Table Of ContentLecture Notes ni
Control and
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70
DFVLR
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Proceedings of an International Seminar
Organized by Deutsche Forschungs- und
Versuchsanstalt und Luft- Raumfahrt fLir )RLVFD(
Germany, Bonn, ,yaM 1985
Edited by .J Ackermann
galreV-regnirpS
Berlin Heidelberg New York oykoT
Series Editors
M.Thoma
Advisory Board
.V.A Balakrishnan L. • .D Davisson • A. G. .J MacFarlane H. • Kwakernaak
.J L. Massey • Ya Z.Tsypkin" A. .J Viterbi
Editor
Dr.-Ing. JiJrgen Ackermann
Institut fLir Dynamik der Flugsysteme
Deutsche Forschungs- und Versuchsanstalt
fur Luft- und Raumfahrt (DFVLR)
D-8031 Wessling/Oberpfaffenhofen
Germany
ISBN 3-540-15533-3 Springer-Verlag Berlin Heidelberg New York oykoT
ISBN 0-38745533-3 Springer-Verlag New York Heidelberg Berlin Tokyo
This work is subject to copyright. All rights are whether reserved, the whole or part of the material
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© Springer-Verlag Berlin, Heidelberg 1985
Printed Germany in
Offsetprinting: Mercedes-Druck, Berlin
Binding: und Berlin Li3deritz Bauer,
2061/3020-543210
PREFACE
The German Aerospace Research Establishment - Deutsche Forschungs- und
Versuchsanstalt fur Luft- und Raumfahrt e.V. (DFVLR) - has initiated
a new series of seminars concerning fundamental problems in applied
engineering sciences. These seminars will be devoted to interdisciplin-
ary topics related to the vast variety of DFVLR activities in the
fields of fluid mechanics, flight mechanics, guidance and control,
materials and structures, non-nuclear energetics, communication tech-
nology, and remote sensing.
The purpose of the series is to bring modern ideas and techniques to
the attention of the DFVLR in order to stimulate internal activities,
and to promulgate DFVLR achievements within the international
scientific/technical community. To this end, prominent speakers are
invited to join in a series of lectures and discussions on topics of
mutual interest.
After the first seminar in 1984 on "Nonlinear Dynamics in Transcritical
Flows" this second seminar deals with "Uncertainty and Control" in
general dynamic systems.
The dividing line between a "system" and its environment is not well
defined. Nevertheless, the line has to be drawn in physical/mathematical
modelling. As a result, unmodelled events in the environment lead to
uncertainties in the structure and parameters of the system or intro-
duce noise. A control system tries to enforce a specified dynamic
behavior in spite of this uncertainty. Feedback of sensor signals in
robust, adaptive and intelligent control systems can reduce the effect
of uncertainties.
In this seminar, the state of the art of the theory for the design of
such control systems will be surveyed and the relation with applied
engineering problems and solutions will be discussed.
Bonn, 7. Mai 1985 Prof. Dr. H.L. Jordan
Chairman of the
Board of Directors DFVLR
CONTENTS
Uncertainty and control - some activities at DFVLR
GROBEL, G ......................................................
System identification
LJUNG, L ....................................................... 48
Uncertainty models and the design of robust control systems
KWAKERNAAK, H .................................................. 84
Multi-model approaches to robust control system design
ACK~RMANN, J ................................................... 108
Adaptive control - a way to deal with uncertainty
~STROM, K.J .................................................... 131
Optimality in adaptive control systems
TSYPKIN, YA.S .................................................. 153
Intelligent control-operating systems in uncertain
environments
SARIDIS, G.N ................................................... 21S
UNCERTAINTY AND CONTROL
-SOME ACTIVITIES AT DFVLR
compiled by
Georg Gr~bel
DFVLR-Institute for Flight Systems Dynamics
D-80310berpfaffenhofen
Summar Z
Some activities at the DFVLR which deal with system modelling and
performance evaluation under uncertainty, as well as feedback
control applications, are reported. The examples are mainly drawn
from activities of the research department 'Flight
Mechanics / Guidance and Control' where active control of air-
craft and helicopters plays a central role. Uncertainty is
related to system parameters, disturbances, operational state
and operator behaviour. In this respect, DFVLR activities in
applied nonlinear parameter identification, on-line wind meas-
urement and prediction, stochastic simulation, and sensor diag-
nosis via analytic redundancy are briefly described.
Applications of feedback control concern model-following control
for inflight simulation, robust stabilization of high-perfor-
mance aircraft, aircraft flutter stability augmentation via
active mode decoupling, and active damping of mechanical
light-weight structures based on finite-element modelling.
2
The DFVLR -the German Aerospace Research Establishment- is the
largest research establishment dealing with engineering sciences
in the Federal Republic of Germany. Beyond its main activities in
aerospace, the DFVLR is applying its know-how to other fields of
engineering, where related technical problems have to be solved.
These fields include energetics and propulsion, environment
engineering, advanced ground transportation and robotics. The
DFVLR has the most up to date test facilities and technical
installations at its disposal.
In the following, some activities at the DFVLR are compiled which
relate to the topic "Uncertainty and Control" as it is understood
in this seminar. The list of these activities is by no means com-
plete. The examples are mainly drawn from activities of the
research department 'Flight Mechanics / Guidance and Control'
where active control of aircraft and helicopters plays a central
role.
VARIOUS ASPECTS OF UNCERTAINTY
We consider the main information and control structure of a
piloted aircraft as depicted in Figure .1
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Figure :I Information and control structure of a piloted
aircraft.
Uncertainty in this pilot-aircraft control loop may be related to
Uncertainty in system parameters
Uncertainty in system parameters is essentially related to the
equations of motion and the dynamic responses of actuators (and
sensors). Using the basic laws of physics and engineering, the
structure of the equations is assumed to be known but the parame-
ters have to be "identified" and they are known only within toler-
ances.
Uncertainty due to disturbances
Uncertainty due to disturbances may be divided into two catego-
ries: unknown effects of the environment such as wind gusts ("ex-
ternal" disturbances) and disturbances generated by the
technical system itself such as sensor noise ("internal" disturb-
ances).
Uncertainty in the operational state
Uncertainty in the operational state may be considered on two
levels: sensor failures in automatic control loops and informa-
tion-display failures in man-machine decision/control loops.
Uncertainty in operator behaviour
Uncertainty in operator behaviour may be attributed to the ques-
tions: How does a human operator behave as a decision-maker to
manage slow "situation dynamics" and how does the operator behave
as an in-the-loop controller to deal with fast motion dynamics?
These four aspects of uncertainty in a pilot-aircraft control
loop are typical for general man-machine systems. We take them as
guideline to survey some DFVLR-activities which aim at reducing
such kind of uncertainty via proper modelling, performance pre-
diction and system layout. Such activities are: (nonlinear)
parameter identification to determine system parameters as accu-
rately as possible, on-line wind measurement and prediction using
Kalman filtering, stochastic simulation to predict nonlinear
system performance under internal and external disturbances, and
sensor diagnosis via analytic redundancy.
PARAMETER IDENTIFICATION
The increasingly demanding requirements imposed on aircraft per-
formance and flight characteristics call for an extended use of
automatic control by implementing active control systems. The
use of active control technology however requires a detailed
understanding of the influence of the anticipated external dis-
turbances, aerodynamic characteristics and control system
responses and requires considerable advances in the ability to
describe and model such phenomena.
While the estimation of static flight mechanics coefficients nor-
mally involves no difficulties, problems may arise in the exper-
imental estimation of dynamic stability parameters. Even more
difficult is the identification of those effects which are
related to high frequency motions as in the case of flight in tur-
bulence. These effects, called the instationary aerodynamic
transient effects, can play an important role in the design of an
active control system like a gust alleviation system [I].
The field of aircraft parameter identification and dynamic flight
testing has by now emerged as an essential tool for the evaluation
of prototype aircraft. Applications of this technique are [12]
the evaluation of aircraft performance characteristics such
as polar drag curve or steady state climbperformance in non-
steady flight conditions,
the identification of nonlinear mathematical models of aero-
dynamic forces and moments, and of primary control force
characteristics for aircraft flight simulation, as well as,
the estimation of linear stability and control derivatives
for the numerical assessment of flying qualities and for the
design of linear control systems.
Parameter identification is based on the following idea (cf. Fig-
ure 2): Assume that the dynamical input-output behaviour of a
physical system be mathematically described by (nonlinear)
equations (I), (2) with yet undetermined parameters .B By excit-
ing the physical system by appropriate input signals u(t), meas-
uring the physical system response as z(tk) = Y(tk) + #(tk)
(usually with some uncertainty due to measurement noise )# and
comparing this measured response with the corresponding "re-
sponse" of the mathematical model, one can try to fitt he physical
and mathematical responses by suitably adjusting the free parame-
ters .6
[ocisyhp metsys
I
e
mode[:
= f[x,u,g(-),(]~] )I[
y =g[×,u,@] )2[
Figure :2 Basic scheme for parameter identification.
Sucessful parameter identification requires expertise in the
following fields:
experimental set up
input signal design
mathematical identification technique
computational efficiency.
• model verification
Experimental set up
As an experimental Set up for aircraft and helicopter parameter
identification essentially two approaches are pursued at the
DFVLR: sub-scale dynamic wind tunnel investigations (Figure 3)
and full-scale free flight tests (Figure 4) [I]. In both cases
expert experimental planning and adequate instrumentation is
required which covers the entire data aquisition process includ-
ing measurement noise and sensor dynamics.
Figure 4: DO 28 TNT full-scale
experimental aircraft
Figure :3 DO 28 TNT I/8-scale model in DFVLR wind tunnel.
Input signal design
The input signals must be designed such that all relevant system
response modes are excited. They have to be "optimized" to
achieve accurate identifications. The shape of an input signal
which is both simple to apply and very efficient for parameter
identification of the longitudinal motion of aircraft is the
DFVLR 3-2-I-i signal for elevator deflections [II] (Figure 5).
Time-scaling of this signal is chosen such that the maximum value
of the input power spectrum is located near the short period
oscillation frequency (approx. i Hz) (Figure 6).
