1. A controller for an AC rotating machine, comprising: an AC rotating machine including a first winding and a second winding which have a phase difference; a first current detector configured to detect current of the first winding; a second current detector configured to detect current of the second winding; a control section configured to compute a first voltage command and a second voltage command, based on a current command and a current detection value of the AC rotating machine; a first voltage applying unit configured to apply voltage to the first winding, based on the first voltage command; a second voltage applying unit configured to apply voltage to the second winding, based on the second voltage command; a first detectability determining unit configured to determine detectability of the current of the first winding by the first current detector, based on at least one of the first voltage command and the second voltage command; and an estimated sum current computing unit configured to compute estimated sum current, which is a sum of the current of the first winding and the current of the second winding, wherein when the first detectability determining unit determines that the first current detector cannot detect the current of the first winding, the control section computes the first voltage command, based on an estimated current value of the first winding which has been calculated by subtracting the current of the second winding detected by the second current detector from the estimated sum current output from the estimated sum current computing unit.