HANDOUT E.19 - EXAMPLES ON FEEDBACK CONTROL SYSTEMS

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1 MEEN 64 Parauram Lctur 9, Augut 5, HANDOUT E9 - EXAMPLES ON FEEDBAC CONTOL SSTEMS Exampl Conidr th ytm hown blow Th opn loop tranfr function i givn by Th clod loop tranfr function i Exampl Conidr th ytm hown a Dtrmin th tranfr function from r to y b Dtrmin th tranfr function from w to y To obtain th tranfr function btwn r to y, aum w to b qual to zro Thrfor th block diagram rduc to,

2 MEEN 64 Parauram Lctur 9, Augut 5, Hnc th opn loop tranfr function i Th clod loop tranfr function i givn by To obtain th tranfr function btwn w and y, aum r to b qual to zro Hnc th block diagram rduc to, For th abov block diagram th opn loop tranfr function i and th fdback tranfr function i givn by H Thrfor th tranfr function from w to y i givn by

3 MEEN 64 Parauram Lctur 9, Augut 5, H W Exampl A unity fdback ytm ha th opn loop tranfr function Find th rror contant p, v and a for th ytm Th clod loop tranfr function i givn a Th tranfr function for th rror ignal i givn by E Thrfor th tady tat rror for th ytm can b obtaind by applying th final valu thorm a lim E Thrfor, lim For a unit tp input, w hav, thrfor th tady tat rror i lim lim p Thrfor th valu of p i givn a

4 MEEN 64 Parauram Lctur 9, Augut 5, p For a ramp input, w hav, thrfor th tady tat rror i lim lim v Hnc th valu of v i givn a v For a parabolic input, w hav, thrfor th tady tat rror i lim lim a Thrfor, a Exampl 4 Th block diagram hown blow how a control ytm in which th output mmbr of th ytm i ubjct to a diturbanc In th abnc of a diturbanc, th output i qual to th rfrnc Invtigat th rpon of thi ytm to a unit tp diturbanc Sinc w ar intrtd in th rpon of th ytm to a unit tp diturbanc, aum th rfrnc input to b qual to zro Thrfor th block diagram rduc to 4

5 MEEN 64 Parauram Lctur 9, Augut 5, Th opn loop tranfr function i givn by, and th fdback tranfr function i givn a J H Thrfor th tranfr function btwn th diturbanc and th output i givn a J W H J J For a unit tp diturbanc, th output rduc to J J Th tady tat valu of th output can b obtaind by applying th final valu thorm a y lim lim lim J J Thrfor th ytm i incapabl of rjcting th diturbanc compltly a thr i a tady tat offt Exampl 5 Conidr a nonunity fdback ytm, who opn loop tranfr function i givn by, T whr in th fdback loop tranfr function i givn a 5

6 MEEN 64 Parauram Lctur 9, Augut 5, H h, with h > Dtrmin th ytm typ with rpct to th rfrnc input Th clod loop tranfr function i givn a H T h T T h Th tranfr function for th rror ignal i givn by T h E T h T h Th tady tat rror i obtaind a T h lim E lim T h For a tp rfrnc input, th rror i T h T h h lim lim T h T h h If th ytm i not unity fdback thn, h, thrfor th ytm i of Typ If th ytm i unity fdback, i, h, thn th ytm i of Typ a th tady tat rror for th tp rfrnc input i zro 6

7 MEEN 64 Parauram Lctur 9, Augut 5, Aignmnt Conidr a unity fdback ytm who opn loop tranfr function i givn by 5 Dtrmin th clod loop tranfr function of th ytm Problm 4a from th txtbook Fdback control of dynamic ytm, by Franklin tal commndd ading Fdback Control of Dynamic Sytm 4 th Edition, by n F Franklin tal pp 5, 4 commndd Aignmnt Fdback Control of Dynamic Sytm 4 th Edition, by n F Franklin tal problm 4, 48, 4, 45, 47 7

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