Loop crossover frequency selection

[Porsche]

Greetings. I am designing a linear power supply with CC/CV capability. The output voltage is controlled by a voltage control loop that controls the current control loop. My current control loop has been compensated so that its crossover frequency is approximately 100 kHz. According to the simulation, a reasonable phase margin was achieved using a simple type I compensator.

Now, I want to close the voltage control loop. However, the plant transfer function is now strongly dependent on the load current and output capacitor parameters. My general goal is to create a stable system for any type of output load. I have modeled some cases of an output load and output capacitor value to estimate the best points to close the loop. According to the plant transfer function, the load variation influence starts at approximately 10 kHz. After 10 kHz, major variation in the plant transfer function shape can be observed under full or no load. Therefore, closing the loop at <10 kHz seems reasonable.
However, the capacitor value at the output drastically changes the whole picture.
Plant transfer functions for different configurations:
1 Output capacitor 100 uF 175 mR, 

2 Output capacitor 470 uF 50 mR,

3 Output capacitor 2200 uF 20 mR,

What is the optimal strategy for compensator design in my case? Is it possible to lower the influence of capacitors and load parameters on the plant transfer function?

[MathWizard]

I haven't tried to calculate something like that yet, but with op-amp's, if you just use ideal op-amp's in the eqn's, so ignoring input currents, and in/output impedance's, would the results be off by much ?

I'm getting used to AC models of BJT's, and how that compare's to LTSpice, but yeah I haven't done more complicated op-amp models.

[EggertEnjoyer123]

With a large capacitor and no load, there is no way to discharge the capacitor. Imagine that your voltage is set to 28 volts. If you change the setpoint to 25 volts, the capacitor will remain charged at 28 volts, since there is no load. The MOSFET will turn off, but that doesn't help discharge the capacitor. This is one of the big reasons why the gain is different for no load and load. If the load is big, then the capacitor will quickly discharge from 28 to 25 volts. Most bench power supplies will exhibit this behavior if you connect a large capacitor to them. I've seen designs with discharging transistors to take care of this case.

Also keep in mind that large amounts of current are needed to change the voltage of a big capacitor at high frequency. A big capacitor also already shorts out high frequency, so there's no advantage to having a high loop bandwidth in that scenario.

[jonpaul]

read about power supply loop stability,    use worst case desing
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[hamza zughibi]

I suggest this paper to you
https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=74640bdf33a1e8b7a319fbbbaeccf681f80861cc
I find it helpful when i was working on a similar project