“il sent” means “he is smelling (something)” and “il se sent” means “he’s feeling” so in the sentence, “il se sent de plus en plus crispé”, “he’s feeling more and more nervous”, makes more sense.
Hope it helps you.

I “Plus en plus” is not the correct locution; “de plus en plus” is the form used when you want to translate the English “more and more”. Here is what we find for “sent plus en plus“.

• Il se sent de plus en plus crispé.
  He is feeling more and more uptight/on edge/rigidity in his muscles.

II The use of the pronominal form provides un alternative to a more complicated form. If you change “se sentir” for “sentir” you must change the syntax because those forms are not mere morphological variants but come with their own syntax and set of particular usages, and those usages are not necessarily the same. Therefore, there is no question of a mere proliferation of words that could be weeded out to make things neat and simple, as we like them.

• Il sentait qu’il était de plus en plus crispé.
• Il sentait son attitude devenir de plus en plus crispée.
• Il sentait ses muscles se crisper de plus en plus.

Let’s take another example so as to explore the syntax and some possibilities.

• Il se sentait fatigué maintenant et pensait devoir arrêter.
• Il sentait la fatigue maintenant et pensait devoir arrêter.

In the first sentence the object is the person who is talking and tiredness is experienced by this person. In the second sentence the object is “tiredness” and only the context will say who is experiencing this tiredness: it can be the person who is talking or some other entity, a group of persons for instance (Il sentait la fatigue chez ses coéquipiers …).
If the context makes it clear that the tiredness in question can’t be someone else’s than that of the person who is speaking, we see that the two sentences do say exactly the same thing. Independently of the context the verb in the second sentence can be still used to the same effect provided a complement is added.

• Il se sentait fatigué maintenant et pensait devoir arrêter.
• Il sentait la fatigue en lui maintenant et pensait devoir arrêter.

The sentences say now the same thing in all possible textual backgrounds.