1st Edition
Tensor Product Model Transformation in Polytopic Model-Based Control
Introduction
Significant paradigm changes
Current computational methods and Applications
Role of the TP model transformation in control design
Part I: Tensor-product Model Transformation of Linear Parameter Varying Models
Higher Order Singular Value Decomposition of Tensors
Basic concept of tensor algebra
Higher Order Singular Value Decomposition (HOSVD)
Approximation trade-off by HOSVD
HOSVD-based canonical form of Linear Parameter-varying Models
Linear Parameter-Varying state-space model
HOSVD-based canonical form of LPV models
Numerical reconstruction of the HOSVD based canonical form
TP model transformation
Algorithm of the TP model transformation
Example of the TORA benchmark system
Computational relaxed TP model transformation
Column equivalence
Modified TP transformation
Evaluation of complexity reduction
Discretization complexity
Computational load of the HOSVD
Computational load of the tensor product
Numerical examples
A simple example
A more complex example
Convex TP model forms of Linear Parameter-varying Models
Convex TP model
Different types of convex TP models
Computation of different convex TP models
Methods for SN, NN and NO type matrices
Inverse, relaxed and normalized convex TP models (lNO, RNO)
The TORA benchmark example
Approximation and complexity trade-off by the TP model transformation
Approximation theory framework
No-where denseness
Examples
Part II: Control Design Examples
TP model transformation based design
Linear Matrix Inequality in system control design
Parallel Distributed Compensation based control design framework
Immediate link between the TP models and the PDC design framework
TP model transformation based control design methodology
Application to 2-D prototypical aeroelastic wing section with structural nonlinearity
Introduction to the prototypical aeroelastic wing section
Finite element convex TP model of the prototypical aeroelastic wing section
State-feedback control design
Observer based output-feedback control design
Application to 3 DOF helicopter with four propellers
Nomenclature
Equations of Motion of the RC Helicopter Dynamics
Finite element convex TP model of the -3-DOF RC helicopter
Control design of the3-DOF RC helicopter
Control results
Application to Parallel Double Inverted Pendulum
Nomenclature
Equations of Motion of the RC Helicopter Dynamics
Finite element convex TP model of the PDIP
Control design of the PDIP
Control results
Biography
Peter Beranyi, Ph.D, D. Sc, is head of the Computer and Automation Research Institute of the Hungarian Academy of Sciences and a professor at the Budapest University of Technology and Economics. He received his D.Sc in Informatics, his Ph.D. in Electrical Engineering, his M.Sc. in Education of Engineering Science, and his M.Sc. in Electrical Engineering at Budapest University of Technology and Economics. His research interest is on LPV- and LMI-based control design, modeling based on TP functions, fuzzy modeling, fuzzy rule interpolation, and calculation complexity reduction of various model types. He has written 48 journal papers for 262 publications.
Yeung Yam, is a professor in the Department of Mechanical and Automation Engineering at the Chinese University of Hong Kong. He obtained his B.Sc. from the Chinese University of Hong Kong, his M.Sc. from the University of Akron, Ohio, USA and his M.Sc., D.Sc. from the Massachusetts Institute of Technology, Cambridge, Massachusetts, USA. He has published over 100 technical papers in various areas of research, including human skill acquisition and analysis, dynamics modeling, control, system identification, fuzzy approximation, and intelligent and autonomous systems.
Peter Valarki, is a professor at the Budapest University of Technology and Economics. He graduated in mechanical engineering in 1971 at the Faculty of Transportation Engineering at the Technical University of Budapest, now the Budapest University of Technology and Economics. He also earned his Ph.D., his C.Sc. and his D.Sc. He is a founding member of the Hungarian Academy of Engineering and the main topics of his research field are the stochastic control theory, statistical system identification, and computational intelligency. He is the co-author of 10 books and more than 250 other scientific and technical publications.
"… well written and easily readable. … The examples and applications to 3 Degrees Of Freedom (DOFs) control schemes for helicopters, models for aeroelastic wing sections and models for controlling the behavior of suspension system in heavy trucks are the main strength of the book. … for control engineers with a solid mathematical formation as well as control theorists and even applied mathematicians."
—zbMATH 1308 in 2015"The book provides an introduction to a method that has potential to significantly advance the theory and practice of control system design. The modeling step is frequently the most time-consuming stage of practical control system design. The unifying TP representation of quasi LPV models described in this book has potential to make this stage more efficient as well as enabling many of the powerful LMI-based control design methods for LPV systems to be applied to practical problems."
—James Whidborne, Cranfield University, Bedfordshire, UK
