Microsoft PowerPoint FundCtrlSys Chapter5 ppt [Compatibility Mode] Lecture NotesLecture Notes Fundamentals of Control SystemsFundamentals of Control Systems Instructor Assoc Prof Dr Huynh Thai Hoang D[.]
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/ December 2013 © H T Hoang - www4.hcmut.edu.vn/~hthoang/ Chapter ANALYSIS OF CONTROL SYSTEM PERFORMANCE December 2013 © H T Hồng - www4.hcmut.edu.vn/~hthoang/ Content Performance criteria Steady state error Transient response The optimal performance index Relationship between frequency domain performances and time domain performances December 2013 © H T Hồng - www4.hcmut.edu.vn/~hthoang/ Performance criteria December 2013 © H T Hồng - www4.hcmut.edu.vn/~hthoang/ Performance criteria: Steady state error yfb(t) R(s) +_ E(s) Yfb(s) G(s) Y(s) ess r(t) e(t) H(s) ess t 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 ) t December 2013 ess lim li sE E ( s) s 0 © H T Hồng - www4.hcmut.edu.vn/~hthoang/ 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 yss yss ymax yss yss No overshoot t t Percentage of Overshoot (POT) is an index to quantify the overshoot of a system, POT is calculated as: y max y ss 100% POT y ss December 2013 © H T Hoàng - www4.hcmut.edu.vn/~hthoang/ 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 steadystate 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 (1)yss yss 0.9yss t ts December 2013 0.1yss t tr © H T Hồng - www4.hcmut.edu.vn/~hthoang/ Steady state error Steady December 2013 © H T Hoàng - www4.hcmut.edu.vn/~hthoang/ Steady state error Steady R( ) R(s) +_ E( ) E(s) Yfb(s) ( ) G(s) Y( ) Y(s) H(s) Error expression: R( s) E (s) G(s) H (s) Steady-state error: sR( s ) ess lim sE ( s ) lim s 0 s 0 G ( s ) H ( s ) Remark: Steady-state error not only depends on the structure and p parameters of the system y but also depends p on the input p signal December 2013 © H T Hoàng - www4.hcmut.edu.vn/~hthoang/ Steady state error to step input Steady Step input: R( s ) / s Steady-state error: ess with 1 Kp K p lim G ( s ) H ( s ) s 0 (position constant) yfb(t) yfb(t) 1 t G(s)H(s) does not have any deal integral factor December 2013 t G(s)H(s) has at least ideal integral factor © H T Hồng - www4.hcmut.edu.vn/~hthoang/ 10