Design de automação não-linear

Automatica, Vol.13,pp. 497 505. Pergamon Press, 1977. Printedin Great Britain

Design of Nonlinear Automatic

Flight Control Systems*

W I L L I A M L. G A R R A R D t and J O H N M. JORDAN++

A nonlinear aircraft automaticflight control system, developedfor use at high angles of attack, reduces altitude loss during stall and increases the magnitude of the angle of attackfrom which the aircraft can recoverfrom stall.

Key Word Index Aerospace control; attitude control; closed loop systems; control nonlinearities; nonlinear control systems;perturbation techniques.

Sommary--A method for the synthesisof nonlinear automatic flight control systems is developed, and the performance of a control systemsynthesizedby use ofthis method is compared to the performance of control systemdesigned by use of linear quadratic optimal control theory.Comparisonsare made on the basis of aircraft dynamic response at high anglesof attack. It is found that the nonlinear controller reduces the altitude loss during stalland increasesthe magnitudeofthe angleofattack for which the aircraftcan recoverfrom stall.

1. INTRODUCTION

MODERN high-performance aircraft often operate in flight regimes where nonlinearities significantly affect dynamic response. For example, fighter aircraft may operate at high angles of attack where the lift coefficient cannot be accurately represented as a linear function of angle of attack or at high roll rates where nonlinear, inertial cross-coupling may result in instabilities. In such situations, dynamic response may be improved if controller design is based on nonlinear rather than linear models of aircraft dynamics.

A number of investigators have studied the problem of using optimal control theory as the basis for the design of suboptimal, feedback controllers for nonlinear systems and a systematic procedure has been developed for systems in which the nonlinearities can be expressed as a power series in the state vector[I-9]. This procedure has been applied to only a few problems of practical interest and results previously reported[10, 11] do not indicate that nonlinear control produces clear-cut improvements in dynamic response when compared with controllers designed using linear quadratic optimal control theory. The objective of this paper is to apply nonlinear feedback control theory to the design of a flight control system which can provide acceptable dyn- amic response over the entire range of angle of attack which a modern high performance aircraft may operate. Control system performance is particularly critical at large angles of attack as the uncompensated dynamic characteristics of the aircraft may result in abnormal and sometimes hazardous flying qualities. The paper is divided into three major sections. In the first section, the nonlinear equations describing the longitudinal motion of an aircraft are developed. The general equations are derived and are applied to a specific aircraft, the F-8 Crusader. Synthesis of the linear and nonlinear controllers is presented in the second section. The lesser known nonlinear case is given the majority of attention. Evaluation of the linear and nonlinear control systems are presented in the third section. It is found that the nonlinear system results in considerably improved dynamic response when compared with the linear system.

2. NONLINEAR DYNAMICAL MODEL

The forces considered and the coordinate system used are shown in Fig. I. The drag is small compared with the lift and weight and is neglected in this analysis. The lift is separated into its wing and tail components[12].

The basic equations of longitudinal motion are

mfi+wO)= -mgsinO÷Lwsin~+Ltsino~ t (1)

m(ff-uO)=mgcos O-LwCOSO~-Ltcosott (2)

IrO=Mw+lLwCOSct-ltLtcosctt-cO (3)

Where

m -- mass of aircraft

u -- velocity of aircraft in X direction

w = velocity of aircraft in Z direction

0 = angular displacement about Y axis, measured

clockwise from the horizon as shown in Fig. 1

Ir = moment of inertia of aircraft about Y axis

Lw -- wing lift

Lt = tail lift

ct= wing angle of attack

ctt = tail angle of attack

Mw= wing moment

/=distance between wing aerodynamic and aircraft center of gravity It = distance between tail aerodynamic center aircraft center of gravity cO = damping moment.

Equations (1)--(3) can be refined into three equations of longitudinal motion in which cubic and lower order terms are retained. The tail and wing lift forces are

Lw = CLqS

L, = CL glS ,

where

CL = coefficient of wing lift

CL, = coefficient of tail lift

q = dynamic pressure

S = wing area

S,