An elongated tokamak plasma is subject to vertical instability. The fast plasma motion can be stabilized by a vacuum vessel and/or axisymmetric conductors. For stabilization of the slow plasma movement, an active feedback control system is required. A detailed simulation of control systems operation and optimization of active coil positioning in the single-turn tokamak IGNITEX is presented. Rigid displacement and full MHD models are utilized. The rigid displacement model defines the machine's stability diagrams. The plasma time response to control signals and the power characteristics of the control system are found using the full MHD model.