【Set】 ,  【settle】 ,  【fix】 ,  【establish】  mean to cause someone or something to be put securely in position.

【Set】 is the most inclusive of these terms, sometimes implying placing in a definite location, especially to serve some definite purpose or to permanently fill some void or 【establish】 some limit and sometimes implying a placing under orders (as in an occupation, a situation, an office, or a sphere of life) or under conditions where something or someone must perform an allotted or prescribed function or occasionally suggesting a prescribing or ordaining of an object or objects on which one or one’s efforts, mind, heart, or eyes concentrates.

【Settle】  comes close to  【set】 but carries a much stronger implication of putting a person or thing in a place or condition of stability, rest, or repose and often a weaker implication of regulative or dictatorial power.

Often the word carries an implication of decisive quieting, calming, or ordering of something that is disturbed, upset, unstable, or fluctuating.

【Fix】  (see also ADJUST 1 ) ( FASTEN ) usually implies more stability and permanence in position, condition, or character than  【set】  or even  【settle】 .

【Establish】  (see also FOUND ) stresses not so much the putting in place or the bringing into existence as the becoming fixed, stable, or immovable, although in some use both ideas are connoted.