The low ratio of sampling frequency to electrical frequency (carrier ratio) is a challenging issue for applications, such as high-speed or high-power drives. In fact, high-speed drives have high fundamental frequency and high-power drives have low switching (sampling) frequency, leading to the same control challenges of having high dynamic and stability with a limited number of control actions in one period. Parameters mismatch occurs due to the converter non-linearities, deadtimes, temperature change, and saturation; hence, providing robust control is a key challenge. This paper starts reviewing the problems of controlling machines with a few switching instances per fundamental period and an analysis of the stateof-the-art current control strategies for permanent magnet synchronous motors (PMSMs). Three different control schemes are analyzed. The discrete-time PI current controller is providing good robustness, while the dynamic performance may not be sufficient for some applications. Second, the deadbeat control offers very fast dynamic performance but is weak under parameter mismatch. The novel application of the Dahlin controller offers a tradeoff between performance and stability. The control algorithms are evaluated based on the stability, robustness, and dynamic and steady-state performances. Their performance and sensitivity to parameter variation are analyzed through simulations, and the experimental measurements are proving the results.INDEX TERMS Dahlin control, deadbeat control, pulse ratio, electric drive, PMSM, current control, pulse-width modulated power converter.The growing research interest in high-speed machines can be observed by the high number of publications in this research area. Rising attention is given to topics related to the hardware for motor drive systems with high-speed machines, such as the machine itself, the converter, the motor filters, as well as research related to the software, i.e. the control or observer design [1]-[4]. For many applications like pumps, fans, or automotive, high-speed machines are becoming more and more popular [5]. Machines up to speed of one Million r/min or a rated power of one Gigawatt are available today [2], [6]. The permanent magnet synchronous machine is the first choice for many applications due to its compact size, high power density and good efficiency.The associate editor coordinating the review of this manuscript and approving it for publication was Ton Do.