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This paper proposes a new control algorithm for a matrix converter permanent magnet synchronous motor (PMSM) drive system. First, a new switching strategy, which applies a backpropagation neural network to adjust a pseudo DC bus voltage, is proposed to reduce the current harmonics of the permanent magnet synchronous motor. Next, a two-degree-of-freedom controller is proposed to improve the system performance. The parameters of this controller are obtained by using a frequency-domain optimization technique. The controller design algorithm can be applied in an adjustable speed control system and a position control system to obtain good transient responses and good load disturbance rejection abilities. The controller design procedures require only algebraic computation. The implementation of this kind of controller is only possible by using a high-speed digital signal processor. In this paper, all the control loops, including current-loop, speed-loop, and position-loop, are implemented by a 32-b TMS320C40 digital signal processor. The hardware, therefore, is very simple. Several experimental results are shown to validate the theoretical analysis.