1. A motor control apparatus, performing control on a motor comprised in a controlled object, wherein the motor control apparatus comprises: a motor control part, generating a driving torque instruction value used to enable the motor to perform driving based on a detection value of a rotation detector that performs detection on a rotational state of the motor; and a model control part, generating a model instruction value based on a model of the controlled object of the motor, and outputting the model instruction value to the motor control part, wherein the model control part comprises a first torque limiting part, wherein the first torque limiting part limits a model torque instruction value comprised in the model instruction value within a first limit range.