Modeling and Identification of Linear Parameter-Varying Systems (Lecture Notes in Control and Information Sciences, 403)

✍ Scribed by Roland Toth

• Publisher: Springer
• Year: 2010
• Tongue: English
• Leaves: 337
• Category: Library

✦ Synopsis

Through the past 20 years, the framework of Linear Parameter-Varying (LPV) systems has become a promising system theoretical approach to handle the control of mildly nonlinear and especially position dependent systems which are common in mechatronic applications and in the process industry. The birth of this system class was initiated by the need of engineers to achieve better performance for nonlinear and time-varying dynamics, c- mon in many industrial applications, than what the classical framework of Linear Time-Invariant (LTI) control can provide. However, it was also a p- mary goal to preserve simplicity and “re-use” the powerful LTI results by extending them to the LPV case. The progress continued according to this philosophy and LPV control has become a well established ?eld with many promising applications. Unfortunately, modeling of LPV systems, especially based on measured data (which is called system identi?cation) has seen a limited development sincethebirthoftheframework.Currentlythisbottleneck oftheLPVfra- work is halting the transfer of the LPV theory into industrial use. Without good models that ful?ll the expectations of the users and without the und- standing how these models correspond to the dynamics of the application, it is di?cult to design high performance LPV control solutions. This book aims to bridge the gap between modeling and control by investigating the fundamental questions of LPV modeling and identi?cation. It explores the missing details of the LPV system theory that have hindered the formu- tion of a well established identi?cation framework.

✦ Table of Contents

Title Page
Preface
Contents
Acronyms
List of Symbols
Introduction
New Challenges for System Identification
The Birth of LPV Systems
The Present State of LPV Identification
The Identification Cycle
General Picture of LPV Identification
LPV-IO Representation Based Methods
LPV-SS Representation Based Methods
Similarity to Other System Classes
Challenges and Open Problems
Perspectives of Orthonormal Basis Function Models
The Gain-Scheduling Perspective
The Global Identification Perspective
Approximation via OBF Structures
The Goal of the Book
Overview of Contents
LTI System Identification and the Role of OBFs
The Concept of Orthonormal Basis Functions
Signal Spaces and Inner Functions
General Class of Orthonormal Basis Functions
Takenaka-Malmquist Basis
Hambo Basis
Kautz Basis
Laguerre Basis
Pulse Basis
Orthonormal Basis Functions of MIMO Systems
Basis Functions in Continuous-Time
Modeling and Identification of LTI Systems
The Identification Setting
Model Structures
Properties
Linear Regression
Identification with OBFs
Pole Uncertainty of Model Estimates
Validation in the Prediction-Error Setting
The Kolmogorov $n$-Width Theory
Conclusions
LPV Systems and Representations
General Class of LPV Systems
Parameter Varying Dynamical Systems
Representations of Continuous-Time LPV Systems
Representations of Discrete-Time LPV Systems
Equivalence Classes and Relations
Equivalent Kernel Representations
Equivalent IO Representations
Equivalent State-space Representations
Properties of LPV Systems and Representations
State-Observability and Reachability
Stability of LPV Systems
Gramians of LPV State-Space Representations
Conclusions
LPV Equivalence Transformations
State-Space Canonical Forms
The Observability Canonical Form
Reachability Canonical Form
Companion Canonical Forms
Transpose of SS Representations
LTI vs. LPV State Transformation
From State-Space to the Input-Output Domain
From the Input-Output to the State-Space Domain
The Idea of Recursive State-Construction
Cut-and-Shift in Continuous-Time
Cut-and-Shift in Discrete-Time
State-Maps and Polynomial Modules
State-Maps Based on Kernel Representations
State-Maps Based on Image-Representations
State-Construction in the MIMO Case
Conclusions
LPV Series-Expansion Representations
Relevance of Series-Expansion Representations
Impulse Response Representation of LPV Systems
Filter Form of LPV-IO Representations
Series Expansion in the Pulse Basis
The Impulse Response Representation
LPV Series Expansion by OBFs
The OBF Expansion Representation
Series Expansions and Gain-Scheduling
The Role of Gain-Scheduling
Optimality of the Basis in the Frozen Sense
Optimality of the Basis in the Global Sense
Conclusions
Discretization of LPV Systems
The Importance of Discretization
Discretization of LPV System Representations
Discretization of State-Space Representations
Complete Method
Approximative State-Space Discretization Methods
Discretization Errors and Performance Criteria
Local Discretization Errors
Global Convergence and Preservation of Stability
Guaranteeing a Desired Level of Discretization Error
Switching Effects
Properties of the Discretization Approaches
Discretization and Dynamic Dependence
Numerical Example
Conclusions
LPV Modeling of Physical Systems
Towards Model Structure Selection
General Questions of LPV Modeling
Modeling of Nonlinear Systems in the LPV Framework
First Principle Models
Linearization Based Approximation Methods
Multiple Model Design Procedures
Substitution Based Transformation Methods
Automated Model Transformation
Summary of Existing Techniques
Translation of First Principle Models to LPV Systems
Problem Statement
The Transformation Algorithm
Handling Non-Factorizable Terms
Properties of the Transformation Procedure
Conclusions
Optimal Selection of OBFs
Perspectives of OBFs Selection
Kolmogorov n-Width Optimality in the Frozen Sense
The Fuzzy-Kolmogorov c-Max Clustering Approach
The Pole Clustering Algorithm
Properties of the FKcM
Simulation Example
Robust Extension of the FK$c$M Approach
Questions of Robustness
Basic Concepts of Hyperbolic Geometry
Pole Uncertainty Regions as Hyperbolic Objects
The Robust Pole Clustering Algorithm
Properties of the Robust FKcM
Simulation Example
Conclusions
LPV Identification via OBFs
Aim and Motivation of an Alternative Approach
OBFs Based LPV Model Structures
The LPV Prediction-Error Framework
The Wiener and the Hammerstein OBF Models
Properties of Wiener and Hammerstein OBF Models
OBF Models vs. Other Model Structures
Identification of W-LPV and H-LPV OBF Models
Identification with Static Dependence
The Identification Setting
LPV Identification with Fixed OBFs
Local Approach
Global Approach
Properties
Examples
Approximation of Dynamic Dependence
Feedback-Based OBF Model Structures
Properties of Wiener and Hammerstein Feedback Models
Identification by Dynamic Dependence Approximation
Properties
Example
Extension towards MIMO Systems
Scalar Basis Functions
Multivariable Basis Functions
Multivariable Basis Functions in the Feedback Case
General Remarks on the MIMO Extension
Conclusions
Appendix A
References
Index