Convex Modeling Techniques for Aircraft Control

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Virginia Tech

The need to design a controller that self-schedules itself during the flight of an aircraft has been an active area of research. New methods have been developed beyond the traditional gain-scheduling approach. One such design method leads to a linear parameter varying (LPV) controller that changes based on the real-time variation of system dynamics. Before such a controller can be designed, the system has to also be represented as an LPV system. The current effort proposes a LPV modeling technique that is inspired by an affine LPV modeling techniques found in recent research. The properties of the proposed modeling method are investigated and compared to the affine modeling technique. It is shown that the proposed modeling technique represents the actual system behavior more closely than the existing affine modeling technique.

To study the effect of the two LPV modeling techniques on controller design, a linear quadratic regulator (LQR) controller using linear matrix inequality (LMI) formulation is designed. This control design method provides a measure of conservatism that is used to compare the controllers based on the different modeling techniques. An F-16 short-period model is used to implement the modeling techniques and design the controllers. It was found that the controller based on the proposed LPV modeling method is less conservative than the controller based on the existing LPV method. Interesting features of LMI formulation for multiple plant models were also discovered during the exercise.

A stability robustness analysis was also conducted as an additional comparison of the performance of the controllers designed using the two modeling methods. A scalar measure, called the probability of instability, is used as a measure of robustness. It was found that the controller based on the proposed modeling technique has the necessary robustness properties even though it is less conservative than the controller designed based on the existing modeling approach.

LPV modeling, LMI, Probability of instability, Convex hull