Regulated power supply 1,5-34 V ~ 40A using LM1084ADJ and TIP122
Let's see what size Cap you would need for 100Hz.

Ic=CdV/dt for dt=10ms and dV~10% input ripple of 34V ~ 4V
C=Ic*dt/dV = 40A * 10ms/4Vpp = 100 mF = 0.1 farad @50V

I don't think you planned on this.

Above is the discharge equation. 

The charge equation depends on the duty cycle which happens to nearly equal the ripple assumed to be near 10~15% of the DC voltage.

This means due to Conservation of Charge Law, if you discharge 40A 90% of the time then you need 10x as much current in 10% of the time to restore the charge or in this case 400 Amps in 1ms every 10ms and hugh dI/dt EMI issues.  This has major consequences for I^2*R=Pd and you would need a supercap ESR with the capacity of small lead acid battery.   However SuperCaps only come in low voltages and batteries of this voltage have too high ESR for this pulse ripple current.  So this is a no-go or a design spec that cannot be reasonably achieved.