06/0/07 UW Britol Indutrial ontrol UFMF6W-0- ontrol Sytem ngineering UFMUY-0- Lecture 5: Block Diagram and Steady State rror Today Lecture Block diagram to repreent control ytem Block diagram manipulation Steady State rror Block Diagram Block Diagram: Block Diagram provide a pictorial repreentation of a ytem Unidirectional operational block repreenting individual tranfer function Three baic element: ectangle - operator Line - ignal ircle - additional or ubtraction y x e r - c x r e c y Block Diagram: y x-bz loed Loop Sytem Simple loed Loop ontrol Sytem x B y z Input rror Feedback Proce Senor Output () () G() () B() H() 07 Univerity of the Wet of ngland, Britol.
06/0/07 loed Loop Sytem Simple loed Loop ontrol Sytem () () G() () B() H() Tranfer function from () to () B H G - B G ü ï ý ï G ï þ - H loed Loop Sytem Simple loed Loop ontrol Sytem () () G() () B() H() Tranfer function from () to () æ ö - H ç H G è G ø G \ G H loed Loop Sytem Simple loed Loop ontrol Sytem () () G() () B() H() Tranfer function from () to () G G H () G G H () loed Loop Sytem Simple loed Loop ontrol Sytem () () G() () B() With unity feedback, H() H G G G G Open Loop Tranfer Function emove the feedback link from umming junction () () G() () Diagram can be manipulated uing the following tranformation ombining Block in Serie: B() H() B Open Loop Tranfer Function given by: G H 07 Univerity of the Wet of ngland, Britol.
06/0/07 Moving a umming junction Moving a pickoff point ahead of a block 4 Moving a pickoff point behind a block Moving a umming point ahead of a block 5 6 liminating a feedback loop B J D G G G H H H onider ubgroup containing G and H : 7 G J G H G 4 07 Univerity of the Wet of ngland, Britol.
06/0/07 B J G G G 4 B J G G G 4 H H onider ubgroup containing G and H : J G G H G 4 onider ubgroup containing G and G 4 : B G G 4 G5 B G G 5 B G G 5 H H onider ubgroup containing G and G 4 : B G G 4 G5 onider ubgroup containing G 5 and H : G5 G H 5 G 6 G G 6 G G 6 onider ubgroup containing G 5 and H : Final loed Loop Tranfer Function G5 G H 5 G 6 GG 6 GG G G G G G 6 ( H GH ) GG 07 Univerity of the Wet of ngland, Britol. 4
06/0/07 Steady State rror No SS rror Feedback control ued to reduce teady-tate error Steady-tate error i error after the tranient repone ha decayed If error i unacceptable, the control ytem will need modification rror are evaluated uing tandardied input Step input amp input Sinuoidal input epone Tranient t Steady State Time No SS rror aue of Steady State rror epone Tranient rror Steady State t Time rror can be caued by factor including. Intrumentation of meaurement error. Sytem non-linearitie deadband, hyterei, aturation etc.. Form of input ignal 4. Form of ytem tranfer function 5. xternal diturbance acting on the ytem, for example: force or torque rror Function () () G() B() H() - B H H G -G H [ G H ] B G H () alculating Value Ue the final value theorem: lim ( t) lim Input can be Step amp G H t G 0 Sytem dependent H Input dependent i tep amplitude i tep velocity 07 Univerity of the Wet of ngland, Britol. 5
06/0/07 Sytem and Feedback Tranfer function: G and H ( rror G H ( ( ( Step input ( ( Steady State rror: ( lim 0 ( ( ( 0( 0t ) 0( 0 ) t 0 a 0 and H(), teady tate output will be ame a input h amp input ( ( Steady State rror: ( lim ( ( ( ( 0t ) ( 0 ) 0 0 t in thi cae i not zero and during application of ramp input will lag by epone Sytem and Feedback Tranfer function: rror t and H( ) G t G H t t Time - 07 Univerity of the Wet of ngland, Britol. 6
06/0/07 Step input t t Steady State rror: t t ( 0t ) t lim 0 t 0t in thi cae, error i not zero and the output will not be equal to the input teady tate output can alo be found uing the Final Value Theorem a follow : - H - H æ t ö æ ö lim ( ) lim ç- ç - 0 0 è t ø è ø æ t ö ç- è t ø reulting repone for : (b) ramp input: æ lim ( ) ( ö ( t 0) 0 lim ç 0 è ( ø ( t 0) 0 error continue to increae which i not acceptable epone Time - Today lecture Block Diagram pictorial repreentation of control ytem ectangle repreent operation Line are ignal Summing junction enable addition/ubtraction Manipulation Technique to reduce block diagram to tranfer function Steady State rror help to determine what happen to ignal in teady tate Block Diagram n electrical motor i ued in a cloed loop ytem to control the angular poition of an inertial load. The poition of the load, which i directly connected to the motor, i meaured by a imple rotary potentiometer. The output ignal from the tranducer i compared with the input demand and the reulting error ignal i paed to a voltage/current amplifier. The input demand i converted from angular diplacement to voltage before being connected to the umming junction. 07 Univerity of the Wet of ngland, Britol. 7
06/0/07 loed Loop Battery ngle ytem block diagram: ngle etting Deired angle (voltage) Gain Gain Turntable D mplifier D motor Tachometer ontrol Device ctuator Proce rror ctual angle mplifier D motor Turntable n electrical motor i ued in a cloed loop ytem to control the angular poition of an inertial load. Meaured angle (voltage) Senor Potentiometer ytem block diagram: ytem block diagram: The poition of the load, which i directly connected to the motor, i meaured by a imple rotary potentiometer. The output ignal from the tranducer i compared with the input demand and the reulting error ignal i paed to a voltage/current amplifier. ytem block diagram: ytem equation: (a) Motor torque - T m k I m (b) mplifier - I V e (c) Load - T J q cq L o o The input demand i converted from angular diplacement to voltage before being connected to the umming junction. (d) Input (e) Feedback - (f) rror - demand - V e V q i k p i q o k T o V V -V i o 07 Univerity of the Wet of ngland, Britol. 8
06/0/07 ytem block diagram q V i i V e k P - V o I k m k T T m J c q o loed Loop Tranfer function for ytem: qo q i J kmkp c k m k T reduced block diagram G() - H() G( ) kmkp J c k H k T P 07 Univerity of the Wet of ngland, Britol. 9