Buck converter charge battery control output voltage

Your schematic is showing current-mode control.

In voltage-mode control the error amplifier compares the output voltage to a reference, then provides an output that is compensated and compared to a sawtooth wave that will vary the PWM duty cycle to drive the error lower.

At low frequencies (esp DC) we want the error to be as small as possible, so we want the error amp/compensation to look like an integrator. Any error will then build up and drive the PWM to force the error to zero. Only zero error will allow the output of the compensation to reach steady state at DC.

If we just used an integrator for the compensation we would have to close the loop at a very low frequency which would mean poor transient response (poor rejection to disturbances). That's because an integrator provides 90 degrees of phase shift and we would have to close the loop well below the L-C output filter resonance which provides another 180 degrees of phase shift. We also wouldn't be able to control transients causing the output filter to ring because our control bandwidth would be lower than the LC resonant frequency. Still, we want to put a pole at DC for good DC regulation.

The output filter L-C has 2 poles. So in order to cancel those two poles we can put 2 zeroes in the compensation. Now we still have that 90 degree phase shift until the switching frequency effects and error amp bandwidth start to come in.

With the two zeroes we form in the compensator we get a couple of poles as well (if we want them or not).

So we put one additional pole in the compensation somewhere around half the switching frequency to filter out noise and ripple, and a pole at the capacitor ESR zero frequency to cancel that. Now we can close the loop at a reasonable frequency with a reasonable phase margin and still get good DC accuracy.

Lead Acid cells have a very low internal resistance. So a LA Battery discharged to 9 V will behave as a 9 V voltage source with a low value resistor in series. So that is why you measure 9V at the output when you connect the discharged battery.

What happens in a "proper" LA battery charger is that it enters current limiting mode which means that is will charge the battery with a predetermined current for example 1 A untill the battery is sufficiently charged. Then the voltage limiting charging will occur.

I see no current limiting measures in your schematic. This is BAD I would never design a battery charger without current limiting. Especially for a switching converter where the inductor can saturate and currents can become exceptionally large.

It can be that the current limiting is in the 18 V supply. Possible but not so elegant. There are plenty of designs that integrate voltage and current limiting in one solution.

Oh that IR2111 is only a driver ! Geez, I expected it to be a proper SMPS chip. So you're just PWM controlling the MOSFET from a microcontroller ? Please consider implementing a proper switched more converter with voltage feedback and all. This is not a design that I would build.

Some other remarks:

Usually temperature controlled charging is not needed unless the LA battery is in an environment which can be very hot or cold. For normal room temperature a maximum charging voltage of 13.6 - 13.8 V is usually all you need.

Discharging a 12 V LA battery to 9 V is not good for the battery, the lower the voltage the more chance you have to permanently damage the battery (sulfite on the plates). I would not go below 11 V to keep the battery in good shape.