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.