Lateral-directional eigenvector flying qualities guidelines and gain weighted eigenspace assignment methodology

John Burdyne Davidson, Purdue University

Abstract

This thesis addresses two limitations of the Direct Eigenspace Assignment methodology; the lack of guidance available for choosing desired system eigenvectors to yield desirable flying qualities, and the lack of direct control over augmentation gain magnitudes. The first limitation is addressed by presenting the development of lateral-directional eigenvector flying qualities guidelines. These guidelines will assist designers in choosing eigenvectors to achieve desired closed-loop flying qualities or performing trade-offs between flying qualities and other important design requirements, such as achieving realizable gain magnitudes or desired system robustness. This has been accomplished by developing relationships between the system's eigenvectors and the roll rate and sideslip transfer functions. Using these relationships, along with constraints imposed by system dynamics, key eigenvector elements are identified and guidelines for choosing values of these elements to yield desirable flying qualities have been developed. These eigenvector flying qualities guidelines are based upon the Military Standard lateral-directional coupling criteria for high performance aircraft. The second limitation is addressed by the development of Gain Weighted Eigenspace Assignment. This provides a designer with a systematic methodology for trading off eigenvector placement versus feedback gain magnitudes, while still maintaining desired closed-loop eigenvalue locations. When used along with the eigenvector flying qualities guidelines, trade-offs can be made between desired flying qualities and gain magnitudes. The approach used is to form a cost function composed of a scalar measure of error between desired and achievable eigenvectors and a scalar measure of gain magnitude, determining analytical expressions for the gradients, and solving for the optimal solution by numerical iteration. An example is presented to demonstrate the method. In this example, solutions yielding achievable eigenvectors "close" to the desired eigenvectors are obtained with significant reductions in gain magnitude compared to a solution obtained using a previously developed eigenspace (eigenstructure) assignment method.

Degree

Ph.D.

Advisors

Andrisani, Purdue University.

Subject Area

Aerospace materials

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