This paper presents the development of the control system architecture for vibration mitigation and autonomous phasing of sub-apertures on a sparse-array test bed. The paper begins with a brief description of the telescope system under consideration, including the actuation system providing 3 degree-of-freedom rigid body correction to each sub-aperture, and the metrology system, comprised of a white-light-based low-bandwidth absolute position sensing system and a high-bandwidth, laser-based relative position sensing system. The control problem posed by the telescope is described, including a discussion of the performance requirements the control system must meet, which include asymptotic set point tracking, broadband and tonal disturbance rejection, and tracking of non-stationary objectives. The use of system identification techniques in development of an accurate model of the input-output dynamics of the system is presented. The overall control system architecture including discussions on aspects such as tolerance of sensor dropouts, and the design of these control systems based on the identified model is presented. The paper presents the results of the application of this control system approach to the experimental system, demonstrating performance of the controlled system.