Stability analysis and non-linear control synthesis for hydraulic servos actuating primary flight controls
by
Andrei Halanay
University Politehnica of Bucharest, Mathematical Department, 313 Splaiul Independentei, 77206, Bucharest, Romania
Coauthors: F. Popescu, C. A. Safta, F. Ursu, I. Ursu

For a mechanohydraulic servo used in the control chain of an airplane, a mathematical model given by four strongly nonlinear ordinary differential equations relating the state variables of the inertial load (position and speed) and the pressures in the two chambers of the hydrocylinder is considered. Taking into account the physical limitations, the equilibria are the points of a bounded subset of a plane. The matrix of first approximation in an equilibrium point has a zero in its spectrum, so a critical case for the stability analysis appears. The problem is treated in the framework of Lyapunov theory and related Malkin theorem. In view of ensuring stability in the whole domain, the case of control synthesis for a derived electrohydraulic servo is also considered. A stabilizing control law is synthesized using the method of backstepping. Here the control law ensures the asymptotic stability of references tracking by constructing a Control Lyapunov Function (CLF) on the errors concerning the state variables and their desired values. An approach based on partitioning the state system into two subsystems - a first one internal stable, and a second one taken as framework of control synthesis - is developed; this is another main contribution of the present paper. The paper's interest stems also from illustrating the key idea of CLFs synthesis using the celebrated Barbalat's Lemma. Numerical simulations are reported from the viewpoint of assessing the servo time constant performance.

Date received: January 20, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakt-28.