Gyroscopes are used for numerous defence and commercial applications. These include stabilization, guidance, and navigation of torpedoes; ballistic missiles and artillery shells; inertial navigation andinertial surveying; autopilot, stabilization and navigation of underwater vehicle, etc. Recently, automotive and consumer goods industries have shown significant attention towards purely commercial applications which include automobile accident-history recorder and stabilization of hand-held video camera. Fiber optic gyroscopes have several advantages over the mechanical and ring laser gyroscopes. The interferometer fiber optical gyroscopes (IFOG) is proven sensor in this field. Many methods exist for the design of proportional-integral-derivative (PID) controllers. This paper describes a constrained optimization aimed at reducing the excess gain-bandwidth of an initial controller thereby improving its performance. This problem can be overcome by implementing the design using FPGA.