Nonlinear H 2/H ∞ Constrained Feedback Control: A Practical Design Approach Using Neural Networks

217 Pages·2006·1.52 MB·English

by  Murad Abu-Khalaf PhD

Advances in Industrial Control
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MuradAbu-Khalaf,JieHuangandFrankL.Lewis
H H
Nonlinear /
∞
2
Constrained Feedback
Control
APracticalDesignApproachUsingNeuralNetworks
With47Figures
123
MuradAbu-Khalaf,PhD JieHuang,PhD FrankL.Lewis,PhD
Automation&Robotics DepartmentofAutomation Automation&Robotics
ResearchInstitute andComputer-aided ResearchInstitute
TheUniversityofTexas Engineering TheUniversityofTexas
atArlington ChineseUniversityof atArlington
FortWorth,Texas HongKong FortWorth,Texas
USA Shatin,NewTerritories USA
HongKong
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AdvancesinIndustrialControlseriesISSN1430-9491
ISBN-10: 1-84628-349-3 e-ISBN 1-84628-350-7 Printedonacid-freepaper
ISBN-13: 978-1-84628-349-9
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AdvancesinIndustrialControl
SeriesEditors
ProfessorMichaelJ.Grimble,ProfessorofIndustrialSystemsandDirector
ProfessorMichaelA.Johnson,Professor(Emeritus)ofControlSystems
andDeputyDirector
IndustrialControlCentre
DepartmentofElectronicandElectricalEngineering
UniversityofStrathclyde
GrahamHillsBuilding
50GeorgeStreet
GlasgowG11QE
UnitedKingdom
SeriesAdvisoryBoard
ProfessorE.F.Camacho
EscuelaSuperiordeIngenieros
UniversidaddeSevilla
CaminodelosDescobrimientoss/n
41092Sevilla
Spain
ProfessorS.Engell
LehrstuhlfürAnlagensteuerungstechnik
FachbereichChemietechnik
UniversitätDortmund
44221Dortmund
Germany
ProfessorG.Goodwin
DepartmentofElectricalandComputerEngineering
TheUniversityofNewcastle
Callaghan
NSW2308
Australia
ProfessorT.J.Harris
DepartmentofChemicalEngineering
Queen’sUniversity
Kingston,Ontario
K7L3N6
Canada
ProfessorT.H.Lee
DepartmentofElectricalEngineering
NationalUniversityofSingapore
4EngineeringDrive3
Singapore117576
ProfessorEmeritusO.P.Malik
DepartmentofElectricalandComputerEngineering
UniversityofCalgary
2500,UniversityDrive,NW
Calgary
Alberta
T2N1N4
Canada
ProfessorK.-F.Man
ElectronicEngineeringDepartment
CityUniversityofHongKong
TatCheeAvenue
Kowloon
HongKong
ProfessorG.Olsson
DepartmentofIndustrialElectricalEngineeringandAutomation
LundInstituteofTechnology
Box118
S-22100Lund
Sweden
ProfessorA.Ray
PennsylvaniaStateUniversity
DepartmentofMechanicalEngineering
0329ReberBuilding
UniversityPark
PA16802
USA
ProfessorD.E.Seborg
ChemicalEngineering
3335EngineeringII
UniversityofCaliforniaSantaBarbara
SantaBarbara
CA93106
USA
DoctorK.K.Tan
DepartmentofElectricalEngineering
NationalUniversityofSingapore
4EngineeringDrive3
Singapore117576
ProfessorIkuoYamamoto
KyushuUniversityGraduateSchool
MarineTechnologyResearchandDevelopmentProgram
MARITEC,Headquarters,JAMSTEC
2-15NatsushimaYokosuka
Kanagawa237-0061
Japan
To my parents Suzan and Muhammad Samir
M. Abu-Khalaf
To Qingwei, Anne and Jane
J. Huang
To Galina
F. L. Lewis
Series Editors’ Foreword
The seriesAdvancesin IndustrialControlaimsto report and encourage technology
transfer in control engineering. The rapid development of control technology has
an impact on all areas of the control discipline. New theory, new controllers,
actuators, sensors, new industrial processes, computer methods, new applications,
new philosophies(cid:125), new challenges. Much of this development work resides in
industrial reports, feasibility study papers and the reports of advanced collaborative
projects. The series offers an opportunity for researchers to present an extended
exposition of such new work in all aspects of industrial control for wider and rapid
dissemination.
Almost all physical systems are nonlinear and the success of linear control
techniques depends on the extent of the nonlinear system behaviour and the careful
attention given to switching linear controllers through the range of nonlinear
system operations. In many industrial and process-control applications, good
engineering practice, linear control systems and classical PID control can give
satisfactory performance because the process nonlinearity is mild and the control
system performance specification is not particularly demanding; however, there are
other industrial system applications where the requirement for high-performance
control can only be achieved if nonlinear control design techniques are used. Thus,
in some industrial and technological domains there is a strong justification for
more applications of nonlinear methods. One prevailing difficulty with nonlinear
control methods is that they are not so easily understood nor are they easy to
reduce to formulaic algorithms for routine application. The abstract and often
highly mathematical tools needed for nonlinear control systems design means that
there is often an “education gap” between the control theorist and the industrial
applications engineer; a gap that is difficult to bridge and that prevents the
widespread implementation of many nonlinear control methods.
The theorist/applications engineer “education gap” is only one aspect of the
complex issues involved in the technology transfer of nonlinear control systems
into industry. A second issue lies in the subject itself and involves the question of
whether nonlinear control design methods are sufficiently mature actually to make
the transfer to industry feasible and worthwhile. A look at the nonlinear control
literature reveals many novel approaches being developed by the theorist but often
x Series Editors’ Foreword
these methods are neither tractable nor feasible nor has sufficient attention been
given to the practical relevance of the techniques for industrial application. We
hope through the Advances in Industrial Control series to explore these themes
through suitable volumes and to try to create a corpus of monograph texts on
applicable nonlinear control methods. Typically such volumes will make
contributions to the range of applicable nonlinear-control-design tools, will provide
reviews of industrially applicable techniques that try to unify groups of nonlinear
control design methods and will provide detailed presentations of industrial
applications of nonlinear control methods and system technology.
This particular volume in Advances in Industrial Control by M. Abu-Khalaf, J.
Huang and F.L. Lewis makes a contribution to increasing the range of applicable
nonlinear control design tools. It starts from a very classical viewpoint that
performance can be captured by a suitably constructed cost function and that the
appropriate control law emerges from the optimisation of the cost function. The
difficulty is that the solution of these optimal control problems for the class of
nonlinear state-space systems selected leads to intractable equations of the
Hamilton–Jacobi type. The authors then propose and develop a solution route that
exploits the approximation properties of various levels of complexity within
nonlinear network structures. Namely, they use neural networks and exploit their
“universal function approximation property” to compute tractable solutions to the
posed nonlinear H - and H -optimal-control problems. Demonstrations of the
2 (cid:146)
methods devised are given for various numerical examples in Chapter 3; these
include a nonlinear oscillator, a minimum-time control problem and a parabolic
tracking system. Later in the volume, the nonlinear benchmark problem of a
Rotational–Translational Actuator (RTAC) system is used to illustrate the power of
the methods devised. An aerospace example using the control design for the F-16
aircraft normal acceleration regulator illustrates a high-performance output
feedback control system application. Thus, the volume has an interesting set of
applications examples to test the optimal control approximation techniques and
demonstrate the performance enhancements possible.
This welcome entry to the Advances in Industrial Control monograph series
will be of considerable interest to the academic research community particularly
those involved in developing applicable nonlinear-control-system methods.
Research fellows and postgraduate students should find many items giving
research inspiration or requiring further development. The industrial engineer will
be able to use the volume’s examples to see what the nonlinear control laws look
like and by how much levels of performance can be improved by the use of
nonlinear optimal control.
M.J. Grimble and M.A. Johnson
Industrial Control Centre
Glasgow, Scotland, U.K.
Preface
Modern Control Theory has revolutionized the design of control systems for
aerospace systems, vehicles including automobiles and ships, industrial processes,
and other highly complex systems in today’s world. Modern Control Theory was
introduced during the late 1950s and 1960s. Key features of Modern Control are
the use of matrices, optimality design conditions, and probabilistic methods. It
allows the design of control systems with guaranteed performance for multi-
input/multi-output systems through the solution of formal matrix design equations.
For linear state-space systems, the design equations are quadratic in form and
belong to the general class known as Riccati equations. For systems in polynomial
form, the design equations belong to the class known as Diophantine equations.
The availability of excellent solution techniques for the Riccati and
Diophantine design equations has brought forward a revolution in the design of
control systems for linear systems. Moreover, mathematical analysis techniques
have been effectively used to provide guaranteed performance and closed-loop
stability results for these linear system controllers. This has provided confidence in
modern control systems designed for linear systems, resulting in their general
acceptance in communities including aerospace, process control, military systems,
and vehicle systems, where performance failures can bring catastrophic disasters.
Physical systems are nonlinear. The push to extend the operating envelopes of
such systems, for instance hyper-velocity and super-maneuverability performance
in aerospace systems and higher data storage densities for computer hard disk drive
systems, means that linear approximation techniques for controls design no longer
work effectively. Therefore the design of efficient modern control systems hinges
on the ability to use nonlinear system models. It is known that control systems
design for general nonlinear systems can be performed by solving equations that
are in the Hamilton–Jacobi (HJ) class. Unfortunately, control design for modern-
day nonlinear systems is hampered because the HJ equations are impossible to
solve exactly for general nonlinear systems.
This book presents computationally effective and rigorous methods for solving
control design equations in the HJ class for nonlinear systems. The approach taken