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I had a few additional resistors. The current was multiplexed among PLTs sequentially to measure temperature at different points on the system.

Voltagecontroller

In this circuit, the resistor R is time variance. My goal is to have a desired current amplitude to be generated through this circuit. My idea is to control the voltage source via a PID controller do you think it is possible? Do you have any other suggestion?

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Current controllercircuit

Anyway, if you deliberately (in analog or digital form) insert a dominant lag that is much longer than the sample time, you can use ordinary PID tuning rules. Suppose your sample frequency is 1kHz and your ADC and DAC respond almost instantly, then you might want a 10Hz cutoff low pass filter on the output.

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Thorlabs laser diode temperaturecontroller

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DCcurrent controller

On the other hand, if the load really looks like a (very linear) R, and if the sample rate is low and the ADC settles completely during each sample time you could simply calculate the estimated R' as Vout/Imeasured and calculate the new V from the estimated R, perhaps with a bit of integral action. This won't work over a wide range if the load is something very nonlinear like an LED, and other precautions would probably be necessary to prevent damaging such a load by overshoot.

DC voltage andcurrent controller

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ACcurrent Controller

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You can certainly close such a loop digitally, but the performance (response time including correction from disturbances such as fast changes in R) will likely be very much inferior to having a good DAC and an analog closed loop.