DC-DC converter inductor current DC component
The duty cycle for a buck converter is (to a first order) independent of load current (but not Vin) in steady state.  Consider the output L-C as a filter giving you the average voltage of the chopped input, providing a constant voltage output.

As load increases, the current in the inductor increases, but the duty cycle remains fixed.  The inductor current ramps up for Ton and down for Toff.

As the load increases, the output voltage drops temporarily.  During the on time the voltage across the inductor is Vin-Vout, so there are more volt-seconds across the inductor.  

During the off time there is less voltage to discharge the inductor.  This causes the inductor current to increase until a new steady-state value is reached and the on and off time currents ramp amplitudes are again equal.  $$(Vin-Vout)*ton/L $$has to equal $$Vout*toff/L$$ for the discharge time.  No dependency on the load current.

If they are again equal, then the duty cycle must have returned to the original value, and the output voltage is again the average value of the chopped Vin.

From Wikipedia:


A control loop wrapped around all this will take out the IR drop errors and correct the output by changing the duty cycle slightly.