A control apparatus is for controlling an AC rotary machine which includes a first and second stator elements and a rotor, in which the first stator element can be turned, or offset, in a circumferential direction relative to the second stator element. The control apparatus includes an actuator for adjusting a voltage induced in a stator coil due to rotation of the rotor by driving the first stator element, a magnetic flux command calculator for calculating a desired magnetic flux amplitude command based on rotating speed of the AC rotary machine, a magnetic flux estimator for estimating magnetic flux amplitude of the AC rotary machine, a speed command calculator for calculating an actuator speed command to be given to the actuator so that the estimated magnetic flux amplitude follows the magnetic flux amplitude command, and an actuator controller for controlling the actuator according to the actuator speed command.