Circumventing Unstable Zero Dynamics in Input-Output Linearization of Longitudinal Flight Dynamics

Abstract

In this paper, we consider the problem of input-output linearization of the longitudinal flight dynamics. In longitudinal flight dynamics, inputs are typically thrust and elevator deflection whereas the outputs are the velocity and the flight path angle. An input-output linearization-based controller can be designed to render the multi-input, multi-output system linear; however, the resulting zero dynamics turns out to be unstable. In this work, we remove the zero dynamics from the closed-loop dynamics by considering an additional output. Although the additional output makes the system tall, which, in general, means that the input-to-output dynamics can not be linearized, we show that in the case of longitudinal flight dynamics, linearization is possible due to special geometric properties of the nonlinear terms.

Figures (7)

• Figure 1: Trim conditions at various aircraft velocities. Note that the elevator deflection and the pitch angles are expressed in degrees.
• Figure 2: Velocity, flight-path angle, and the pitch angle response of the longitudinal aircraft dynamics with the linearizing controller. Note that the output is shown in solid blue and the corresponding reference is shown in dashed black.
• Figure 3: Absolute value of the velocity error, flight-path error, and the pitch angle error in the closed-loop simulation on a logarithmic scale.
• Figure 4: Thrust and elevator-deflection angle given by the linearizing controller.
• Figure 5: Components of $|\Lambda(x)\alpha(x)|$ on a logarithmic scale. Note that asymptotic convergence $\Lambda(x)\alpha(x)$ to $0$ allows complete linearization of the tall MIMO system.

Theorems & Definitions (3)

• Definition III.1
• Definition III.2
• Definition III.3