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This paper proposes a new closed loop speed control of an induction motor fed by a high performance Z-source inverter (ZSI), the speed control is based on V/F control and indirect field-oriented control (IFOC) strategies. The indirect field-oriented control based on PWM voltage modulation with voltage decoupling compensation is used to insert the shoot-through state within the switching signals. A dual loop controller is designed to control the peak dc link voltage of the ZSI, where the peak dc-link voltage is estimated by measuring the input and the capacitor voltages. The peak dc link voltage control is designed based on a small signal model using the bode diagram. Also, the parameters of the PI controllers in the IFOC method are calculated based on the required dynamic specifications. The proposed speed control methods, with reduced DC input voltage compared with the standard adjustable speed drives (ASD), are able to change the motor speed from zero to the rated speed with the rated load torque. The performance of the proposed speed control methods is verified by MATLAB simulation of a 15 kW induction motor fed by a high performance ZSI. The simulation results during start up, load disturbance and input voltage change are presented. The simulation results have verified the validity of the proposed closed loop speed control methods. Also it indicate that, the performance of the indirect field-oriented control based on PWM voltage modulation is more efficient than the V/F control for speed control of the induction motor fed by the high-performance ZSI. Experimental setup of a high-performance ZSI is under progress.