The paper proposes some design strategies of static anti-windup control schemes for systems describing cross-directional processes. These are processes in which the variations of a variable in a profile orthogonal to the direction of propagation of the variable are controlled. Actually, the anti-windup synthesis approach takes advantages of the particular structure of such systems for which the interaction map between sensors and actuators along the propagation direction is expressed in terms of reduced singular value decompositions. The approach is developed within the framework of a synchrotron machine, in which electrons are accelerated in a closed circular path and bent by strong electromagnetic fields. Different results are proposed with increasing computational complexity to evaluate the potential interest of low dimension problems to solve the anti-windup design problem.