Singular Perturbation Margin of INDI-Based Flight Control Systems With Delays

Abstract

A linear singularly perturbed system (SPS) based on a linear approximation of Incremental Nonlinear Dynamic Inversion (INDI) is formulated for a general INDI-based flight control system. This system includes first-order actuator dynamics where its time constant is taken as the singular perturbation parameter. The stability of the singularly perturbed system (SPS) is studied, which gives an understanding of the sensitivity of INDI to delays. Two sources of delay are considered, one coming from the state derivative measurement and the other coming from the delayed input signal. It is shown in this paper that the upper bound of the singular perturbation parameter serves as a robustness metric of the SPS to the two types of delays. Consequently a relative singular perturbation margin (SPMR) is proposed as a delay margin. The results are confirmed with two aircraft simulation cases for MIMO and SISO systems. In the latter, the relationship between the relative singular perturbation margin (SPMR) and the phase margin (PM) is analyzed. © 1965-2011 IEEE.