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[en] This paper describes digital Low Level Radio Frequency (LLRF) control applied to Heavy ion Radio Frequency Quadrupole (RFQ) cavity. A prototype RFQ, fabricated for the proposed ECR based heavy ion accelerator at BARC, has an unloaded quality factor (Q) of 8950. This high Q results in a bandwidth of a few kHz, so small perturbations in the resonant frequency of the RFQ can result in changes in the magnitude and phase of cavity electric field for a fixed frequency driving signal. As a result, it is necessary to use a LLRF controller that can compensate for perturbations as they occur. The development and testing of a FPGA based IQ digital LLRF controller implemented on indigenously developed 1 Giga sample per second (GSPS) data acquisition card shall be discussed. The LLRF controller is tested with a FPGA based cavity simulator which feeds signals representing the cavity dynamic response to the LLRF controller. For cavity analysis, a generic electrical model is developed to represent the RFQ cavity dynamic response. For the simulation of the RFQ cavity in real-time using FPGA, a mathematical technique is introduced to map the cavity resonant frequency to baseband, leading to a baseband equivalent model for the cavity.(author)