I need a positive word to describe a person who usually sets a lot of rules for himself and also for others and always adheres to his rigid principles. For example, a man who is always punctual, keeps promises, avoids what he thinks they are hamful to his health, so on.
What is wrong with principled?
of a person or their behavioracting in accordance with morality and showing recognition of right and wrong
A stickler is a person who insists on behaving a certain way (usually adherent to a fixed principle or set of principles).
A person who insists on a certain quality or type of behaviour.
‘he's a stickler for accuracy’
‘I'm a stickler when it comes to timekeeping’
So you can say (for example): "He's a stickler for punctuality." and so on.
I'd call such a man disciplined (or self-disciplined if I wanted to point out that they're setting the rules for themselves). Scrupulous is also a good word to point out their strict adherence to rules.
"Rigid principles" might convey some negative connotations about the person to which "perfectionist" might be a suitable description, but we are asked for a positive word. I suggest "conscientious": SOED: "habitually governed by a sense of duty; scrupulous."