An application of invariance principle to pilot model for NT-33 aircraft with variable coefficients and delays†

Abstract

A method is presented for analysing pilot-induced oscillations (PIO) for the NT-33 closed-loop pilot model when retardations and coefficients are not constant. The variation of retardations and coefficients results from the effect of wind shear and the neuromuscular dynamics of the pilot reported in available data. Non-linearities in the model are also considered. The method is based on the use of a new description of such systems in terms of convolution equations. Spectral factorization is applied to the entire functions of exponential order. The result is a criterion for the PIO-system with variable coefficients and variable delays. The criterion assumes continuity and boundedness of the coefficients and delays. A Lyapunov functional is constructed which gives a criterion on the roots of a certain ‘ quasi-polynomial ’, i.e. a polynomial in a variable and the exponential of that variable. The largest domain of attraction is obtained from the ‘ invariance principle’ of LaSalle (1975).