Dynamic Inversion Flight Control Design for Aircraft with Non-Minimum Phase Response

Nonlinear dynamic inversion (DI) has emerged as an area of increased application for flight control law design during recent years. It is well known that the DI control law will cause the open-loop zeros to become the poles of the closed-loop system. Hence, for a vehicle with non-minimum phase (NMP) transmission zeros, closing the loop using dynamic inversion will result in instability. In this paper, physical conditions where NMP response can occur in various air vehicle designs are first reviewed. Examples are presented for aircraft with highly flexible structure, reentry vehicle with lateral departure tendency, and hypersonic vehicle with extreme forward instantaneous center of rotation. Common design practices, including sensor blending, control mixing and vehicle configuration design changes, to eliminate the NMP response are first described. In the case where the NMP zeros cannot be totally eliminated, an extension to the DI synthesis methodology with additional decoupling terms to achieve stability in the presence of NMP dynamics is then presented. Numerical examples for two reentry vehicles are used to demonstrate this modified dynamic inversion design technique.