response curves are rarely smooth in practice. The trends shown on
http://www.contek-systems.co.uk/UTune%20trend%20noise.jpg were recorded while tuning a compressor CCC anti-surge controller a few months back and are fairly typical of fast acting process measurements. However, since many tuning methods are based on a simple model of delay and first order lag, its generally easy enough to fit the model to the 'noisy' curve i.e. rather than trying to remove the noise from the data, try to position the model to minimise the differences between the model and the data.

If you do a search on Ziegler Nichols, you'll find lots of tutorials on step response methods. The gain produced by Z-N is often rather on the high side, but if you can get hold of the book 'PID controllers, theory, design and tuning' by Astrom and Hagglund, they write about several methods giving much better results. If its any help, I have a free tuning calculator on my website http://www.contek-systems.co.uk/Products.htm .
Regards John Greene Contek Systems Ltd Aberdeen, UK
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The Zeigler Nichols Method is a very old method of tuning PID controllers with delay and a first order response.
The general idea is that it quarters the amplitude of the response in closed loop after a certain time...(If i remember correctly)
If it is an experimental setup and you are considering digital control - and you are using Matlab - you might consider looking at switching a relay on and off with a pseudo random binary sequence. and then Identifying a *better* model than can be had by using ZN
Take a look at matlabs system id toolbox - its a very impressive difference - but requires a little more work
HTH
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System that I wish to control have great inertia. ZN, Chein, Astrom... gives procedures for determining PID parameters for system with time delay - time object ratio greater than 0,1. For my system that ratio is little over 0,07.
How to find point on the step response curve in witch I should draw tangent? How to find intersection of tangent and setpoint line?
I know principle and theory, my curve is not smooth becouse of noise, I need to filter it somehow.
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