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Iterative Learning Control An Optimization Paradigm

:	David H. Owens
:	Iterative Learning Control An Optimization Paradigm
:	Springer-Verlag
:	9781447167723
:	Advances in Industrial Control
:	1
:	CHF 114.50
:

:	Elektronik, Elektrotechnik, Nachrichtentechnik
:	English

:	473
:	DRM
:	PC/MAC/eReader/Tablet
:	PDF

This book develops a coherent theoretical approach to algorithm design for iterative learning control based on the use of optimization concepts. Concentrating initially on linear, discrete-time systems, the author gives the reader access to theories based on either signal or parameter optimization. Although the two approaches are shown to be related in a formal mathematical sense, the text presents them separately because their relevant algorithm design issues are distinct and give rise to different performance capabilities.

Together with algorithm design, the text demonstrates that there are new algorithms that are capable of incorporating input and output constraints, enable the algorithm to reconfigure systematically in order to meet the requirements of different reference signals and also to support new algorithms for local convergence of nonlinear iterative control. Simulation and application studies are used to illustrate algorithm properties and performance in systems like gantry robots and other electromechanical and/or mechanical systems.

Iterative Learning Control will interest academics and graduate students working in control who will find it a useful reference to the current status of a powerful and increasingly popular method of control. The depth of background theory and links to practical systems will be of use to engineers responsible for precision repetitive processes.

Professor Owens has 40 years of experience of Control Engineering theory and applications in areas including nuclear power, robotics and mechanical test. He has extensive teaching experience at both undergraduate and postgraduate levels in three UK universities. His research has included multivariable frequency domain theory and design, the theory of multivariable root loci, contributions to robust control theory, theoretical methods for controller design based on plant step data and involvement in aspects of adaptive control, model reduction and optimization-based design. His area of research that specifically underpins the text is his experience of modelling and analysis of systems with repetitive dynamics. Originally arising in control of underground coal cutters, my theory of 'multipass processes' (developed in 1976 with follow-on applications introduced by J.B. Edwards) laid the foundation for analysis and design in this area and others including metal rolling and automated agriculture. This work led to substantial contributions (with collaborator E. Rogers and others) in the area of repetitive control systems (as part of 2D systems theory) but more specifically, since 1996, in the area of iterative learning control when I introduced the use of optimization to the ILC community in the form of 'norm optimal iterative learning control'. Since that time he has continued to teach and research in areas related to this topic adding considerable detail and depth to the approach and introducing the ideas of parameter optimal iterative learning to simplify the implementations. This led to his development of a wide range of new algorithms, supporting analysis and applications to mechanical test. This work is also being applied to the development of data analysis tools for control in gantry robots and stroke rehabilitation equipment by collaborators at Southampton University. Work with S. Daley has also seen applications in automative test at Jaguar and related industrial sites.
David Owens was elected a Fellow of the Royal Academy of Engineering for his contributions to knowledge in these and other areas.

	Series Editors’ Foreword	7
	Preface	10
	Acknowledgments	17
	Contents	19
	1 Introduction	27
	1.1 Control Systems, Models and Algorithms	28
	1.2 Repetition and Iteration	29
	1.2.1 Periodic Demand Signals	29
	1.2.2 Repetitive Control and Multipass Systems	30
	1.2.3 Iterative Control Examples	32
	1.3 Dynamical Properties of Iteration: A Review of Ideas	35
	1.4 So What Do We Need?	38
	1.4.1 An Overview of Mathematical Techniques	39
	1.4.2 The Conceptual Basis for Algorithms	41
	1.5 Discussion and Further Background Reading	42
	2 Mathematical Methods	44
	2.1 Elements of Matrix Theory	44
	2.2 Quadratic Optimization and Quadratic Forms	52
	2.2.1 Completing the Square	52
	2.2.2 Singular Values, Lagrangians and Matrix Norms	53
	2.3 Banach Spaces, Operators, Norms and Convergent Sequences	54
	2.3.1 Vector Spaces	54
	2.3.2 Normed Spaces	56
	2.3.3 Convergence, Closure, Completeness and Banach Spaces	58
	2.3.4 Linear Operators and Dense Subsets	59
	2.4 Hilbert Spaces	62
	2.4.1 Inner Products and Norms	62
	2.4.2 Norm and Weak Convergence	64
	2.4.3 Adjoint and Self-adjoint Operators in Hilbert Space	66
	2.5 Real Hilbert Spaces, Convex Sets and Projections	71
	2.6 Optimal Control Problems in Hilbert Space	73
	2.6.1 Proof by Completing the Square	75
	2.6.2 Proof Using the Projection Theorem	76
	2.6.3 Discussion	77
	2.7 Further Discussion and Bibliography	78
	3 State Space Models	80
	3.1 Models of Continuous State Space Systems	82
	3.1.1 Solution of the State Equations	83
	3.1.2 The Convolution Operator and the Impulse Response	84
	3.1.3 The System as an Operator Between Function Spaces	84
	3.2 Laplace Transforms	85
	3.3 Transfer Function Matrices, Poles, Zeros and Relative Degree	86
	3.4 The System Frequency Response	88
	3.5 Discrete Time, Sampled Data State Space Models	89
	3.5.1 State Space Models as Difference Equations	89
	3.5.2 Solution of Linear, Discrete Time State Equations	90
	3.5.3 The Discrete Convolution Operator and the Discrete Impulse Response Sequence	91
	3.6 mathcalZ-Transforms and the Discrete Transfer Function Matrix	92
	3.6.1 Discrete Transfer Function Matrices, Poles, Zeros and the Relative Degree	93
	3.6.2 The Discrete System Frequency Response	94
	3.7 Multi-rate Discrete Time Systems	95
	3.8 Controllability, Observability, Minimal Realizations and Pole Allocation	95
	3.9 Inverse Systems	97
	3.9.1 The Case of m=ell, Zeros and ?*	97
	3.9.2 Left and Right Inverses When m neqell	99
	3.10 Quadratic Optimal Control of Linear Continuous Systems	101
	3.10.1 The Relevant Operators and Spaces	101
	3.10.2 Computation of the Adjoint Operator	103
	3.10.3 The Two Point Boundary Value Problem	106
	3.10.4 The Riccati Equation and a State Feedback Plus Feedforward Representation	107
	3.10.5 An Alternative Riccati Representation	109
	3.11 Further Reading and Bibliography	110
	4 Matrix Models, Supervectors and Discrete Systems	112
	4.1 Supervectors and the Matrix Model	112
	4.2 The Algebra of Series and Parallel Connections	113
	4.3 The Transpose System and Time Reversal	114
	4.4 Invertibility, Range and Relative Degrees	115
	4.4.1 The Relative Degree and the Kernel and Range of G	117
	4.4.2 The Range of G and Decoupling Theory	118
	4.5 The Range and Kernel and the Use of the Inverse System	121
	4.5.1 A Partition of the Inverse	121
	4.5.2 Ensuring Stability of P-1(z)	123
	4.6 The Range, Kernel and the mathcalC* Canonical Form	124
	4.6.1 Factorization Using State Feedback and Output Injection	124
	4.6.2 The mathcalC* Canonical Form	125
	4.6.3 The Special Case of Uniform Rank Systems	127
	4.7 Quadratic Optimal Control of Linear Discrete Systems	129
	4.7.1 The Adjoint and the Discrete Two Point Boundary Value Problem	130
	4.7.2 A State Feedback/Feedforward Solution	131