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To advance the performance of AC adjustable speed system and to reduce the pollution to power network, this paper proposes a compound control strategy which combines matrix converter (MC) and direct torque control (DTC). The MC controlled by this strategy cannot only achieve DTC to a asynchronous machine but also acquire good input currents and adjustable power factor. The principle of this strategy is: firstly transform MC into an equivalent topology that is a combination of a rectifier and an inverter, and then perform DTC on inverter and current space vector modulation on the rectifier, at last combine two sides' strategies and change them into the control signals of the MC's nine bidirectional switches. A simulation about MC driving asynchronous machine has been done and the results prove that the strategy proposed by this paper is not only feasible but also excellent.