ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 2010/2011 CONTROL ENGINEERING. SHEET 2 Bode Plot
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1 CAIRO UNIVERITY FACULTY OF ENGINEERING ELECTRONIC & COMMUNICATION DEP. 3rd YEAR, 00/0 CONTROL ENGINEERING HEET Bode Plot [] Drw the symptotic Bode plots for ech of the followig trsfer fuctios: ) ( 0.5 s) ( 0.4s) Gs () b) G( s) ( 0. s)( 0.4 s) s ( 0.s)( 0.05s) [] A servomotor with field cotrol hs mechicl time costt of 0. sec., field electricl time costt of sec., d velocity gi costt of 00 rpm/v. ( s) ketch the Bode plots for the velocity trsfer fuctio of the motor. v f ( s) [3] A uity feedbck system hs G ( s) : s( s )( s 0.) ) Drw the symptotic Bode plots for the bove system. b) Determie the gi crossover d the phse crossover frequecies. c) Determie the gi d phse mrgis d) Is the closed loop system stble? Check usig Routh method. ( ) [4] (Midterm 003) uity feedbck cotrol system hs Gs () ) Costruct the symptotic Bode plots. b) From the plots, determie the gi K required to hve criticlly stble system. c) From the plots, fid K for GM = 0 db, the get PM ew. d) Fid the pure dely required to hve PM=0 o. :
2 9 ( 0.5)( 3 9) [5](Midterm 004)A uity feedbck cotrol system hs Gs () () Drw the symptotic bode plots for the bove system. (b) uppose tht gi K is cscded with G().Fid the vlue of K to hve GM of 0 db, the get the ew PM, d. gc s (c) uppose tht K e is cscded with G() (isted of K ).Determie the vlue of K d to mke the system criticlly stble with gc rd/sec. [6](Fil 99) ) Determie the trsfer fuctio correspodig to the Bode plots show below ssumig tht they re miimum phse. b) Discuss the stbility of ech system. c) If the system i fig (b) is used i closed uity feedbck loop system d the cotroller is pure time dely s e pc, clculte the dely time for PM=30 o. : 50 [7] Cosider the circuit show: C R R _ V o V s + ) Alyze the circuit to get the trsfer fuctio Vo ( ) H ( ). V ( ) b) If the time costt of the system equls 0. msec d the DC gi equls -0, drw the Bode plot of the system. c) Form the plots, wht is the fuctio of this circuit? s
3 [8] The imge below shows severl trsfer fuctios. For ech trsfer fuctio, there is lso sigle mtchig Pole-Zero digrms, Bode Plot, d tep Respose. Your job is to mtch them up by fillig out the tble (e.g., which step respose goes with Trsfer fuctio A?).
4 ummry of Bode Plot: ) Poles or zeros t origi of order : G( ) ( j) G( ) 0 log, G( ) *90 The slope of the mg. Lie = These lies pss through w= ) imple Pole or Zero of order : G( ) ( ) ( j ) G( ) (, G( ) ( ) t G( ) ( j ) 0 db / decde G( j) G( j) G ( ) ( j ) G( j) lope=+0 db/decde G( j) lope=-0 db/decde G( j) 0 0. lope=+45 deg/dec -90 G( ) ( j ) 0 G( j) lope=+45 deg/dec G ( ) ( j ) lope=-45 deg/dec lope=-45 deg/dec G( ) ( j ) G ( ) ( j )
5 3) Qudrtic poles d zeros: G ( ) For mgitude: ) Determie the turl frequecy from G(s). ) Before o chge i the mgitude, After For phse: ) G Clculte the phse t 0.,, d 0. ( ) t there is chge equls -40 db/decde. ) The phse t =0 equls zero, t = equls -90, t = equls ) Pure time Dely: j T e d No effect o mgitude 80 Its phse = T d *,which mes tht y pure dely i the system will shift dow the 80 phse plot of the origil system by T d *. 5) Reltio betwee system type d bode plot: For type 0 system: We begi the mg. Plot with horizotl lie t 0 log K p. For type system: We begi the mg. Plot with lie of slope -0db/dec, d this lie itersects with the 0 db lie t K v. For type system: We begi the mg. Plot with lie of slope -40db/dec, d this lie itersects with the 0 db lie t K. 6) Defiitios: gi crossover frequecy : gc, G(j gc ) G(j gc ) 0log G(j gc ) 0 (from grph) phse crossover frequecy : pc, G(j pc) 80 (from grph) Gi mrgi: GM G ( j ) (from grph) Phse mrgi: PM 80 G ( j gc ) (from grph) pc db The system is stble iff: (GM d PM re both +ve) ( ) db gc pc
6 7) Plottig Rules: ) For Mgitude: Determie the corer frequecies o the plot. G( j) Drw the mgitude usig the followig rule: slope log fil strt strt fil b) For Phse: G( j) Determie the poits lies before d fter decde for Ech corer frequecy. Drw the phse usig the followig rule: slope log fil strt strt fil
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