Traditional speed control of permanent magnet synchronous motors (PMSMs) includes a cascaded speed loop with proportional-integral (PI) regulators. The output of this outer speed loop, i.e. electromagnetic torque reference, is in turn fed to either the inner current controller or the direct torque controller. This cascaded control structure leads to relatively slow dynamic response, and more importantly, larger speed ripples. This paper presents a new dual cost function model predictive direct speed control (DCF-MPDSC) with duty ratio optimization for PMSM drives. By employing accurate system status prediction, optimized duty ratios between one zero voltage vector and one active voltage vector are firstly deduced based on the deadbeat criterion. Then, two separate cost functions are formulated sequentially to refine the combinations of voltage vectors, which provide two-degree-of-freedom control capability. Specifically, the first cost function results in better dynamic response, while the second one contributes to speed ripple reduction and steady-state offset elimination. The proposed control strategy has been validated by both Simulink simulation and hardware-in-the-loop (HIL) experiment. Compared to existing control methods, the proposed DCF-MPDSC can reach the speed reference rapidly with very small speed ripple and offset.INDEX TERMS Model predictive control, direct speed control, hardware-in-the-loop, permanent magnet synchronous machine.