Full State Feedback Controller for a Helicopter

Abstract:
Full state feedback offers theoretically guaranteed multi-axis stability, making it superior to conventional PID controllers. There is however one drawback, a full state controller has a mathematical difficulty if the B matrix is not square and thus not invertible. This is the case for helicopters with 6 degrees of freedom and 4 inceptors. Variations of linear quadratic regulators are a work around, however complexity dramatically increases. Best would be a direct solution to the original problem. This is the breakthrough result of this paper. This paper documents an approach which removes the analysis roadblock by partitioning the 6 x 6 system "A" matrix into two groups of 4 x 4 matrices. The 4x4 matrices are individually stabilized with full state gain matrices. One matrix is designated “Driver Matrix” which provides actuator commands. The other matrix is designated "Reference Matrix" which provides references. The two matrices are coupled together by requiring that the driver matrix follow references generated by the reference matrix. With each matrix individually stabilized, the coupled combination is also stabilized. Computation of flight dynamics states (u, v, w, p, q, r) is shared between the matrices. Initial results are very encouraging, showing an originally sluggish, heavy lift helicopter having now concise decoupled responses to pitch and roll commands. Stability derivatives are recomputed during flight allowing coverage over the whole flight envelope. A handling qualities task has been defined to relocate a 40 ft standard seaborne container directed by a pilot in a ground control station. Cooper Harper ratings of this task have demonstrated favorable Level 1 handling qualities if use is made of an automated lateral repositioning command.

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