Lecture Fundamentals of control systems: Chapter 5 - TS. Huỳnh Thái Hoàng

Lecture "Fundamentals of control systems - Chapter 5: Analysis of control system performance" presentation of content: Performance criteria, steady state error, transient response, the optimal performance index,... Invite you to reference.
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Lecture Fundamentals of control systems: Chapter 5 - 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/6 December 2013 © H. T. Hoang - www4.hcmut.edu.vn/~hthoang/ 1 Chapter 5 ANALYSIS OF CONTROL SYSTEM PERFORMANCE6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 2 Content Performance criteria Steady state error Transient response The optimal performance index Relationship between frequency domain performances and time domain performances.6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 3 Performance criteria6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 4 Performance criteria: Steady state error yfb(t) Y(s) essR(s) E(s) r(t) +_ G(s) Yfb(s) e(t) ess H(s) t 0 Error: is the difference between the set-point set point (input) and the feedback signal. e(t )  r (t )  y fb (t )  E ( s )  R ( s )  Y fb ( s ) Steady-state error: is the error when time approaching infinity. ess  lim li e(t )  ess  lim li sE E ( s) t  s 0 6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 5 Performance criteria – Percent of Overshoot (POT) Overshoot: refers to an output exceeding its steady-state steady state value. value y(t) y(t) overshoot ymax ymax yss yss yss yss No overshoot t t 0 0 Percentage of Overshoot (POT) is an index to quantify the overshoot of a system, POT is calculated as: y max  y ss POT   100% y ss 6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 6 Performance criteria – Settling time and rise time Settling time (ts): is the time required for the response of a system to reach and stay within a range about the steady- state value of size specified by absolute percentage of the steady-state value (usually 2% or 5%) Rise time (tr): is the time required for the response of a system to rise from 10% to 90% of its steady-state steady state value. value y(t) y(t)(1+)yss yss yss(1)yss 0.9yss 0.1yss t t 0 0 ts tr 6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 7 Steady--state error Steady6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 8 Steady--state error Steady R( ) R(s) E( ) E(s) Y( ) ...