Maybe try to modify the following lines :

Code:

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var speed = 0.5; // play with 0.5
// first rotate the turret's body
//ang_rotate(my.pan, vector(ang(ang_to_ent.pan - my.pan),0,0));
my.pan += ang(ang_to_ent.x-my.pan) * speed * time_step;

//now rotate the barrel
//vec_set(you.pan, my.pan);
//ang_rotate(you.pan, vector(0,ang(ang_to_ent.tilt - you.tilt),0));


my.tilt += ang(ang_to_ent.y-my.tilt) * speed  * time_step;