Abstract
Aircraft longitudinal dynamics is approximated by short-time mode and phugoid mode from experience. In this article, a rigorous mathematical method is provided based on the singular perturbation theory to deal with this decoupling problem. The longitudinal decoupling and singular perturbation are first introduced. The longitudinal equations are normalized and transformed into a canonical form to extract the perturbation coefficient. Thus, the entire dynamics model is partitioned into boundary-layer equations and slow equations according to singular perturbation theory, which presents a proof to the experience method. The simulation results show that the proposed decoupling approach is sufficiently excellent to approximate the underlying model both in time domain and frequency domain.
Highlights
Aircraft flight mechanics has always been an important issue for more than a century
In the classical flight control theory, the equations are generally partitioned into two modes, phugoid mode and shorttime mode, but there is no rigorous theoretical support to this decoupling
We present a decoupling approach based on the singular perturbation theory
Summary
Aircraft flight mechanics has always been an important issue for more than a century. Adaptive control for the decoupling model of aircraft flight mechanics is an interesting topic.[18,19,20] The singular perturbation method can be found in the composite learning control of flexible-link manipulator.[21,22] B Xu et al.[23,24] studied the longitudinal dynamics of the hypersonic flight These studies made use of the decoupled model, but did not give a reasonable interpretation of the approximation. X1 represents the the phugoid mode and X2 the short-period mode These two modes are decoupled in terms of the response time scale. The short-period mode describes the dynamics of the pitch rate and the angle of attack, which is often regulated as an inner loop of the longitudinal controllers. R0 sin l0 which is equivalent to the residualization method It proves that equations (6) and (7) provide the same decoupling approach with singular perturbation. For the example in section ‘‘Example of longitudinal decoupling,’’ its relevant matrices in the normalized equations are calculated as
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