Control of a light source

Hello,
I'm developing a control system to stabilize the luminance and the color temperature of a light source (an incandescent lamp). Both the
luminance and the color temperature depend on the current supplyed to the lamp. I have these specifations: - if the color temperature variation is less than 10K follow only the luminance variations, else correct the current supplyed and check whether the luminance satisfies with its specifications; - if the luminance variation is less than 0.5% but greater than 0.1% (0.1% is the uncertainty on the luminance measure) there is only an offset correction, else if the variation is greater than 0.5% correct the current supplyed and check whether the luminance satisfies with its specifications; - if luminance and color temperature come into conflict alert the operator to do a new calibration.
I know that, when the lamp is supplyed with its nominal current, the relation between current and luminance is L = A + B*I, while a variation a 4.5mA causes a variation of 1K. I read the value of luminance and color temperature from a photodiode.
Till now I have only developed simple LTI closed control loop using simulink, I don't know how to manage this problem. I'd like if someone of you could give me some suggestions.
Thank you
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tucker wrote:

Your message raises many questions.
What does "follow (only) the luminance variations" mean?
What is an offset condition?
How do you propose to control luminance and temperature separately?
How can you determine color temperature with a single diode?
Are the relations of color temperature and luminance to temperature really linear, as your message suggests?
Have you modeled the resistance of the filament as a function of current?
Jerry
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Jerry Avins wrote:
...

...
Make that "Are the relations of color temperature and luminance to current really linear, as your message suggests?"
Jerry
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Jerry Avins wrote:

I mean that, for the color temperature, a correction of the supplyed current is necessary only if the error is > 10K

When the lamp is supplyed with its nominal current of 6.8 A, the relation between current and luminance is L = A + B*I for small variations of luminance. I can vary the current only with step of 4.5 mA that correspond to a variation of 0.5% of luminance. If the luminance error is in 0.1% - 0.5% I cannot vary the current, I have to change the term A (L = A + B*I) in order to have an error < 0.1%.

I cannot control luminance and color temperature separately because a change of the current supplyed causes a modification of both the luminance and the temperature. It is not guaranteed that both the specifications on luminance and color temperature can be achieved.

Doing two measurements on the light source using first a red filter and then a blue filter.

They are not linear, that relations were estimated by a physicist that worked on the project.

No, all the information I have on the plant come from a doctoral thesis.
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tucker wrote:

Are you saying you can vary the A term? Surely not.

Frightening
Even more frightening.
Depending on the hardware that you're using to implement your controller you may be able to get better resolution on the luminance that 0.5% -- see my article about sigma-delta converters on http://www.wescottdesign.com/articles/sigmadelta.html .
Your lamp is going to have some time-dependent behavior, and you can never be sure of estimated gains (the 'B' term in your equation). Unless you can afford to have the system respond very slowly you should measure this behavior -- I advocate using swept-sine measurements, but there are plenty of people who feel you should get a step response and do an ARMA system identification procedure. Then you should use this measured behavior to determine the feasibility of increasing your apparent DAC resolution through dithering, and to design a solid controller with some sort of stability guarantees.
Were it me, I would first determine if I could make an ultra-conservative controller. If I could I'd just make a PI controller, possibly with a sigma-delta output stage to increase the current resolution, possibly with some deadband to prevent a limit cycle around the current step. I'd design and tune the PI controller per the methods outlined in http://www.wescottdesign.com/articles/pidwophd.html .
If I needed better time response than what an ultra-conservative controller would give me I'd do a swept-sine measurement and design a PID controller using frequency domain techniques. I'd measure the response per http://www.wescottdesign.com/articles/FreqMeas/freq_meas.html , and design it per chapter 6 in my book "Applied Control Theory for Embedded Systems" (http://www.wescottdesign.com/actfes/actfes.html ).
--

Tim Wescott
Wescott Design Services
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Tim Wescott ha scritto:

Many thanks for your suggestions.
I read the photodiode voltage using a digital voltmeter and the current is supplyed using a programmable DC power supply, both connected to a pc through IEEE488. I'd like to do a swept-sine measurement but I have not at my disposal the necessary instrumentations, I can try to get a step response instead. The system hasn't any requirement on the time response so a PI controller should works fine.
Tucker
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tucker wrote:

I think the first thing you need to do is clarify you specifications. Your first item sounds OK, your second bullet sounds like design rather than specifications, and your third item sounds like an alarm, not control, which contradicts your opening paragraph.
If you just need to hold the luminance steady and sound an alarm if the color temperature goes off too far then an LTI controller for luminance and a threshold -- possibly with a filter -- around the color temperature measurement should be all that you need.
--

Tim Wescott
Wescott Design Services
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Sounds like a great place for an LM3524 if they still make them..I've built this circuit...does a great job for less than $10.
http://www.hep.fsu.edu/~wahl/phy3802/expinfo/electronics/AN-292.pdf
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