The X29 aircraft poses an interesting control problem owing to its forward-swept wing design. The center of gravity lies behind the aerodynamic center of pressure, rendering the pitch-axis dynamics statically unstable. So it is necessary to design a control system that stabilizes the aircraft during the flight.
Your job is to design an H∞ controller for a simple model of the pitch-axis dynamics of the aircraft. The airplane has three types of control surfaces: canard wings, flaperons on the main wings, and strakes on the tail. To simplify the model, the action of these control surfaces are lumped into one equivalent actuator model with first-order dynamics. Hence, the transfer function of the system can be represented by the following SISO plant (see Dahleh/Diaz-Bobillo, "Control of Uncertain Systems", Prentice Hall, 1995):
The airframe factor corresponds to a simplified model of the pitch-axis dynamics. The overhead factor is an approximate representation of the collected phase lag contributed by gyroscopic sensor dynamics, the actuator servo dynamics and the airframe flexible modes. The plant is unstable and non-minimum-phase. This will restrict the achievable performance significantly.
You have seven degrees of freedom in varying the performance weights in this exercise.