This work presents a solution for controlling an Asynchronous Motor Drive (AMD) using a Gamma Z Source Inverter (GZSI) in combination with a high-gain Quadratic Boost Converter (QBC). The higher voltage gain of QBC and GZSI reduces the voltage rating of PV. Reduced output voltage ripple of QBC improves the performance of the AMD system. The proposed PV-QBC-GZSI-AMD system aims to regulate the motor's speed for applications requiring a constant speed. The approach involves implementing a closed-loop control system and evaluating different controllers: Current-mode-Fractional Order Proportional Integral (CM-FOPI), Current-mode-Proportional Resonant (CM-PR), and Current Mode-Hysteresis Controller (CM-HC). Also, FOPI improves the robustness and the hysteretic controller reduces the current-ripple implemented in this model. Hence, the system's performance is assessed using MATLAB/Simulink, showcasing enhanced dynamic performance in speed and torque characteristics within the time domain when employing CM-FOPI, CM-PR, and CM-HC control strategies for PV-QBC-GZSI-AMD. Simulation outcomes are compared against actual motor speed and torque data, highlighting the superior performance of the closed-loop-CM-HC control in PV-QBC-GZSI-AMD over closed-loop-CM-FOPI and CM-PR methods. Closed-loop-CM-HC control also provides over current protection. The study also includes hardware results from the PV-QBC-GZSI-AMD system, validating the simulation findings. Furthermore, the performance of the proposed converter topology is compared with notable existing works, considering essential factors such as the number of stages, loops, control method, load type, performance parameters, and associated limitations.