Lecture Fundamentals of control systems: Chapter 8 - TS. Huỳnh Thái Hoàng

Lecture "Fundamentals of control systems - Chapter 8: Analysis of discrete control systems" presentation of content: Stability conditions for discrete systems, extension of Routh - Hurwitz criteria, jury criterion, root locus,... Invite you to reference.

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Lecture Fundamentals of control systems: Chapter 8 - TS. Huỳnh Thái Hoàng Lecture Notes Fundamentals of Control Systems Instructor: Assoc. Prof. Dr. Huynh Thai Hoang Department of Automatic Control Faculty of Electrical & Electronics Engineering Ho Chi Minh City University of Technology Email: hthoang@hcmut.edu.vn huynhthaihoang@yahoo.com Homepage: www4.hcmut.edu.vn/~hthoang/ www4 hcmut edu vn/ hthoang/6 December 2013 © H. T. Hoang - www4.hcmut.edu.vn/~hthoang/ 1 Chapter 8 ANALYSIS OF DISCRETE CONTROL SYSTEMS6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 2 Content Stability conditions for discrete systems Extension of Routh-Hurwitz criteria Jury J criterion it i Root locus Steady St d statet t error Performance of discrete systems6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 3 Stability conditions for discrete systems6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 4 Stability conditions for discrete systems A system is defined to be BIBO stable if every bounded input to the system results in a bounded output. I s Im I z Im Stable Re s Stable Re z Res  0 | z | 1 1 z  eTs The region of stability for a The region of stability for a contin o s system continuous s stem is the di discrete t system t i th is the left-half s-plane interior of the unit circle6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 5 Characteristic equation of discrete systems Discrete systems described by block diagram: R(s) Y(s) + GC(z) ZOH G(s)  T H(s) Characteristic equation: 1  GC ( z )GH ( z )  0 Discrete systems described by the state equation  x( k  1)  Ad x( k )  Bd r ( k )   y ( k )  Cd x( k ) Characteristic equation: det( zI  Ad )  0 6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 6 Methods for analysis the stability of discrete systems Algebraic stability criteria  The extension of the Routh-Hurwitz criteria  Jury’s J ’ stability t bilit criterion it i The root locus method6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 7The extension of the Routh- Routh-Hurwitz criteria6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 8 The extension of the Routh Routh--Hurwitz criteria Characteristic C a acte st c equat equation o oof d discrete sc ete syste systems: s a0 z n  a1 z n 1    an  0 Im z Im w Region R i off Region of stability Re z stability Re w 1 1 w z 1 w The extension of the Routh-Hurwitz criteria: transform zw,, and then apply pp y the Routh – Hurwitz criteria to the characteristic equation of the variable w.6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 9 The extension of the Routh Routh--Hurwitz criteria – Example Analyze the stability of the following system: R(s) + Y(s)  ZOH G(s) T  0.5 H(s) 3e  s 1GiGiven ...