Field-oriented control (FOC) has proven effective for controlling ac drives with good dynamic performance. However, operation at low-switching frequencies and the sensitivity of traditional feedforward loops to system parameters pose severe limitations on the achievable performance and require a tedious tuning procedure. In this paper, we present a systematic cascade explicit model predictive control framework for the FOC of electrical drives, resolving the aforementioned issues while being sufficiently simple to be widely implemented on various ac drive systems. The resulting closed-loop system exhibits high dynamic performance for all operating points, even at low-switching frequencies. We present experiments with a permanent-magnet machine and an induction motor, demonstrating the practical feasibility and the merits of the proposed framework over traditional controller designs for electrical drives.