1. An electric power steering apparatus comprising: a control unit that calculates an assist controlled variable based on a plurality of types of state variables indicating steering statuses and controls a motor that serves as a generation source of an assist force applied to a steering mechanism of a vehicle based on the assist controlled variable, wherein the control unit is configured to separately set limit values, which limit a change range of the assist controlled variable according to the respective state variables used to calculate the assist controlled variable, to the respective state variables, arithmetically add up the limit values to generate ultimate limit value for the assist controlled variable, and perform limitation processing to limit the ultimate limit value for an assist controlled variable having a sign opposite to a sign of a steering torque that is one of the plurality of types of state variables.