A technique facilitates control over a downhole well operation. The technique utilizes an electronic control system for controlling actuation of a downhole application-specific attachment. According to an embodiment, the system comprises a universal actuator module which may be selectively combined with a variety of application-specific attachments, e.g. well tools. The universal actuator module is electrically powered via, for example, electricity supplied to drive an electric motor which, in turn, may be used to drive a hydraulic pump or other type of mechanical device. Additionally, a given application-specific attachment can be readily interchanged with other application-specific attachments (e.g. well tools) for performing a desired downhole operation or operations.