The discrete-time model for salient machines with accurate discretization is quite complicated due to different <i>dq</i>-axes inductances. This paper proposes an approximation for the discrete-time model with high accuracy and efficient calculation. Various patterns of pulse-width-modulation updating and current sampling that result in one-sample or a-half-sample computational delay are studied, and corresponding current controllers are directly designed in the discrete-time domain with the simplified model. Decoupled responses between <i>dq</i>-axes are realized in reference tracking. Active resistance is also employed to improve the disturbance rejection. The experimental verification is performed on an interior permanent magnet synchronous machine.