Hi,
Your soft starter turns Q3 on which turns Q2 off, and Q2 being off means that Q4 is off…..that is a problem because Q4 is what you rely on to “brake” your smps.
Also,I don’t see a RC snubber across your sec diode.
I think what you need to do is just first of all set it up as a simple 28vout smps, and put a load on of 28v/1.4a…then when you have it working like that you can go forward.
So go back into “power calc”, (or whatever powerint call it), and do a design for 28vout and 1.4a out, and solder that circuitry in and then go from there….it will probably give you a tl431 circuit.
I woudl put your bjt based soft starter and current (amps) regulator circuit into ltspice and check it out in there.
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Also, is your c14 too big?......what is its value....what does your control pin voltage look like...is it rising up quick enough?......if not then youre into max peak current threshold territory