I will make it quick and simple!
You mentioned about 도록.
The grammar rule is -하도록.
Okay between 위해 vs 도록.
The English translation for each a bit differs.
1. -(하기) 위해 = in order to, for the sake of...
2. -(하)도록 = so that... so as to,
I mentioned and explained about 1 already.
Okay, here is about -(하)도록.
Examples: Verb-Stem + 도록
1. 아침 일곱 시에 밥을
먹도록 (먹다 "to eat" - 먹 is verb-stem) 준비해 주세요.
"Please prepare my meal so that I can have it at 7:00"
If I change this sentence by using 위해 instead of 도록, for example 먹기위해, sounds not quite right!
아침 일곱 시에 밥을 먹기위해 준비해 주세요...??
2. 넌 이것을 하도록 해!
"You should do it so as I (said/mentioned)"
If I use 위해 instead of 도록, for example 하기위해, the sentence is wrong!
넌 이것을 하기위해 해!... NO!
3. 이 버스를 타도록 빨리 일어나야 해!
"(We) should get up early so as to take this bus!"
If I use 위해 instead of 도록, for example 타기위해, the sentence is totally okay!
이 버스를 타기위해 빨리 일어나야 해! .. OKAY!
See, how complicated it becomes!
This is enough for now. I can explain more with details but that's too much for me and for you.
cheers,
Tim