LINEAR SYSTEM THEORY
Academic Year 2015/2016 - 2° YearCredit Value: 9
Scientific field: ING-INF/04 - Systems and control engineering
Taught classes: 49 hours
Term / Semester: 2°
ENGLISH VERSION
Learning Objectives
Detailed Course Content
1. LTI System Internal Representation: Definition of a Dynamical System - Systems Classification - Linear Time Invariant (LTI) Systems in continuous and discrete time – State space representation - State equation solution by Lagrange - State transition matrix - Equivalent systems and similarity transformations – System modes in continuous and discrete time. Multi-input/Multi-output systems.
2. LTI Input/Output System Representation: Mathematical note on the Laplace and Zeta operator – Relations between the S plane and Z plane (Tustin transformation) - Transfer function - Systems connection and block diagrams – System realizations and minimality - Jordan canonical form.
3. Stability for LTI Systems: Definition of Stability - Internal stability and eigenvalues - Input/output stability and poles (BIBO stability) – Asymptotic stability criteria (Routh and Hurwitz) – Stability in connected systems – Stability and relation between the S plane and Z plane.
4. Input/Output Response in Time Domain : Pulse and step response for first order and second order systems – Step response and pole placement - Step response and zero.
5. Input/Output Response in Frequency Domain: Harmonic function - Frequency response for LTI System - Bode diagrams – Characteristics of the frequency response for first and second order systems – Minimum phase systems.
6. Structural Properties for LTI Systems: Controllability - State feedback controller design for eigenvalues placement - Control canonical form - System decomposition based on the controllability – Observability - Asymptotic observer design (the state estimator) - Control canonical form - System decomposition based on the observability - Principle of separation of estimation and control - Kalman decomposition and transfer function.
Textbook Information
T1) G. F. Franklin et al, Feedback control of dynamic systems, Addison Wesley
T2) R.C.Dorf and R.H. Bishop, Modern Control Systems, Addison Wesley