ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 2010/2011 CONTROL ENGINEERING SHEET 4 PID Controller

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1 CAIRO UNIVERSITY FACULTY OF ENGINEERING ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 00/0 CONTROL ENGINEERING SHEET 4 PID Controller [] The block dagram of a tye ytem wth a cacade controller G c () hown n fgure. The objectve to degn a controller G c () o that: Maxmum overhoot < 0% Settlng tme < Degn the controller that atfe the erformance ecfcaton gven above. R() 0000 c() G c () ( 50) [] The block dagram of a guded mle atttude control ytem hown n fgure r(t) the reference nut and d(t) rereent the dturbance. The objectve of th roblem to tudy the effect of the controller G c (). a. Let G c ()=. Fnd the teady tate error when r(t) a unt te functon. b. Let G c ()= (5)/. fnd the teady tate error when r(t) a unt te. c. Set r(t)=0, G c ()= (5)/. Fnd the teady tate error when d(t) a unt te. What the effect of the roortonal controller n art a and roortonal lu ntegral controller n art b on the teady tate reone of the ytem? D() R() 00( ) c() G c () ( )

2 [3] (Fnal 000) Conder a unty feedback controller ytem whoe feedforward tranfer functon : G ( ) ( )( 8) a. Fnd the tatc error coeffcent and the error ere for unt ram nut. b. Degn a comenator o that the cloed loo domnant ole are located at j 3 [4](Fnal 98) A control ytem wth a tye 0 roce and PID controller hown n fgure. Degn the arameter of the PID controller o that the followng ecfcaton are atfed: a. Settlng tme 0. b. Max. Overhoot 5 ercent. c. Steady tate error due to unt te dturbance =zero. D() R() k Td c() T I [5] The ytem hown n fgure a PID control of a econd order lant G(). It aumed that the reference nut r(t) normally held contant and the reone charactertc to dturbance are of a very mortant conderaton n th ytem. The ecfcaton requre that the reone to the unt te dturbance uch that the ettng tme ec. and the ytem ha a reaonable damng. Degn PID controller that acheve the above ecfcaton. Then obtan the mrovement n the teady tate error to the unt te dturbance nut. D() R() c() k Td T I 3.6 9

3 [6](Fnal00)Fgure () how the block dagram of the lqud level control ytem. The lqud level rereented by c(t), and N denote the number of nlet. It dered that N=0. Degn a controller G c (S) uch that: The overhoot zero. The tank flled to the reference level wthn.5 ec. What the effect of the controller on the teady tate reone? And why? R(S). Σ G c (S) 0N S( S )( S 0) C(S) [7](Fnal 003)A large antenna ued to receve atellte gnal and mut accurately track the atellte a t move acro the ky. The control ytem ue an armature controlled motor and a controller to be elected a hown n Fgure. The ytem ecfcaton requre an overhoot to a te nut le than or equal 0% wth a ettlng tme le than or equal econd. Degn a controller G c (S) to acheve the requred ecfcaton and lot the reultng reone. Determne the effect of the dturbance [D(S)=Q/S] on the teady tate outut. D(S) Motor and antenna R(S) Controller Y(S) 0 G c (S) S( S 5)( S 0) _

4 [8](Fnal 004)Conder the control ytem hown n the ffure.degn a comanator uch that the followng ecfcaton are atfed: The teady tate error to unt ram nut elmnated. One of the domnant cloed loo ole located at : j 6 R(S) Σ G c (S) 0 S( S ) C(S) [9](Fnal 003) Conder a unty feedback control ytem wth the forward tranfer functon: PID controller of the form: G ( S) ( S )( S S 3) Gc ( S ) ( TdS ) TS ued to acheve a reaonable tranent reone. Aly the econd method of ZeglerNchol tunng rule t determne the value of the arameter, T d and T I. I [0](Fnal 004) Conder a unty feedback control ytem wth the forward tranfer functon: GS ( ) S ( S )( S 3) Gc S ds S PID controller of the form: ( ) ued to acheve a reaonable tranent reone. Aly the econd method of ZeglerNchol tunng rule t determne the value of the arameter of the controller.

5 Summary:. P controller: G c ( S ) = Secfcaton: Imrove e. to a certan value. Decreae the damng n the ytem(the ytem more ocllatory) A, e,.. PI controller: G c ( S ) = ( ) or ( ) T S S Secfcaton: Ued to acheve teady tate ecfcaton. Elmnate the teady tate error. Increae the ettlng tme of the ytem. 3. PD controller: G c ( S ) = ( T S ) or ( S ) d d Secfcaton: Ued to acheve tranent reone ecfcaton or a dered locaton of the domnant ole. Imrove the tranent reone ( M, t ). Add damng to the ytem ( ) and thu ermt the ue of larger value of the gan, whch wll decreae e. 4. PID controller: G c ( S ) = ( Td S ) or ( ds ) T S S Secfcaton: Ued to acheve tranent reone ecfcaton and teady tate ecfcaton Imrove the tranent reone ( M, t ) and elmnate the teady tate error.

6 5. Tunng Rule For PID Controller: Zegler Nchol Rule: a) Method : ) Obtan exermentally the reone of the lant to a unt te nut. ) Such a unt reone curve may look lke an Shaed curve a hown n the fgure, f not, th method doe not aly. 3) Determne the value of both, T and L (from grah). 4) The equaton of the PID : T Gc ( S ). ( 0.5 LS ) L LS. LS C ( S ) e R ( S ) TS b) Method : ) Set T, Td 0.(ue only the roortonal mode) ) Increae from 0 to cr where the outut exhbt utaned ocllaton (f the outut doe not ocllate for whatever value, then th method doe not aly). 3) Determne both value of cr and P cr where P cr the correondng erod of ocllaton (ee the fgure). NOTE: we ue routh crtera to get both cr and P cr. 4) The equaton of the PID : Gc ( S ) 0.6 cr ( 0.5 Pcr S ). 0.5PS cr