Compressed air energy storage is a well-used technology for application in high voltage power systems, but researchers are also investing efforts to minimize the cost of this technology in medium and low voltage power systems. Integration of this energy storage requires a robust control of the power electronic converter to control the power injection due to the dynamic behavior of the system. The conventional linear control design requires a thorough knowledge of the system parameters, but the uncertain disturbances caused by the mechanical properties of the energy storage is neglected in the design and the system fails in presence of such instances. In this paper an adaptive control-based boost converter and sliding mode control-based three phase inverter for a grid integrated compressed air energy storage system of up to 1 kW has been presented that can mitigate any uncertain disturbances in the system without prior knowledge of the system parameters. The experimental results along with the simulation results are also presented to validate the efficiency of the system.