Conrol Sysm Enginring (EE0T) Assignmn: PART-A (Tim Domain Analysis: Transin Rspons Analysis). Oain h rspons of a uniy fdack sysm whos opn-loop ransfr funcion is (s) s ( s 4) for a uni sp inpu and also calcula Damping raio, Ovrshoo, sling im a ±% and ±5% olranc.. Opn loop ransfr funcion of uniy fdack sysm is (s) whr and T ar s( Ts) consans. Drmin facor y which gain should muliplid so ha ovrshoo of uni sp rspons rducd from 75% o 5%.. Th opn loop ransfr funcion of uniy fdack sysm is (s). For his sysm s Ts ( ) T ovrshoo rducd from 0.6 o 0. du o chang in only. Show ha 4. T whr and ar valus of for 0.6 and 0. ovrshoo rspcivly. 4. Th lock diagram of a simpl srvo sysm is shown in h following figur. Drmin h characrisic quaion of h sysm. Hnc calcula h undampd frquncy of oscillaions, damping raio, damping facor, maximum ovrshoo, firs undrshoo, im inrvals afr which maximum and minimum occurs, sling im and h numr of cycls compld for h oupu is sld wihin % of h final valu. Th inpu o h sysm is a uni sp. 0. 5(s )(0.s ) C( s) 5. A scond ordr conrol sysm is rprsnd y a ransfr funcion is givn y Q T 0( s) ( s) Js fs Whr Q 0 (s) is h proporional oupu and T is h inpu orqu. A sp inpu 0N-m is applid o h sysm and s rsuls ar givn as M p 6%, T p s, h sady sa oupu of h sysm is 0.5 radian. Drmin h valu of J,, and f. 6. A sysm has 40% ovrshoo and rquirs a sling im of 4 sc whn givn a sp inpu. Th sady sa rror is %. Drmin h ransfr funcion of h scond ordr sysm. Also find ris im and pak im. 7. A sandard scond ordr sysm has 50% ovrshoo and sling im of sconds. Drmin ω n, ξ, T p and T r. 5 6 Prpard y: Mr. Saish Choudhury (Ass. Profssor, Dp. of. EICE Pag of 5 W: www.schoudhury.n Email: saish@schoudhury.n, saishchoudhury@soaunivrsiy.ac.in
Conrol Sysm Enginring (EE0T) Assignmn: 8. For a uniy fdack conrol sysm having (s), find h following: s(st ) i.th facor y which h gain mus muliplid so ha h damping raio incrass from 0. o 0.9. ii.th facor y which h im consan T mus muliplid so ha h damping raio dcrass from 0.9 o 0.. T iii.show ha. 9 whn h sysm ovrshoo rducs from 70% o 0% whr and T ar valus of for 70% and 0% ovrshoo. 9. Th figur shown low shows h sp rspons of a scond ordr sysm for an inpu u(). Assuming uniy fdack, drmin ξ, ω n and opn loop ransfr funcion of h sysm. C().5.0 0.8 Tim (sc) 0. A uniy fdack sysm has h loop ransfr funcion (s). If is im rspons o hav an s s a ( ) ovrshoo of lss han 5% and sling im no xcding 4 sconds, drmin suial valus for and a.. A uniy fdack sysm is characrizd y a opn loop ransfr funcion (s). 0) Drmin h gain so ha h sysm will hav a damping raio of 5.0. For his valu of drmin sling im, pak ovrshoo and im o pak ovrshoo for a uni sp inpu.. Find pak im, sling im, and prcnag of ovrshoo for h approxima scond ordr rspons C() 0.009804 0.000857 0.009990 cos(9.796) 0.0094 5. sin(9.796). 4. A uniy fdack conrol sysm has an opn loop ransfr funcion (s). Drmin h ) ris im, pak im, pak ovrshoo, % of ovrshoo and h sling im whn a sp displacmn of 5 is givn o h sysm. 4. Drmin h valus of and T of h closd loop sysm shown in figur low, so ha h maximum ovrshoo in uni sp rspons is 0% and h pak im is.5s. Assum ha Jkg-m. Prpard y: Mr. Saish Choudhury (Ass. Profssor, Dp. of. EICE Pag of 5 W: www.schoudhury.n Email: saish@schoudhury.n, saishchoudhury@soaunivrsiy.ac.in
Conrol Sysm Enginring (EE0T) Assignmn: Js C( s) Ts 5. Drmin h sling im for h sysm givn in Q. for 4%, 6%, 9%. 6. A posiion conrol sysm is sailizd y mans of acclraion fdack. If h sysm has a momn of inria of 0-5 g-m ; viscous fricional orqu of 0-4 Nm/rad/sc and h moor orqu is givn y dθ0 dθ0 Tm 4 0 N m, whr θi θ0; Acclraion fdack d d i. Draw is lock diagram ii. Drmin h valu of for criical damping iii. Drmin h sady sa rror ss whn h inpu is a consan vlociy of 0rpm. PART-B (Tim Domain Analysis: Sady sa Analysis). Drmin h sp, ramp and paraolic rror consans of h following uniy fdack conrol sysms. Th opn loop ransfr funcions ar givn 00 ( s) ( 0.s)( 0s) s(s (s) s (s 00 00, 0s 00) s( 0.s)( 0.5s) 00 000 ( s)( 4s) 0s 00) 0)(s 00) s (s s ). Calcula saic rror cofficin for a uniy fdack sysm wih 6 (s).if inpu givn is ) r () 4 hn drmin sady sa rror. For h aov sysm of ss o rducd o 0% of xising valu, wha would h prcnag chang in gain?. Find rror cofficins for h givn uniy fdack sysm having 4. A uniy fdack conrol sysm has 4(s 0s 00) (s). )(s s 0) 0(s 4) (s), if inpu )(s s ) h sysm hn drmin h sady sa rror of h sysm. 5. A uniy fdack conrol sysm has (s) )(s s 5) i. For a uni ramp inpu i is dsird ha ss 0.. Drmin minimum valu of. ii. Drmin ss if inpu r() 4. Assum 0. r() 6 is givn o Prpard y: Mr. Saish Choudhury (Ass. Profssor, Dp. of. EICE Pag of 5 W: www.schoudhury.n Email: saish@schoudhury.n, saishchoudhury@soaunivrsiy.ac.in
Conrol Sysm Enginring (EE0T) Assignmn: 6. Using gnralizd rror sris calcula h sady-sa rror of uniy fdack sysm has 0 (s) for h following xciaion: s i. r () ii. r () iii. r() & iv. r() 7. Using gnralizd rror sris drmin h sady-sa rror of h sysm for h inpu r() 5. s s 5 00 0.5 s s C(s) 5(s ) 8. An opn loop ransfr funcion of a uniy fdack conrol sysm is (s). Using h (s )(s ) gnralizd rror sris, drmin h rror signal and sady sa rror of h sysm whn i is xcid y i. r () ii. r () iii. r() & iv. r() 9. Considr a uniy fdack conrol sysm wih h closd loop ransfr funcion C(s) R(s) s. s as Drmin h opn loop ransfr funcion (s). Show ha h sady sa rror in h uni-ramp a rspons is givn y. 0. Th figur low shows a closd loop conrol sysm which rgulas h gnraor rminal volag E 0. Th valus of and H ar 0 and 0.. Drmin h following i. Th valu of E r o kp E 0 60V. ii. Th prcnag chang in h gnraor rminal volag if h forward pah gain rducs y %. Find h rsuls (i) and (ii) whn h sysm is opn loop and closd loop. ****ALL THE BEST**** Prpard y: Mr. Saish Choudhury (Ass. Profssor, Dp. of. EICE Pag 4 of 5 W: www.schoudhury.n Email: saish@schoudhury.n, saishchoudhury@soaunivrsiy.ac.in
Conrol Sysm Enginring (EE0T) Assignmn:. C().5 0.5 Answrs (Par-A). 9.6., 4 6 4. 5rad/sc, 0.6, 4rad/sc, 9.5%, 0.94%, 0.785sc,.57sc,.sc, 0.85scs. 5..8gm, 6.4Nm/rad/sc 6. 0.5409, 0.96 7. 6.9, 0.54, 0.597, 0.958 8., 9 9 9. 0.495, 0.rad/sc, 4.98) 0., a. 00, 0.8, 6.%, 0.6. sc, 0.07, 0., 5.66%..9,.8,.445, 6.%, 4sc (±%), sc (±5%) 4. 5.54, T0.88 5. Answr no givn 6..4 0 sc, ο Answrs (Par-B). ( 000,0,0),(,,0),(,0),( ),( 0),( )., ss.5 p v 40.,0 4. 5. 50, 4 0 6. () 0. 5 () () 7 7. () 0.04 0.66 0.05 8. Answr no givn 9. Answr no givn 0..8V,.8V, %, 0.495% 0 44 78 () 0.98 0.40 0.08 Prpard y: Mr. Saish Choudhury (Ass. Profssor, Dp. of. EICE Pag 5 of 5 W: www.schoudhury.n Email: saish@schoudhury.n, saishchoudhury@soaunivrsiy.ac.in