1. An electric power steering system comprising: a controller that controls a motor that is a source of an assist force to be applied to a steering system of a vehicle, wherein the controller computes an assist controlled variable based on multiple kinds of state quantities indicating a steering system state, and controls the motor based on the assist controlled variable, and the controller individually sets, for the respective state quantities, limits that limit a variation range of the assist controlled variable based on the respective state quantities used to compute the assist controlled variable, and limits a value of the assist controlled variable using the limits.