Variable phase-pole machines have the potential to extend the operational range to higher speeds through magnetic pole changes. The state-of-the-art vector-space decomposition (VSD) cannot model the transient behavior of the pole change for any possible phase-pole configuration as it creates a discontinuity. The proposed harmonic-plane decomposition (HPD) theory solves this issue by generalizing the VSD to the fullest extent by using its discrete Fourier transformation interpretation. The theory for indirect rotor field-oriented control is developed using the HPD. A controlled, loaded pole change on a wound independently-controlled stator-coils machine using two transition strategies shows the HPD-based controller's ability to maintain torque in the transition. Additionally, the proposed controller accomplishes real harmonic injection and balanced steady-state operation.