Sorry, I don't have those TI models and don't want to install them.I replaced all athe ADI parts with equivalent TI Parts.Lot of ringing at the output.Can you please check the attached file.

May I know How do I design resistors.With no emitter resistors Q1 and Q2 have a lot of voltage gain in the loop. I would add emitter resistors to both such that the conversion of Q1 base voltage to Q2 collector current is much more predictable and linear. As needed add loop gain by adding gain to U2 via boosting R4. I'm also wondering if a series RC from Q2 collector to U2 - input might also help kill oscillation.
That is a PI controller. C1 is a part of that.Until the capacitors charge to a stable voltage the circuit will not be in the stable conditions. Designing to avoid startup transients is often a challenge. Just exactly WHAT is C1 (22nF) doing for you?? That is undoubtedly the source of your spike, aside from the effects of assorted stray couplings.