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The Control Loop Cookbook from TI explained about sub-harmonic oscillation as below.
I am really confused by the part "cross over each other at their points of intersection".
This is probably due to my English language. If two waveforms cross over then they should cross at their intersection points, don't they?
Yes, average control measures the average current in the inductor and uses that in the inner current loop.
One advantage is that you don't get subharmonic oscillations at duty cycles >50% as you do in peak current mode control (without slope compensation.) Also, the average inductor current is the true state variable that you're trying to control, the peak inductor current is only an approximation. The peak to average ratio changes with operating condition.
Disadvantages are: More complex to measure the average current. Current limit may not be cycle-by-cycle.
For digital control, it's fairly simple. Create a in inner current loop by measuring the average inductor current, and use the outer voltage loop's error to drive the current reference just like you would in analog.
Rather than going into the mathematics of this, it's quite easy to see this graphically. Consider a peak current mode controller operating at <50% duty cycle. Then you can see below that perturbing the system results in the perturbation decaying and the system returning to steady-state operation.
But at >50% duty-cycle the system does not return to steady state operation. Instead, it enters a "sub-cycle oscillation" mode.
Simple as that.
See source for a more detailed explanation.
Best Answer
Here's a SIMPLIS simulation of an average current mode loop similar to this figure:
From this TI app note
Note that the compensator inverts the sensed inductor current, so the down-slope becomes the up-slope in the figure.
If the inverted downslope of the inductor current is equal or just less than the ramp slope there is optimal gain because any additional gain will result in subharmonic instability. This looks like the following. The red trace is the sensed inverted inductor current, the green is the ramp and the blue is the switch. You can see the regular duty cycle with no subharmonic oscillation by looking at the switch.
Since this is average current mode we want the loop to respond to the average current, not the peak current. Once the inverted downslope of the current has a slope that's greater than the ramp you get the situation below. The extra crossing of the ramp now changes the duty cycle in an unintended way. The inverted inductor up-slope is always well above the comparator trip point so it's only the downslope that can cause this kind of trouble.
In practice subharmonic instability in average current mode control isn't nearly as troublesome as peak current mode control. There's no need to add a compensating ramp or avoid duty cycles greater than 50% (or even less). If you do see it in average current mode control you can just raise the value of the R1 resistor lowering the compensator gain a bit. (Doing the math to be sure you have a robust compensation.) (Actually it's not a big deal in peak current mode either as most controllers have built-in slope compensation these days which makes it very easy to use.)
Here's a more extreme example with higher compensator gain (Again, the sensed inductor current is inverted so inductor current ramp up is a down slope here):
And back to stability: