1 / 16

Linear Systems Theory 線 性系統理論 ( 239014) 2011 Fall, 4bcd

Linear Systems Theory 線 性系統理論 ( 239014) 2011 Fall, 4bcd. Kai-Yew Lum 林繼耀 Associate Professor Dept. of Electrical Engineering BST-1 #421, ext. 4725 http://staffweb.ncnu.edu.tw/kylum. Objectives. Motivation

coen
Download Presentation

Linear Systems Theory 線 性系統理論 ( 239014) 2011 Fall, 4bcd

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Linear Systems Theory線性系統理論 (239014)2011 Fall, 4bcd Kai-Yew Lum林繼耀 Associate Professor Dept. of Electrical Engineering BST-1 #421, ext. 4725 http://staffweb.ncnu.edu.tw/kylum

  2. Objectives • Motivation • Linear Systems Theory is the foundation of systems, control and signal processing. • Past development of this discipline has produced a mature and fairly complete set of concepts and methods • These are fundamental knowledge in electrical engineering, communications, mechanical engineering, medical engineering, etc. • Course Objectives • Explore the basic theory of linear systems and its applications. • Provide the necessary tools for engineering problems: • mathematical description • analysis (especially numerical analysis)

  3. Time Line of Systems Theory in Control Engineering 1950’s Linear Systems Theory Ziegler-Nicholas LQR Kalman filter LQG 1960’s Transfermatrix LyapunovTheory Matrix-fraction description 1970’s AdaptiveControl LQG/LTR Sliding Mode 1980’s DynamicInversion H∞ -Synthesis MPC 1990’s Adaptive Back-Stepping 2000’s State-spacetechniques Nonlineartechniques Classical & frequencydomain techniques

  4. Lesson Plan • Introduction • Mathemetical Description of Dynamical Systems • Review of Linear Algebra -- Matrix Theory • State-Space Solution • Controllability & Observability, Stability • Transfer Matrix Description and Realization • State Feedback and State Estimators • Introduction to Linear Sampled-Data Systems

  5. What You Should Expect to Learn • Mathematical Description of Dynamical Systems • When we study a dynamical system, i.e. a system that evolves in time with memory effects, we need to describe (represent) its behavior in equations in order to conduct meaningful analysis and computation. • You should also learn the key characteristics that make a system “linear”, the concept of “state”, and the correspondence between the state-space representation and what you already know in frequency domain description (transfer functions).

  6. What You Should Expect to Learn • Review of Linear Algebra • Matrix notations • Properties: determinant, rank, eigenvalues • Characteristic polynomial; Cayley-Hamilton theorem • Special matrices: • Definite matrices • Orthogonal matrices • Singular values & SV decomposition (SVD) • Transformation & diagonalization • Generalized eigenvalues & Jordan blocks

  7. What You Should Expect to Learn • State-Space Solution • The solution of a dynamical system is its “trajectory” from an initial state, either on its own or under influence of an external input. • The solution of a linear system is structured and easy to understand if you think of it as linear combination of some “template” solutions: a basis of solutions. • Though there is an infinite number of solutions, the dimension of this basis is finite.

  8. What You Should Expect to Learn • Controllability, Observability, Stability • By now you should know that a linear dynamical system has internal states, which are described in the state-space representation but not the input-output (transfer) description. • However, whether the states can be driven by any input, and observed at the output, is not obvious. • Also not obvious is whether the internal states are stable, even if the output is well-behaved.

  9. What You Should Expect to Learn • Transfer Matrix & Realization • Here, we go in the reverse direction: given an input-output transfer description, can we find a state-space representation that describes the system’s behavior? • There is in fact an infinite number of representations for the same system, so we look for some “good” qualities: • Minimal representation • Canonical (controllable or observable) forms • Jordan form (spectral description)

  10. What You Should Expect to Learn • State Feedback and State Estimators • These are immediate applications of controllability and observability concepts. • More later …

  11. What You Should Expect to Learn • Introduction to Linear Sampled-Data Systems • The basic theory of linear systems is discussed in continuous time. • However, in engineering problems and especially using digital computers for control and measurement, we deal with sampled data and therefore discrete-time systems. • A quick overview of the discrete theory should equip you for future learning & practice.

  12. Lesson Plan

  13. Core Competency 核心能力 • 具備電機工程專業領域及背景知識EE domain & background knowledge • 具備探索新知與解決問題的能力Continued learning and problem solving • 具備獨立研究、撰寫論文與研發創新之能力Independent research and development • 掌握國際趨勢具全球化競爭挑戰能力Global competitiveness • 具備專業倫理道德及社會責任認知Social ethics and moral duties

  14. Course Map

  15. Text & References • C.T. Chen, Linear Systems Theory and Design,3rd ed. Oxford University Press, 1999. • T. Kailath, Linear Systems, Prentice-Hall, 1998. • Franklin, Powell and Workman, Digital Control of Dynamic Systems, 3rd ed. Addison Wesley, 1998. • Kailath, Sayed and Hassibi, Linear Estimation, Prentice-Hall, 2000. • 鄭大鐘 , 《線形系統理論》,第二版,北京:清華大學出版社, 2002。 • http://staffweb.ncnu.edu.tw/kylum

  16. Analytical Softwares (4th generation programming languages) • MATLAB (1984-) By MathWorksCommercial LINPACK (1970-1980) BLAS (1979-) Basic Linear Algebra Subprogram • GNU Octave (1992-) Open source, public license • Scilab (1990-) Open source Developed by INRIA, France LAPACK (1980-)Linear AlgeraPACKage Common Tools Fortran/C++ LibrariesFree!

More Related