the rotational position data 7 provided by the controller 5 module 10 stores in memory the characteristics of all the return springs associated with the heddles of the harness of the system 2 with the result that knowing at any moment the rotational position data 7 the return effort or force of each spring as a function of the position in height of the heddle in question and the direction of displacement of the heddles weaving information 8 it can calculate the unbalanced forces or torques at each instant as a function of the difference of elastic return efforts between the heddles which rise and the heddles which descend module 11 stores in memory the inertias of the parts of the shed forming system to be driven and it may calculate on the one hand the speed of these parts as a function of the variation of the angular position 7 in time t value d7 dt on the other hand the acceleration of said parts as a function of the variation of speed dv dt these values enabling the inertia force to be calculated finally module 12 takes into account memorized or inputted constant forces for example the constant or frictional forces data 13 unbalance forces 14 inertia forces and 15 constant forces respectively supplied by modules 10 11 and 12 of the calculator 9 are sent to an electronic adder or comparator 16 in.