cs [uandistar.org]

2 . t h e c l os e d l o op tr a n s f e r f u n c t i on of t h e o p e n l o o p t r an s f e r f u n c t i o n , Gs= K S ( 1 + S T ) o f a u n i ty f e e d b a ck s y s t e m i s( a) K ( 1 + s T ) S ( b ) K S 2T + s + k ( c ) K s ( T + s T ) ( d ) K / S

3 . T h e s e n s i t i v i ty of a c l o s e d - l o o p s y s t e m to g a i n ch a n ge s a nd l oa d d i s tur b a n c e s d e p e n d s u p o n( a) l o op ga i n ( b ) f o r war d g ai n ( c ) f o r war d g ai n , l o op ga i n a n d f r e q u e n c y( d) f r e q u e n c y

4 . I n th e f o l l ow i n g , p i ck o u t t h e n o n l i n e ar s ys te m s ( i ) d 3 y( t ) /d t 3 + t 3 d 2 y(

t) / d t 2 + t d y ( t )/ d t + y 2 = 2 0 s i n w T ( i i ) d 2 y ( t) / d t 2 + ( 1/ t ) d y /d t + y = 4 ( i i i )d 2 y ( t) / d t 2 ] + d y / d t + y (t ) = 5( a) ( I I ) an d (I I I ) ( b ) ( I ) a n d ( I I ) ( c ) ( I ) a n d ( I I I ) ( d ) I I o n l y

5 . Tra n s f e r f u n c t i on of a s y s t e m i s u s e d t o c al c u l at e( a) t h e o r d e r o f t h e s y s t e m ( b ) t h e o u t p u t f o r any g i ve n i n p u t ( c ) t h e m ai n c o n s t a nt ( d ) t h e s te ad y s ta t e g ai n .

6 . O n e o f t h e d i s ad vant a ge s o f a s e rvo m ot o r i s th a t( a) i t c a n h a n d l e o n l y l i g ht l oa d s ( b ) i t h a s l ow s ta r ti n g t o r qu e ( c ) i t ha s l ow r e l i a b i l i ty ( d ) i t d e ve l o p s c o m mu n i c a ti o n p r o b l e m7 . A n e two r k h as a p o l e a t s = - 1 a n d a z e r o a t s = - 2. i f t h i s n e two r k i s e xc it ed by s i nu s o i d al i n p ut , th e o u tp u t( a) i s i n p h a s e w i th i n p u t ( b ) l a gs t h e i n p u t ( c ) d e c ay s e x p o n e nt i al l y t o

z e ro ( d ) l e a d s t h e i n p u t

8 . T wo b l o ck s h avi n g r e s p e c t i ve f u n c t i o n s a s G 1 ab d G 2 a r e c o n n e c t e d i npa ra l l e l . T h e i r r e s u l t ant w i l l b e ( a) G 1 G 2 ( b ) G 1 o r G 2 w h i ch e ve r i s h i g he r( c ) G 1 o r G 2 w h i ch e ve r i s l owe r ( d ) G 1 +G 2

9 . A f e e d b a ck l o o p c on s i s ti n g o f on l y o n e b r a n ch i s( a) i n p u t l o op ( b ) s e l f l o op ( c ) f o r war d l o o p ( d ) o u tp u t l o o p

1 0. T h e ch ar a c t e r i s t i c e q u a t i on o f th e s e c on d or d e r s ys te m i s g i ve n by s 2 +2c w 0 s +w 0 2 = 0 . I f c =1 , t h e s y s t e m e x h i b i t s( a) n o ove r s h o ot ( b ) l a rg e ove rs h o o t ( c ) s m a l l ove r s h o o t ( d ) l a rg e u n de

rs h o o t

1 1. T h e ch ar a c t e r i s t i c e q u a t i on o f th e s e c on d or d e r s ys te m i s g i ve n by s 2 +2c w 0s + w 0 2 = 0 . I f ? = 0 1 , t h e p o l e s a r e( a) + o r - j c w 0 ( b ) + o r - j w 0 ( c ) + o r - j w 0 2 ( d ) + o r - j c w 0 2

1 2. A s e c o n d o r d e r s y s t e m w i t h n o z e r os h a s i t s p o l e s l o c at e d at - 3+ j 4 a n d-

3- j 4 i n th e s - p l an e t h e un d a m p e d n at u r a l f r e q u e n c y a n d t h e d am p i n g fa c t o r of t h e s ys te m ar e r e s p e c ti ve l y( a) 5 ra d / s e c an d 0 . 6 0 ( b ) 3 ra d / s e c a nd 0. 6 0 ( c ) 4 ra d / s e c a nd 0. 7 5 ( d ) 5 ra

d /s e c an d 0 . 8 0

1 3. Ve l os i ty e r r o r c o ns t ant o f a s y s t e m i s m e as u r e d w h e n t h e i n p u t t o th e sy s t e m i s u n i f u n c t i o n( a) I m p u l s e ( b ) S t e p ( c ) p a ra b o l i c ( d ) R am p

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1 4. I n a c ont r ol s y s t e m i nt e g ra l e rr o r c o m p e n s a t i on s t e a d y s t a te e r r or( a) d e c r e a s e s( b ) n o th i n g c a n t e l l ( c ) i n c r e a s e s ( d ) d o e s n ot h ave any e ff e c t o n



1 5. T h e e rr o r s i gn a l p r o d u c e d i n a c ont r ol s y s t e m i s Q r= a +b t . i f o n l y p ro p ort i o n al a c t i o n i s u s e d , t h e i n p u t i s gi ve n t o t h e fi n a l c o nt ro l e l e m e nt w h e n PI D a c t i on i s u s e d , w i l l b e( a) - ( K a + K 1b t + K 2 a+ K 2 b t) ( b ) ( ( K a+ K 1 ( a+ b t )+ K 2 (a t +b t 2 ) ) ( c ) - K (a + btK 1( a t+ b t 2K 2 b ) ) ) ( d ) ( ( K a+ K 1 ( a+ b t )+ K 2 (a t +b t 2 ) )

1 6. i n R - H c r i t e r i on , i f t h e r e a r e ch a n ge s o f s i n gs i n t h e E l e m e nt s of t h e fi r st c ol u m n , th e n t h e nu mb e r of s i g n ch a n ge s i n d i c a t e( a) T h e nu mb e r of r o ot s w i t h p o s i t i ve r e al p ar t ( b ) T h e nu mb e r of p a i r of r o o

t s o f p os i ti ve s i gn ( c ) t h e nu mb e r o f ro o t s w i t h ne ga t i ve r e al p ar t ( d ) T h e numb e r of p a i r of r o o t s o f s am e s i g n

1 7. A s te p f u n c t i o n i s ap p l i e d t o th e i n p u t o f s y s t e m an d ou t p u t i s of t h e f or my = t, t h e s y s t e m i s( a) u n s t a b l e ( b ) n o t n e c e s s ar i l y s ta b l e ( c ) c o n d i t i on a l l y s t ab l e ( d ) s t ab l e

1 8. A s ys te m h a s l o o p g ai n a s G ( s ) H ( s ) = K /s (s +1 ) (s +2 ) (s +3 ) . t h e nu mb e r of p ole s a n d z e ro s re s p e c t i ve l y a re ( a) 4 , 0 ( b ) 2 , 2 ( c ) 1 , 3 ( d ) 1 , 4

1 9. I n ro o t l o c u s p l o t d i ff e r e nt r o ot s h ave t h e s am e( a) g ai n m ar gi n an d p h as e m a rg i n ( b ) p h a s e ( c ) g ai n ( d ) p h a s e a n g l e

2 0. A d d i n g i n t h e z e r os i n t h e t ra n s f e r f u n c t i on c a u s e s( a) n o c o m p e n s a t i on ( b ) l e a d c o m p e n s a t i on ( c ) l a g- c om p e n s at i o n ( d ) l

e a d - l a g c om p e n s a ti o n

1 . T h e op e n l o op c o nt r o l s y s t e m i s o n e i n w h i ch( a) o u tp u t i s d e p e n d ant o n c o ntr o l i n p u t ( b ) o u tp u t i s i n d e p e n d ant o n c o ntr o l i n p u t ( c )

i n p u t i s i n d e p e n d a nt on c ont r ol l e r ( d ) o n l y s y s t e m p a r am e t e r s h ave e ff e c t o n t h e c ont rol ou t p u t

2 . T h e c l o s e d l o o p tr a n s f e r f u n c t i on o f t h e o p e n l o o p t r a n s f e r f u n c t i on , G ( s ) = K / [ s (1+ s T ) ] o f a u n i ty f e e db a ck s ys te m i s( a) K ( 1 + S T ) S 2 ( b ) k /s (T +s T ) ( c ) k ( 1+ s T ) / s ( d ) k /( s T +s + k )

3 . I n c l os e d l o op c ont r ol s y s t e m w i t h p os i ti ve val u e o f f e e d b ack g a i n t h e ove r a l l g ai n of t h es y s te m( a) b e u n e ff e c t e d ( b ) i n c r e a s e ( c ) N o th i n g c an t e l l ( d ) d e c r e a s e

4 . T h e p o s i t i on y of a m ov i n g o b j e c t o f c o n s t a nt ma s s M i s r e l a t e d t o t h e t o t al f or c e f a pp l ie d t o t h e o b j e c t by d i ff e r e nt i al e q u at i o n M d 2 y /d t 2 = f i ts t ra n s f e r f u n c t i o n w i l l b e( a) F ( s ) = M s ( b ) F ( s ) = 1 /M s 2 ( c ) F ( s ) = 1 /M s 3 ( d ) F ( s ) = 1 /M s

5 . T h e t r an s f e r f u n c t i o n o f t h e s ys te m w h o s e i n p u t a n d ou t p u t a r e r e l a t e d by t h e f ol l owi n g d i ff e r e nt i al e q u at i o n i s g i ve n by d 2 y /d t 2 + 3 d y /d t + 2 y = x + d x /d t( a) ( s + 2) / (s 2 + 3s + 2 ) ( b ) s / ( s 2 + 3s + 2 ) ( c ) ( s + 1) / (s 2 + 3s + 2 ) ( d ) 1 /( s 2 + 3s + 2 )

6 . W h i ch o f th e f o l l ow i n g s t a t e m e nts i s n ot c or r e c t f or s e r vo m e ch a n i s m s ?( a) A s e r vo w i t h b e t te r f r e q u e n c y r e s p on s e n e e d n ot b e s ta b l e ( b ) s t e a d y s t a te a c c u r acy of a s e r vo is b e t t e r t h a n t h a t of a r e gu l a t or ( c ) A m o t or m ay b e ad d e d t o c onve r t a r e g u l ator i nt o a s e rvo ( d ) S o m e s e rvo s d o n o t n e e d to b e s t a b l e , s i n c e t h e y a r e i nt e n d e d f or u s e w it h s t e ad y s i gn a l s

7 . T h e t ra n s f e r f u n c t i on i s ( 1 +0 . 5 s ) /( 1+ s ) . I t re p re s e nt s a



( a) l e a d n e twor k ( b ) l a g- l e ad n e two r k ( c ) l a g n e two r k ( d ) p r op or t i on a l c o nt ro l l e r

8 . T wo b l o ck s h avi n g r e s p e c t i ve f u n c t i o n s a s G 1 an d G 2 a re c o n n e c t e d i n s e r i e s c a s c a de . T h e i r re s u l ta nt w i l l b e( a) G 1 G 2 ( b ) G 2 /G 1 ( c ) G 1 + G 2 ( d ) G 1 /G 2

9 . A f e e d b a ck l o op c on s i s ti n g o f on l y o n e b r a n ch i s( a) s e l f l o op ( b ) o u tp u t l o o p ( c ) i n p u t l o op ( d ) f o r war d l o o p

1 0. N a tu r a l f r e q u e n c y of a u n i ty f e e d b a ck c o nt r ol s y s t e m o f tr a n s f e r f u n c t i on G ( s ) = 10 /s ( s + 1 ) i s( a) 4 . 6 ra d / s e c ( b ) 0 . 5 ra d / s e c ( c ) 3 . 16 r a d /s e c ( d ) 4 . 16 r a d /s e c

1 1. T h e ty p e - 2 s y s t e m h a s( a) n o n e t p o l e at t h e or i g i n ( b ) s i m p l e p o l e a t t h e o r i gi n ( c ) two p ol e s a t t h e o r i gi n ( d ) ne t p ol e at t h e or i g i n

1 2. I n c ont r ol s y s t e m e xc e s s i ve b a n d w i d t h s h o u l d b e avo i d e d b a c au s e( a) n o i s e i s p r op or t i on a l t o b a n d w i d t h ( b ) i t l e a d s to h i g h s p e e d o f re s p o n s e ( c ) i t l e a ds to s l ow s p e e d of r e s p o n s e ( d ) i t l e a d s to l ow r e l a t i ve s t ab i l i ty

1 3. Ve l os i ty e r r o r c o ns t ant o f a s y s t e m i s m e as u r e d w h e n t h e i n p u t t o th e s y s t e m i s u n i f un c t i o n( a) I m p u l s e ( b ) R am p ( c ) p a ra b o l i c ( d ) S t e p

1 4. T h e p o s i t i on e rr o r c o e ffi e c i e nt f or a u n i ty f e e d b ack s y s t e m i s d e fi n e d a s( a) L i m S 2 G ( s ) s ? 0 ( b ) L i m S * G ( s ) s ? 0 ( c ) L i m G ( s )/ s s ? 0 ( d ) L i m G ( s ) s ? 0

1 5. T h e e rr o r s i gn a l p r o d u c e d i n a c ont r ol s y s t e m i s Q r= a +b t . i f o n l y p ro p o rt i o n al a c t i on i s u s e d , t h e i n p u t i s gi ve n t o t h e fi n a l c o nt ro l e l e m e nt w h e n P I D a c t i on i s u s e d , w i l l b e( a) - K (a + b tK 1( a t+ b t 2K 2 b ) ) ) ( b ) ( ( K a+ K 1 ( a+ b t )+ K 2 (a t +b t 2 ) ) ( c ) - ( K a + K 1b t + K 2 a+K 2 b t) ( d ) ( ( K a+ K 1 ( a+ b t )+ K 2 (a t +b t 2 ) )

1 6. t h e t r a n s f e r f u n c ti o n o f a u ni ty f e e d b ack s y s t e m i s G ( s ) = K / s ( s + s ) ( s +5 ) . th e r an g e ofK f or s ta b l e o p e r a t i on i s( a) K = 0 ( b ) 0 < K < 3 0 ( c ) K = 10 ( d ) K > 4 0

1 7. G i ve n , G ( s ) = ( 1- s ) /( s ( s + 2) ) . T h e s y s t e m w i t h t h e t r a n s f e r f u n c ti o n i s op e ra t e d i n aC l o s e d - l o op w i th u n i ty f e e d b ack . T h e c l os e d - l o op s y s t e m i s( a) u n s t a b l e ( b ) c o n d i t i on a l l y s t ab l e ( c ) m a rg i n a ll y s t ab l e ( d ) s t a b l e

1 8. T h e r o o t l o c u s p l ot i s s y m m e t r i c a l ab ou t t h e r e al ax i s b e c a u s e( a) a l l r o ot s o c c u r i n p a i r s ( b ) c o m p l e x r o ot s o c c u r i s c on j u ga te p a i rs ( c ) r o ot s o c c u r s

i mu l t an e o u s l y i n l e f t h a n d a n d r i g ht h a n d p l a n e ( d ) r o ot s ar e re a l

1 9. G ( s ) H ( s ) = K /s (s +1 ) (s +2 ) (s +3 ) t h e r o ot l o c i l y i n g on th e r e al ax i s ar e b e twe e n( a) s = - 1 a n d s = - 2 ; s =- 2 a n d s =- 3 ( b ) s = - 1 an d s = 0; s = - 2 a n d s = - 3 ( c ) s = - 1a n d s = 0 ; s = - 1 an d s =- 2 ( d ) s = - 2 a n d s = - 3; s = - 1 an d s = - 2

2 0. T h e e ff e c t of ad d i n g p ol e s a nd z e r o s c a n b e d e t e r m i n e d qu i ck l y by w h i ch of t h e f o l l owi n g( a) b o d e p l ot ( b ) r o ot l o c u s ( c ) N i ch o l as ch ar t ( d ) ny qu i s t p l ot

1 . W h i ch o f th e f o l l ow i n g s t a t e m e nts i s n ot n e c e s s a r i l y c o r re c t f o r op e n l o o p c o nt r o l s ys t e m ?



( a) l e s s e x p e n s i ve ( b ) G e n e ra l l y f r e e f r om p r ob l e m s o f n o n - l i n e a r i ti e s ( c ) P r e s e n c eo f n o n - l i n e ar i t i e s c au s e s m a l - f u n c ti o n i n g ( d ) I n p u t c om m a n d i s th e s o l e f ac t o r r e s po n s i b l e f or p rovi d i n g t h e c o nt r ol ac ti o n

2 . I nt r o d u c ti o n o f n e ga t i ve f e e d b a ck i n a s ys te m d o e s n o t l e a d t o r e d u c t i o n i n( a) i n s t a b i l i ty ( b ) ove r a l l ga i n ( c ) b a n d w i d th ( d ) d i s t o rt i o n

3 . I n c l os e d l o op c ont r ol s y s t e m w i t h p os i ti ve val u e o f f e e d b ack g a i n t h e ove r a l l g ai n of t h es y s te m( a) N o th i n g c an t e l l ( b ) i n c r e a s e ( c ) d e c r e a s e ( d ) b e u n e ff e c t e d

4 . T h e d e s c r i b i n g e q u a ti o n o f a m a s s d am p e r s p r i n g s y s t e m is g i ve n by 2 d 2 x /d t 2 + d x/d t + 0 . 5 x = f ( t ) W h e r e f ( t ) i s t h e e xt e r n a l f or c e ac ti n g on t h e s ys te m a n d x i s th e d i s p l a c em e nt of m a s s . T h e s te ad y s t at e d i s p l ac e m e nt c o r re s p o n d i ng t o a f o r c e of 2 N e w t on s i s gi ven by( a) 2 m ( b ) 4 m ( c ) 0 . 5m ( d ) 0 . 25 m

5 . T h e p o l e s o f F ( s )( s 2 - 1 6 )/ ( s 5 - 7 s 4 - 3 0 s 3 ) a r e l o c a te d a t( a) s = 0 (t r i p l e p ol e ) , - 3 a n d 10 ( b ) s = 0 (t r i p l e p ol e ) , - 3 a n d 10 ( c ) s = 4, 4 ( d ) s = 0, 4, 16

6 . T h e fi e l d of a d . c s e r vo - m o t or i s s e p ar a t e l y e x c i t e d by a d . c a m p l i fi e r o f ga i n K = 9 0. I ft h e fi e l d h a s a n i n d u c t an c e o f 2 H an d a r e s i s t an c e o f 5 0 oh m s t h e val u e of t h e fi e l d c o n s tant w i l l b e( a) 0 . 04 s e c ( b ) 0 . 01 s e c ( c ) D 0. 5 s e c ( d ) 0 . 02 s e c

7 . T h e tr a n s f e r f u nc ti o n o f a s i m p l e R- C n e twor k f u n c t i o n i n g as a c ont ro l l e r i s G ( s ) = ( s+Z 1) / ( s +P 1) . T h e c on d i t i o n f o r R - C n e two r k t o ac t as a p h as e l e a d c o nt ro l l e r i s( a) P 1 < Z 1 ( b ) P 1 = 0 ( c ) P 1 > Z 1 ( d ) P 1 = Z 1

8 . T wo b l o ck s h avi n g r e s p e c t i ve f u n c t i o n s a s G 1 ab d G 2 a r e c o n n e c t e d i n p a ra l l e l . T h ei r r e s u l t ant w i l l b e( a) G 1 +G 2 ( b ) G 1 o r G 2 w h i ch e ve r i s l owe r ( c ) G 1 o r G 2 w h i ch e ve r i s h i g h e r ( d ) G 1 G 2

9 . A n o d e w i t h o n l y i n c o m i n g b ra n ch e s i s c a l l e d as( a) n o d e ( b ) s i n k n o d e ( c ) i n p u t n o d e ( d ) b r an ch n o d e

1 0. T h e ch ar a c t e r i s t i c e q u a t i on of th e s e c on d or d e r s ys te m i s g i ve n by s 2 + 2c w 0s + w 0 2 =0 . I f c = 1 , t h e p ol e s o f t h e tr a n s f e r f u n c t i on w i l l b e( a) e q u a l t o - 1 ( b ) r e a l a n d e q u al ( c ) i m a gi n a r y an d e q u al ( d ) c o m l e x c o n j u g at e

1 1. T h e ch ar a c t e r i s t i c e q u a t i on of th e s e c on d or d e r s ys te m i s g i ve n by s 2 + 2c w 0 s +w 0 2 =0 . I f c < 1 , t h e p ol e s ar e( a) c o m p l e x c o n j u g at e ( b ) i m a gi n a r y an d e q u al ( c ) r e a l a n d u n e q u al ( d ) r e a l a n d e q ual

1 2. A u n i ty f e e d b ack s ys te m h a s t r an s f e r f u n c t i o n G ( s ) = 9 S ( s + 3 )( a) d a m p i n g r a t i o= 0. 8 ( b ) n a tu r a l f r e q u e n c y = 9 ( c ) n a tu r a l f r e q u e n c y = 3 ( d ) d a m p in g r a t i o= 0 . 6

1 3. T h e ty p e 0 s y s t e m h a s a t t h e o ri g i n( a) two p ol e s ( b ) n e t p ol e ( c ) n o p o l e ( d ) s i m p l e p o l e

1 4. T h e s t e a d y s t at e ac c e l e r at i o n e r r or f or a ty p e 1 s ys te m i s( a) B e twe e n 0 an d 1 ( b ) I n fi n i t e ( c ) 0 ( d ) 1



1 5. i n a f or c e b al a n c e ty p e p n e u m at i c c o nt r ol l e r , t h e nu mb e r of b e l l ow s r e q u i r e d f or P I- a c t i on( a) 3 ( b ) 2 ( c ) 4 ( d ) 1

1 6. t h e ch a r ac t e r i s t i c e q u at i o n o f a u n i ty f e e d b ack s y s t e m i s g i ve n by s 3 + s 2 + 4s + 4 =0( a) t h e s ys te m h a s two p ol e s i n th e R H s - p l an e ( b ) t h e s ys te m i s as y m p t ot i c a l l y s t a b l e ( c )n o t s t ab l e ( d ) t h e s ys te m h a s n o p o l e s i n t h e R H s - p l an e

1 7. G i ve n , t h e ch a r ac t e r i s t i c e q u at i o n a s F ( S ) = 3 (S ) ( S ) +1 0( S ) ( S ) +5 S +5 S +2 = 0, T h e n t he nu mb e r of r o o t s t h a t a re o n t h e R . H . S o f t h e S - P l an e ar e ( a) 1 ( b ) 3 ( c ) 2 ( d ) 4

1 8. w h i ch of t he f o l l ow i n g s ta t e m e nt s i s n ot tr u e f o r r o o t l o c u s te ch n i qu e( a) c a n t t e l l f r o m t h e op t i o ns g i ve n ( b ) i t i s m os t u s e f u l f o r s i n gl e - i n p u t a n d s i n g l e - ou t p u t s y s t e m ( c ) i t i s u s e d to o b t ai n c l os e d - l o o p p o l e c o n fi g u ra t i on f r om op e n - l o op p ole s a n d z e ro s ( d ) i t p r ov i d e s t h e p a t te rn of m ove m e nt o f c l os e d - l o op p ol e s w h e n o p e n - l o op g ai n var i e s

1 9. G ( s ) H ( s ) = K /s (s +1 ) (s +2 ) (s +3 ) T h e n , t h e a n gl e o f a s y m p t ot e s w i t h r e a l a xi s r e s p e c t ive l y a r e( a) 4 5 0 , 1 35 0 , 2 25 0 , 3 1 5 0 ( b ) 4 5 0 , 1 35 0 ( c ) 4 5 0 , 1 35 0 , 2 25 0 ( d ) 3 4 0 , 4 5 0

2 0. A d d i n g a z e r o ve r y c l o s e t o o ri g i n i n t h e T . F h as i m p ac t on( a) i m p u l s e r e s p o n s e ( b ) t r an s i e nt re s p o ns e ( c ) s t e a d y s t a te r e s p o n s e ( d ) n o e ff e c t

on r e s p o n s e

2 . I n a s y s t e m , i f f o rwa r d g ai n i s 7 6 an d on e f o u rt h of th e vol t a ge i s f e e d b ack , th e o u tp u t e rr o r is( a) 5 p e r c e nt o f th e e r r or w i th o u t f e e d b ack ( b ) 1 5 p e r c e nt o f t h e e r ro r w i t h o u t f e e d b a ck ( c

) 1 0 p e r c e nt o f t h e e r ro r w i t h o u t f e e d b a ck ( d ) 2 0 p e r c e nt o f t h e e r ro r w i t h o u t f e e d b a ck

3 . R e ge n e r at i ve f e e d b ack i m p l i e s f e e d b ack w i th( a) p o s i t i ve s i g n ( b ) s t e p i n p u t ( c ) o s c i l l a ti o n s ( d ) n e g at i ve s ig n

4 . T h e d e s c r i b i n g e q u a ti o n o f a m a s s d am p e r s p r i n g s y s t e m is g i ve n by 2 d 2 x /d t 2x /d t + 0 . 5 x = f ( t ) W h e r e f ( t ) i s t h e e xt e r n a l f or c e ac ti n g on t h e s ys te m a n d x i s th e d i s p la c e m e nt of m a s s . T h e s te ad y s t at e d i s p l ac e m e nt c o r re s p o n d i ng t o a f o r c e of 2 N e w ts i s gi ve n by( a) 0 . 25 m ( b ) 4 m ( c ) 0 . 5m ( d ) 2 m

5 . T h e p o l e s o f F ( s )( s 2 - 1 6 )/ ( s 5 - 7 s 4 - 3 0 s 3 ) a r e l o c a te d a t( a) s = 4, 4 ( b ) s = 0, 4, 16 ( c ) s = 0 (t r i p l e p ol e ) , - 3 a n d 10 ( d ) s = 0 (t r i p l e p ol e ) , - 3 a n d 10

6 . W h i ch o f th e f o l l ow i n g d e v i c e c a n b e u s e d to c o nt ro l t h e p o s i t i on o f ve r y s m al l l oa( a) s y n ch r o ( b ) P M M C m ove m e nt ( c ) D C s e r vo m o to r ( d ) AC s e r vo m o t or

7 . T h e t ra n s f e r f u n c t i on i s ( 1 +0 . 5 s ) /( 1+ s ) . I t re p re s e nt s a( a) p r op or t i on a l c o nt ro l l e r ( b ) l a g n e two r k ( c ) l e a d n e twor k ( d ) l a g- l e ad n e two r k

8 . T wo b l o ck s h avi n g r e s p e c t i ve f u n c t i o n s a s G 1 ab d G 2 a r e c o n n e c t e d i n p a ra l l e l . Th e i r r e s u l t ant w i l l b e( a) G 1 G 2 ( b ) G 1 o r G 2 w h i ch e ve r i s l owe r ( c ) G 1 o r G 2 w h i ch e ve r i s h i g h e r ( d ) G 12



9 . A s ys te m va r i ab l e t h at e qu a l s th e s u m of al l th e i n c o m i n g s i gn a l s i s d e fi n e d a s( a) o u tp u t no d e ( b ) i n p u t n o d e ( c ) b r an ch ( d ) n o d e

1 0. T h e ch ar a c t e r i s t i c e q u a t i on o f th e s e c on d or d e r s ys te m i s g i ve n by s 2 + 2 c w 0 s +0 2 = 0 . I f c =1 , t h e s y s t e m i s ( a) a b s ol u t e l y da m p e d ( b ) ove r d a m p e d ( c ) u n d e r d a mp e d ( d ) c r i t i c a l l y d am p e d

1 1. Fo r t h e f ol l ow i n g d i ff e r e nt i al e q u at i o n 2 d 2 y /d t 2 + 4 d y /d t + 8 y = 8 x, th e d a m p i n gra t i o i s ( a) 2 ( b ) 0 . 7 ( c ) 1 ( d ) 0 . 5 D

1 2. I n c ont r ol s y s t e m e xc e s s i ve b a n d w i d t h s h o u l d b e avo i d e d b a c au s e ( a) n o i s e i s pop or t i on a l t o b a n d w i d t h ( b ) i t l e a d s to h i g h s p e e d o f re s p o n s e ( c ) i t l e a d s to s l ow s pe e d of r e s p o n s e ( d ) i t l e a d s to l ow r e l a t i ve s t ab i l i ty A

1 3. T h e ty p e 0 s y s t e m h a s a t t h e o ri g i n ( a) s i m p l e p o l e ( b ) n o p o l e ( c ) two p ol e s ( dn e t p ol e B

1 4. E r r or c on s ta nt of t h e s ys te m a re a m e a s u r e o f ( a) s t e a d y s t a te r e s p o n s e ( b ) r e l a tive s t ab i l i ty ( c ) s t e a d y s t a te a s we l l tr a n s i e nt r e s p on s e ( d ) t r an s i e nt s t at e r e s p on sA

1 5. I nt r o d u c ti o n o f i nt e g r al ac t i o n ch a n ge s a s y s t e m ( a) f r o m typ e - 1 t o ty p e - 0 ( b ) f ro m typ e - 0 t o ty p e - 1 ( c ) f r o m typ e - 1 t o ty p e - 2 ( d ) f r o m typ e - 2 t o ty p e - 1 C

1 6. i n R - H c r i t e r i on , i f t h e r e a r e ch a n ge s o f s i n gs i n t h e E l e m e nt s of t h e fi r s t c ol u m n ,th e n t h e nu mb e r of s i g n ch a n ge s i n d i c a t e ( a) T h e nu mb e r of p a i r of r o o t s o f s am e s i g( b ) T h e nu mb e r of r o ot s w i t h p o s i t i ve r e al p ar t ( c ) t h e nu mb e r o f ro o t s w i t h ne ga t i ve re al p ar t ( d ) T h e nu mb e r of p a i r of r o o t s o f p os i ti ve s i gn B

1 7. G i ve n , t h e ch a r ac t e r i s t i c e q u at i o n a s F ( S ) = 3 (S ) ( S ) +1 0( S ) ( S ) +5 S +5 S +2 = 0, T hn t h e nu mb e r of r o o t s t h a t a re on t h e R . H . S o f t h e S - P l an e ar e ( a) 3 ( b ) 4 ( c ) 1 ( d ) 2D

1 8. w h i ch of th e f o l l ow i n g s ta t e m e nt s i s n ot tr u e f o r ro o t l o c u s te ch n i qu e ( a) i t p r ov ie s t h e p a t te rn of m ove m e nt o f c l os e d- l o op p ol e s w h e n op e n - l o o p g ai n var i e s ( b ) i t i s mos t u s e f u l f or s i n gl e - i n p u t a n d s i n g l e - o u t p u t s y s t e m ( c ) i t i s u s e d to o b t ai n c l os el o o p p o l e c o n fi g u ra t i on f r om op e n - l o op p ol e s a n d z e ro s ( d ) c a n t t e l l f r o m t h e op t i ons g i ve n D

1 9. T h e as ym p t o te s a n d t h e b re ak p o i nt c o i n c i d e at s = - 2 . t r an s f e r f u n c t i o n c a n b e (K / ( s +1 ) ( s +2 ) ( s =3 ) ( b ) K ( s + 2) / ( s +1 ) ( s +3 ) ( c ) K / ( s +1 ) ( s +2 ) ( d ) K / ( s +2 ) 3D

2 0. A d d i n g o f p o l e s i n t h e t r a n s f e r f u n c ti o n c au s e s t o ( a) n o o s c i l l a to r y ( b ) ove r so o t ( c ) d e g r ad e s t h e r e l a t i ve s t ab i l i ty ( d ) i n c r e a s e th e s t ab i l i ty C

1 . w h i ch s t at e m e nt i s n ot c or r e c t f or o p e n l o op c ont r ol s y s t e m ? ( a) S i m p l e c on s t r u c t i oo f m ai nt e n a n c e ( b ) L e s s e x p e n s i ve ( c ) To m ai nt ai n th e r e q u i re d q u al i ty i n th e ou t pti o n i s n o t r e q ui r e d ( d ) D i s t u r b an c e s c a u s e e r ro r s C

2 . I n a s y s t e m , i f f o rwa r d g ai n i s 7 6 an d on e f o u rt h of th e vol t a ge i s f e e d b ack , th e o u tp u t e rp e r c e nt o f th e e r r or w i th o u t f e e d b ack ( b ) 2 0 p e r c e nt o f t h e e r ro r w i t h o u t f e e d b a cknt o f t h e e r ro r w i t h o u t f e e d b a ck ( d ) 1 0 p e r c e nt o f t h e e r ro r w i t h o u t f e e d b a ck A



3 . I n a n e ga t i ve f e e d b ack s y s t e m w i t h l o o p g ai n T , t h e n oi s e ( N ) a s i n p u t t o t h e a m pS =S i g n a l ) ( a) N o e ff e c t o n S /N r at i o ( b ) i n c r e a s e i n S /N r at i o by ( 1- T ) ( c ) d e c r e a s e i n( 1 +T ) ( d ) d e c r e a s e i n S / N r at i o by ( 1 - T ) C

4 . T h e d e s c r i b i n g e q u a ti o n o f a m a s s d am p e r s p r i n g s y s t e m is g i ve n by 2 d 2 x /d t 2f ( t ) W h e r e f ( t ) i s t h e e xt e r n a l f or c e ac ti n g on t h e s ys te m a n d x i s th e d i s p l a c e m e nt of m aad y s t at e d i s p l ac e m e nt c o r re s p o n d i ng t o a f o r c e of 2 N e w t on s i s gi ve n by ( a) 4 m ( b )d ) 0 . 5m A

5 . A r o t at i o n al s y s t e m i s d e s c r i b e d by t h e fi r s t o r d e r d i ff e r e nt i al e q u at i o n 2 d w / d t +th e ri g ht h an d s i d e g i ve s t h e c o n s t ant t or q u e a c t i n g on t h e s ys te m an d w r e p r e s e nt sl o c i ty. T h e s o l u ti o n f o r w i s g i ve n by ( a) 5 e - t/ 2 ( b ) 5 ( 1 - e t /2 ) ( c ) 5 ( 1 + e - t/ 2 ) ( d ) 5

6 . W h i ch o f th e f o l l ow i n g i s d i s a d va nt a ge of a d c s e r vo m o t or ? ( a) I t r e q u i r e s h i gh s( b ) I t r e q u i r e s h i gh s t or i n g f o r qu e , d r aw s l ar g e c u rr e nt s an d i t s s p e e d r e g u l at i o n i s pr aw s l a r ge c u r r e nts ( d ) I t s s p e e d r e gu l a t i on i s p o o r B

7 . T h e t ra n s f e r f u n c t i on i s ( 1 +0 . 5 s ) /( 1+ s ) . I t re p re s e nt s a ( a) l e a d n e twor k ( b ) p r oro l l e r ( c ) l a g- l e ad n e two r k ( d ) l a g n e two r k D

8 . T wo b l o ck s h avi n g r e s p e c t i ve f u n c t i o n s a s G 1 an d G 2 a re c o n n e c t e d i n s e r i e s c a s c as u l ta nt w i l l b e ( a) G 2 /G 1 ( b ) G 1 /G 2 ( c ) G 1 G 2 ( d ) G 1 + G 2 C

9 . T h e p r o d u c t of t h e b r a n ch ga i n s of t h e l o o p i s ( a) f e e d b a ck p at h g a i n ( b ) Fo r warp a th ga i n ( d ) l o op ga i n D

1 0. N a tu r a l f r e q u e n c y of a u n i ty f e e d b a ck c o nt r ol s y s t e m o f tr a n s f e r f u n c t i on G ( s ) =( a) 3 . 16 r a d /s e c ( b ) 4 . 16 r a d /s e c ( c ) 0 . 5 ra d / s e c ( d ) 4 . 6 ra d / s e c A

1 1. T h e ch ar a c t e r i s t i c e q u a t i on o f th e s e c on d or d e r s ys te m i s g i ve n by s 2 + 2c w 0s + w1 , t h e p o l e s a r e ( a) + o r - j w 0 ( b ) + o r - j c w 0 2 ( c ) + o r - j w 0 2 ( d ) + o r - j c w 0

1 2. A u n i ty f e e d b ack s ys te m h a s t r an s f e r f u n c t i o n G ( s ) = 9 S ( s + 3 ) ( a) d a m p i n g r am p i n g r a t i o= 0. 8 ( c ) n a tu r a l f r e q u e n c y = 9 ( d ) n a tu r a l f r e q u e n c y = 3 D

1 3. T h e ty p e 0 s y s t e m h a s a t t h e o ri g i n ( a) s i m p l e p o l e ( b ) n o p o l e ( c ) two p ol e s ( dB

1 4. E r r or c on s ta nt of t h e s ys te m a re a m e a s u r e o f ( a) s t e a d y s t a te a s we l l tr a n s i e nt r e s pan s i e nt s t at e r e s p on s e ( c ) r e l a ti ve s t ab i l i ty ( d ) s t e a d y s t a te r e s p o n s e

1 5. T h e nu mb e r of o p e r at i o n al am p l i fi e r re qu i r e d to d e s i gn an e l e c t r i c P I D - c o ntr o l l e r1 ( c ) 2 ( d ) 3 B

1 6. A s ys te m h a s s o m e ro o t s w i t h r e a l p a r t s e q u a l t o z e r o , b u t n o n e w i t h p os i ti ve res ol u t e l y un s ta b l e ( b ) a b s ol u t e l y s t ab l e ( c ) m a rg i n a ll y s t ab l e ( d ) r e l a ti ve l y s ta b l e

1 7. G i ve n , G ( s ) =1 /s (1 +6 s ) t h e s y s t e m i s ( a) u n s t a b l e ( b ) m a rg i n a l ly s t ab l e ( c ) u ny s t ab l e ( d ) s t a b l e B

1 8. w h i ch of th e f o l l ow i n g s ta t e m e nt s i s n ot tr u e f o r ro o t l o c u s te ch n i qu e ( a) i t i s m os t u sgl e - i n p u t a n d s i n g l e - o u t p u t s y s t e m ( b ) i t p r ov i d e s t h e p a t te rn of m ove m e nt o f c l ow h e n op e n - l o o p g ai n var i e s ( c ) i t i s u s e d to o b t ai n c l os e d - l o o p p o l e c o n fi g u ra t i on f r op ol e s a n d z e ro s ( d ) c a n t t e l l f r o m t h e op t i o ns g i ve n D



1 9. T h e t ra n s f e r f u n c t i on i s K /( s + 1) ( s + 2) ( s + 3) t h e n , t h e b r e a k away p o i nt w i l l b e b en d - 3 ( b ) - 1 a n d - 2 ( c ) 0 a n d - 1 ( d ) - 2 a n d - 3 B

2 0. A d d i n g a z e r o ve r y c l o s e t o o r i gi n i n t h e T . F h as i m p ac t on ( a) i m p u l s e r e s p o n s e (nt re s p on s e ( c ) s t e a d y s t a te r e s p o n s e ( d ) n o e ff e c t on r e s p o n s e B

1 . W h i ch o f th e f o l l ow i n g i s an op e n l o o p c ont r ol s ys t e m ? ( a) Wa r d l e o n ar d c ont r ol ( b ) S tr ob o s c o p e ( c ) M e t a d y n e ( d ) F i e l d c ont r ol l e d d . c m o t or D

2 . s a t u ra t i on i n a s t a b l e c o nt ro l s ys te m c a n c a u s e ( a) c o n d i t io n a l s t a b i l i ty ( b ) l ow l e vel o s c i l l a t i on ( c ) h i g h l e ve l o s c i l l a t i on ( d ) ove r d a mp i n g A

3 . I n a n e ga t i ve f e e d b ack s y s t e m w i t h l o o p g ai n T , t h e n oi s e ( N ) a s i n p u t t o t h e a m p l i fi e rl e a d s to ( S =S i g n a l ) ( a) i n c r e a s e i n S /N r at i o by ( 1- T ) ( b ) d e c r e a s e i n S / N r at i o by ( 1 - T )( c ) d e c r e a s e i n S / N r at i o by ( 1 +T ) ( d ) N o e ff e c t o n S /N r at i o C

4 . T h e d e s c r i b i n g e q u a ti o n o f a m a s s d am p e r s p r i n g s y s t e m is g i ve n by 2 d 2x /d t 2 + d x /d t+ 0 . 5 x = f ( t ) W h e r e f ( t ) i s t h e e xt e r n a l f or c e ac ti n g on t h e s ys te m a n d x i s th e d i s p l a c e m ent of m a s s . T h e s te ad y s t at e d i s p l ac e m e nt c o r re s p o n d i ng t o a f o r c e of 2 N e w t on s i s gi ve nby ( a) 0 . 5m ( b ) 0 . 25 m ( c ) 2 m ( d ) 4 m D

5 . Tra n s f e r f u n c t i on of a s y s t e m i s u s e d t o c al c u l at e ( a) t h e m a i n c o n s t a nt ( b ) t h e s te ady s ta t e g ai n . ( c ) t h e o u t p u t f o r any g i ve n i n p u t ( d ) t h e o r d e r o f t h e s y s t e mC

6 . A s c om p a r e d t o o rd i n a r y m o to r s , s e r vo m o to r s h ave s m a l l m o to r d i a m e t e r b e c au s e i ns e r vo m o t or s ( a) s m a l l s i z e i s m ai n c on s i d e r at i o n ( b ) t or q u e an d i n e rt i a a r e p r op or t i ona l t o s q u a re o f d i a m e t e r ( c ) t or q u e an d i n e rt i a a r e p r op or t i on a l t o d i a m e t e r ( d ) t or q ue an d i n e rt i a a r e p r op or t i on a l t o s q u a re o f d i a m e t e r a n d i n e r t i a i s p r o p or t i o n al to d i a me t e r D

7 . T h e tr a n s f e r f u nc ti o n o f a s i m p l e R- C n e twor k f u n c t i o n i n g as a c ont ro l l e r i s G ( s ) = ( s+Z 1) / ( s +P 1) . T h e c on d i t i o n f o r R - C n e two r k t o ac t as a p h as e l e a d c o nt ro l l e r i s ( a) P 1 = Z1 ( b ) P 1 < Z 1 ( c ) P 1 > Z 1 ( d ) P 1 = 0 C

8 . T wo b l o ck s h avi n g r e s p e c t i ve f u n c t i o n s a s G 1 an d G 2 a re c o n n e c t e d i n s e r i e s c a s c a de . T h e i r re s u l ta nt w i l l b e ( a) G 1 + G 2 ( b ) G 2 /G 1 ( c ) G 1 G 2 ( d ) G 1 /G 2 C

9 . i s a c ont i nu ou s , u n i d i r e c t i on a l s u c c e s s i on o f b ra n ch e s al o n g w h i ch n o n o d e i s t r ave r se d m or e th a n o n c e . ( a) p a th ( b ) n o d e ( c ) b r an ch ( d ) g ai n A

1 0. T h e ch ar a c t e r i s t i c e q u a t i on o f th e s e c on d or d e r s ys te m i s g i ve n by s 2+ 2 c w 0 s +w 0 2= 0. I f c =1 , t h e s y s t e m e x h i b i t s ( a) l a rg e u n de rs h o o t ( b ) l a rg e ove rs h o o t ( c ) n o ove r s h o ot( d ) s m a l l ove r s h o o t C

1 1. T h e ch ar a c t e r i s t i c e q u a t i on o f th e s e c on d or d e r s ys te m i s g i ve n by s 2+ 2c w 0s + w 0 2= 0 .c = 0 , t h e s y s t e m r e s p o n s e w i l l b e ( a) c r i t i c a l l y d am p e d o s c i l l a to r y ( b ) c o n s t ant a m pl i t u d e s i nu s o i d a l ( c ) d a m p e d o s c i l l a t or ( d ) z e r o B

1 2. b a n d w i d t h i s u s e d as a m e a n s o f s p e c i f y i n g p e r f o r m an c e o f a c o nt ro l s ys te m r e l at e dt o ( a) t h e c on s t a nt ga i n ( b ) T h e va r i ab l e ga i n ( c ) r e l a ti ve s t ab i l i ty of s y s t e m ( d ) t h e s pe e d of re s p o n s e D



1 3. I n c l os e d - l o o p s y s t e m i n w h i ch t h e ou t p u t i s t h e s p e e d o f a r o t or , t h e o u t pu t ra t e c ontr ol c an b e u s e d t o ( a) l i m i t t h e t o r qu e o u tp u t o f m ot o r ( b ) r e d u c e t he d a m p i n g of th e s y s te m ( c ) l i m i t t h e s p e e d of m ot o r ( d ) l i m i t t h e a c c e l e r at i o n o f t h e s ys te m D

1 4. T h e ve l o c i ty e r r o r c o e ffi e c i e nt f or a u n i ty f e e d b a ck s y s t e m i s d e fi n e d as ( a) L i m G (s )s ? 0 ( b ) L i m S * G ( s ) s ? 0 ( c ) L i m G ( s )/ s s ? 0 ( d ) L i m S 2 G ( s ) s ? 0 B

1 5. i n a f or c e b a l an c e typ e p n e u m a t i c c o nt ro l l e r , t h e nu mb e r of b e l l ow s r e q u i r e d f or P ID a c t i on i s ( a) 3 ( b ) 2 ( c ) 4 ( d ) 1 C

1 6. t h e ch ar a c t e r i s t i c e qu a t i on o f a s y s t e m h as r o ot s w i t h n e ga t i ve r e a l p a r ts i f a n d o n l yif e l e m e nts o f t h e fi r s t c o l u m n o f t h e Ro u t hs t ab l e h ave ( a) n e g at i ve s i gn . ( b ) S a m e s i g n .( c ) p o s i t i ve s i g n . ( d ) A l t e r n at e p os i t ive an d n e ga t i ve s i g n B

1 7. G i ve n , t h e ch a r ac t e r i s t i c e q u at i o n a s F ( S ) = 3 (S ) ( S ) +1 0 (S ) ( S ) +5 S +5 S +2 = 0, T h e n t he s y s t e m i s ( a) m a rg i n a ll y s t ab l e ( b ) s t a b l e ( c ) u n s t a b l e ( d ) c o n d i t i on a l l y s t ab l eB

1 8. t h e r o o t l o c i o f a s y s t e m h as t h r e e a s y m p t ot e s . T h e s ys te m c a n h ave ) t h r e e p o l e s . ( a)t h r e e p ol e s . ( b ) Fo u r p o l e s an d on e z e r o ( c ) c a n t t e l l f r o m t h e op t i on s g i ve n ( d ) F i ve po l e s an d f ou r z e r os . C

1 9. Fo r r o ot l o c i w h i ch o f th e f o l l ow i n g a r e t h e s ta r t i n g p oi nt s ? ( a) c l o s e d l o o p p o l e s ( b) o p e n l o o p p o l e s ( c ) c l o s e d l o o p z e ro s ( d ) o p e n l o o p z e r o sB

2 0. A d d i n g o f p o l e s i n t h e t r a n s f e r f u n c ti o n c au s e s ( a) l e a d - l a g c om p e n s a ti o n ( b ) l ag c o m p e n s a t i on ( c ) n o c o m p e n s a t i on ( d ) l e a d - c o m p e n s a t i on D

1 . A t e m p e r at u r e c o nt ro l s ys te m i s kn ow n a s ( a) O u tp u t C ont r ol s y s t e m ( b ) S e r vom e ch aa s c a d e c o nt ro l s ys te m s ( d ) P r o c e s s c o ntr o l s y s t e mD

2 . T h e c l o s e d l o o p tr a n s f e r f u n c t i on o f t h e o p e n l o o p t r a n s f e r f u n c t i on , G ( s ) = K / [n i ty f e e db a ck s ys te m i s ( a) k /s (T +s T ) ( b ) k ( 1+ s T ) / s ( c ) k /( s T +s + k ) ( d ) K ( 1 + S T ) S 2

3 . R e ge n e r at i ve f e e d b ack i m p l i e s f e e d b ack w i th ( a) p o s i t i ve s i g n ( b ) o s c i l l a ti o n sn ( d ) s t e p i n p u t A

4 . T h e t ra n s f e r f u n c t i on of t h e d i ff e re nt i a l e q u a ti o n y ( t ) = x (t - T ) i s gi ve n by ( a) Y ( s ) = S- T / (s +1 ) ( c ) Y ( s ) = e - 1/ ( s + 1) ( d ) Y ( s ) = e - S T / (s +1 ) B

5 . I n a s y s t e m w i t h ro t at i n g m a s s , t h e t i m e c o n s t ant o f th e s y s t e m c an b e d e c r e as e d byf r i c t i o n ( b ) o u tp u t ra t e f e e d b ack ( c ) i n c r e a s i n g t h e i n e r t i a o f t h e s ys t e m ( d ) i n c r e at o s y s t e m B

6 . I f a c o nve nt i on a l s e rvo - m o to r i s u s e d f or s e r vo a p p l i c a ti o n s , t h e s y s t e m b e c o m e su s e ( a) t h e r o t or d i a m e t e r i s l ar g e ( b ) t h e r o t or r e s i s ta n c e i s l ow ( c ) t h e a p p l i e d vo l taway s t o b e b al a n c e d ( d ) t h e r o t or r e s i s ta n c e i s h i g h B

7 . T h e t ra n s f e r f u n c t i on i s ( 1 +0 . 5 s ) /( 1+ s ) . I t re p re s e nt s a ( a) l e a d n e twor k ( b ) p r opl l e r ( c ) l a g n e two r k ( d ) l a g- l e ad n e two r k C

8 . T wo b l o ck s h avi n g r e s p e c t i ve f u n c t i o n s a s G 1 ab d G 2 a r e c o n n e c t e d i n p a ra l l e l . T h eant w i l l b e ( a) G 1 +G 2 ( b ) G 1 o r G 2 w h i ch e ve r i s l owe r ( c ) G 1 G 2 ( d ) G 1 o r G 2 w h i ch eA



9 . T h e p r o d u c t of t h e b r a n ch ga i n s of t h e l o o p i s ( a) f e e d b a ck p at h g a i n ( b ) l o op ga i n ( cat h g ai n ( d ) p a th ga i n B

1 0. T h e ch ar a c t e r i s t i c e q u a t i on o f th e s e c on d or d e r s ys te m i s g i ve n by s 2 + 2c w 0 s +w 0m c i s c a l l e d ( a) d a m p i n g f ac t o r ( b ) f r e q u e n c y f ac t o r ( c ) p o l e f ac t o r ( d ) s t a b i l i ty f aA

1 1. T h e t ra n s f e r f u n c t i on of a fi r s t o rd e r c o nt r o l s y s t e m is o f t h e ty p e ( a) T s ( b ) 1 /T s1 /T s 2 + 1 C

1 2. A s e c o n d o r d e r s y s t e m w i t h n o z e r os h a s i t s p o l e s l o c at e d at - 3+ j 4 a n d - 3- j 4 i n th e sd a m p e d n at u r a l f r e q u e n c y a n d t h e d am p i n g f a c t o r of t h e s ys te m ar e r e s p e c ti ve l y (0. 6 0 ( b ) 5 ra d / s e c an d 0 . 8 0 ( c ) 5 ra d / s e c an d 0 . 6 0 ( d ) 4 ra d / s e c a nd 0. 7 5 C

1 3. T h e p o s i t i on a n d ve l o c i ty e r r or s of a ty p e 2 s y s t e m ar e ( a) Z e ro , c on s t a nt ( b ) c o n s t a( c ) c o n s t ant , i n fi n i ty ( d ) Z e ro , z e r o D

1 4. Ty p e 1 s y s t e m u n d e r p a r ab ol i c i n p u t w i l l h ave w h i ch o f th e f o l l ow i n g ? ( a) p a ra b) A c t u a ti n g s i gn a l w h i ch w i l l i n c r e a s e w i t h t i m e ( c ) A c t u a ti n g s i gn a l w h i ch w i l l d e c rm e ( d ) s t e p ou t p u t B

1 5. W h e n d e r i va ti ve a c t i o n i s i n c l u d e d i n p ro p o r ti o n al c o nt r o l l e r , t h e p r o p or t i o nm a i n s u n a ff e c t e d ( b ) d e c r e a s e s ( c ) i n c r e a s e s ( d ) d e p e n d s u p o n d e r i vat i ve t i m e c onA

1 6. T h e b e s t m e th o d f or d e t e r mi n i n g t h e s t i b i l i ty an d t r a n s i e nt r e s p o n s e i s ( a) r o ote p l ot ( c ) ny qu i s t p l ot ( d ) n i ch o l as ch ar t A

1 7. A s te p f u n c t i o n i s ap p l i e d t o th e i n p u t o f s y s t e m an d ou t p u t i s of t h e f or m y = t, t h e s y s tt n e c e s s ar i l y s ta b l e ( b ) s t a b l e ( c ) u n s t a b l e ( d ) c o n d i t i on a l l y s t ab l e

1 8. A s ys te m h a s l o o p g ai n a s G ( s ) H ( s ) = K /s (s +1 ) (s +2 ) (s +3 ) . t h e nu mb e r of p ol e s a n d z e rol y a re ( a) 1 , 4 ( b ) 1 , 3 ( c ) 2 , 2 ( d ) 4 , 0 B

1 9. I n ro o t l o c u s p l o t d i ff e r e nt r o ot s h ave t h e s am e ( a) g ai n m ar gi n an d p h as e m a rg i n (h a s e a n g l e ( d ) g ai n A

2 0. T h e e ff e c t of ad d i n g p ol e s a nd z e r o s c a n b e d e t e r m i n e d qu i ck l y by w h i ch of t h e f o l l owch o l as ch ar t ( b ) r o ot l o c u s ( c ) ny qu i s t p l ot ( d ) b o d e p l ot

1 . W h i ch o f th e f o l l ow i n g i s an op e n l o o p c ont r ol s ys t e m ? ( a) M e t a d y n e ( b ) Wa r d l e o n ar d c onl d c ont r ol l e d d . c m o t or ( d ) S t r ob o s c o p e C

2 . I nt r o d u c ti o n o f n e ga t i ve f e e d b a ck i n a s ys te m d o e s n o t l e a d t o r e d u c t i o n i n ( a) d i s t o rtl ga i n ( c ) i n s t a b i l i ty ( d ) b a n d w i d th D

3 . I n a n e ga t i ve f e e d b ack s y s t e m w i t h l o o p g ai n T , t h e n oi s e g e n e r at e d w i t h i n t h e b a s i c am p lm a i n s u n a ff e c t e d by th e f e e d b a ck ( b ) i n c r e a s e by a f ac t o r o f ( 1 - T ) ( c ) d e c r e a s e s by a f a cd e c r e a s e by a f ac to r o f ( 1 +T ) C

4 . s p r i n g f or c e i s a n on - l i n e ar f u n c t i o n o f t h e d i s p l a c e m e nt xm e a s u r e d f r om t h e r e s t p o squ a t i on o f m ot i o n o f m a s s M i s ( a) M d 2 x /d t 2 + d x /d t = 0 ( b ) d x d t + x = 0 ( c ) M d 2 x /d t 2 +d x/ d t + f s (x ) = 0 C

5 . T h e p o l e s o f F ( s )( s 2 - 1 6 )/ ( s 5 - 7 s 4 - 3 0 s 3 ) a r e l o c a t e d a t



( a) s = 0 (t r i p l e p ol e ) , - 3 a n d 10 ( b ) s = 0 (t r i p l e p ol e ) , - 3 a n d 10 ( c ) s = 4, 4 ( d ) s = 0, 4, 16

6 . T h e fi e l d of a d . c s e r vo - m o t or i s s e p ar a t e l y e x c i t e d by a d . c a m p l i fi e r o f ga i n K = 9 0. I f t h e fin d u c t an c e o f 2 H an d a re s i s t an c e o f 5 0 oh m s t h e val u e of t h e fi e l d c o n s t ant w i l l b e( a) 0 . 04 s e c ( b ) D 0. 5 s e c ( c ) 0 . 01 s e c ( d ) 0 . 02 s e c

7 . T h e tr a n s f e r f u nc ti o n o f a s i m p l e R- C n e twor k f u n c t i o n i n g as a c ont ro l l e r i s G ( s ) = ( s +Z 1) /c on d i t i o n f o r R - C n e two r k t o ac t as a p h as e l e a d c o nt ro l l e r i s( a) P 1 > Z 1 ( b ) P 1 < Z 1 ( c ) P 1 = Z 1 ( d ) P 1 = 0

8 . T wo b l o ck s h avi n g r e s p e c t i ve f u n c t i o n s a s G 1 an d G 2 a re c o n n e c t e d i n s e r i e s c a s c a d e . T hnt w i l l b e( a) G 1 + G 2 ( b ) G 1 /G 2 ( c ) G 2 /G 1 ( d ) G 1 G 2

9 . A s ys te m va r i ab l e t h at e qu a l s th e s u m of al l th e i n c o m i n g s i gn a l s i s d e fi n e d a s( a) i n p u t n o d e ( b ) n o d e ( c ) b r an ch ( d ) o u tp u t no d e

1 0. T h e ch ar a c t e r i s t i c e q u a t i on o f th e s e c on d or d e r s ys te m i s g i ve n by s 2 + 2 c w 0 s +w 0 2 =s t e m e x h i b i t s ( a) l a rg e u n de rs h o o t ( b ) s m a l l ove r s h o o t ( c ) n o ove r s h o ot ( d ) l a rg e ove rs h o

1 1. T h e t ra n s f e r f u n c t i on of a fi r s t o rd e r c o nt r o l s y s t e m is o f t h e ty p e( a) T s ( b ) 1 /T s 2 + 1 ( c ) 1 /T s +1 ( d ) 1 /T s

1 2. A u n i ty f e e d b ack s ys te m h a s t r an s f e r f u n c t i o n G ( s ) = 9 S ( s + 3 )( a) d a m p i n g r a t i o= 0 . 6 ( b ) n a tu r a l f r e q u e n c y = 9 ( c ) n a tu r a l f r e q u e n c y = 3 ( d ) d a m p i n g r

1 3. I n c as e o f ty p e - 1 s y s t e m s t e a d y s t a te a c c e l e r a ti o n i s( a) u n i ty ( b ) Z e ro ( c ) 1 0 ( d ) i n fi n i ty

1 4. T h e s t e a d y s t at e ac c e l e r at i o n e r r or f or a ty p e 1 s ys te m i s( a) I n fi n i t e ( b ) 0 ( c ) 1 ( d ) B e twe e n 0 an d 1

1 5. t h e nu mb e r o f op e ra t i on a l a m p l i fi e r r e q u i r e d t o d e s i g n a n e l e c t ri c P I D - c ont r ol l e r i s( a) 3 ( b ) 4 ( c ) 1 ( d ) 2

1 6. a t t h e p o i nt w h e r e 18 0 0 l o c u s c r os s e s t h e j - a x i s , th e s y s t e m i s( a) ove r d a m p e d ( b ) a b s ol u t e l y un s ta b l e ( c ) u n d e r d a m p e d ( d ) a b s ol u t e l y s t ab l e

1 7. T h e s y s t e m w i th tr a n s f e r f u n c t i on K / S 2 ( 1+ s T ) i s o p e r a te d i n c l o s e d l o op w i th u n i tyc l os e d - l o op s y s t e m i s ( a) s t a b l e ( b ) m a rg i n a l ly s t ab l e ( c ) u n s t a b l e ( d ) c o n d i t i on a l l y

1 8. w h i ch of th e f o l l ow i n g s ta t e m e nt s i s n ot tr u e f o r ro o t l o c u s te ch n i qu e ( a) i t i s m os t u s e f u l fp u t a n d s i n g l e - o u t p u t s y s t e m ( b ) i t p r ov i d e s t h e p a t te rn of m ove m e nt o f c l os e d- l o op p ol eo o p g ai n var i e s ( c ) c a n t t e l l f r o m t h e op t i on s g i ve n ( d ) i t i s u s e d to o b t ai n c l os e d - l o o p pi on f r om op e n - l o op p ol e s a n d z e ro s

1 9. G ( s ) H ( s ) = K /s (s +1 ) (s +2 ) (s +3 ) T h e n , t h e a n gl e o f a s y m p t ot e s w i t h r e a l a xi s r e s p e c t i ve l y( a) 3 4 0 , 4 5 0 ( b ) 4 5 0 , 1 35 0 , 2 25 0 ( c ) 4 5 0 , 1 35 0 ( d ) 4 5 0 , 1 35 0 , 2 25 0 , 3 1 5 0

2 0. A d d i n g a z e r o ve r y c l o s e t o o r i gi n i n t h e T . F h as i m p ac t on( a) t r an s i e nt re s p on s e ( b ) n o e ff e c t on r e s p o n s e ( c ) i m p u l s e r e s p o n s e ( d ) s t e a d y s t a te

1 . A t e m p e r at u r e c o nt ro l s ys te m i s kn ow n a s( a) S e r vom e ch a n i s m ( b ) P r o c e s s c o ntr o l s y s t e m ( c ) O u tp u t C ont r ol s y s t e m ( d ) C a s c a

d e c o nt ro l s ys te m s



2 . n o i s e i n c o nt r ol s y s t e m c an b e avo i d e d by( a) a tt e nu a ti n g t h o s e f r e q u e n c i e s at w h i ch e x t e r n al s i gn a l g e t c ou p l e d i nt o t h e s y s t e m

( b ) R e d u c i n g t h e b a n d w i dt h a n d a t t e nu at i n g t h o s e f r e q u e n c i e s a t w h i ch e xt e r n a l s i gna l ge t c o u p l e d i nt o th e s y s t e m ( c ) R e d u c i n g t h e b a n d w i d t h ( d ) B y i n c r e as i ng f re qu e n cy

3 . W i t h f e e d b a ck s y s t e m( a) t h e t r a ns i e nt r e s p o n s e d e c ay s m or e qu i ck l y ( b ) t h e t r a ns i e nt r e s p o n s e ge t s m ag n i fie d ( c ) t h e t r a ns i e nt r e s p o n s e d e c ay s s l ow l y ( d ) t h e t r a ns i e nt r e s p o n s e d e c ay s at a c on st a nt r at e

4 . T h e t ra n s f e r f u n c t i on of t h e s ys te m w h o s e i n p u t ar e r e l a t e d by t h e f ol l ow i n g d i ff e r nti al e q u at i o n i s gi ve n by d 2y /d t 2 + 3 d y /d t + 2 y = + d x/ d t( a) 1 /( s 2+ 3s + 2 ) ( b ) ( s + 1) / (s 2+ 3s + 2 ) ( c ) s / ( s 2+ 3s + 2 ) ( d ) ( s + 2) / (s 2+ 3s + 2 )

5 . I n f or c e c u r r e nt A n al o g y, i n d i c a t e t h e tr u e s t at e m e nt( a) p r i n g c on s ta nt i s an a l og o u s t o r e c i p r o c al of c a p ac i t a n c e ( b ) m a s s i s a n al o go u s to i n

d u c t a n c e ( c ) v i s c o u s f ri c ti o n c o e ffi e nt i s a n al o go u s to r e c i p ro c a l o f r e s i s t an c e ( d ) f o rc e i s a n al o go u s t o vol t a ge

6 . W h i ch o f th e f o l l ow i n g s t a t e m e nts i s n ot c or r e c t f or s e r vo m e ch a n i s m s ?( a) s t e a d y s t a te a c c u r ac y of a s e r vo is b e t t e r t h a n t h a t of a r e gu l a t or ( b ) A m o t or m ay b e

ad d e d t o c onve r t a r e g u l at or i nt o a s e rvo ( c ) S o m e s e rvos d o n o t n e e d to b e s t a b l e , s i n c e t he y a r e i nt e n d e d f or u s e w i t h s t e ad y s i gn a l s ( d ) A s e r vo w i t h b e t te r f r e q u e n c y r e s p on s en e e d n ot b e s ta b l e

7 . T h e t ra n s f e r f u n c t i on i s ( 1 +0 . 5 s ) /( 1+ s ) . I t re p re s e nt s a( a) p r op or t i on a l c o nt ro l l e r ( b ) l a g n e two r k ( c ) l a g- l e ad n e two r k ( d ) l e a d n e twor k

8 . T wo b l o ck s h avi n g r e s p e c t i ve f u n c t i o n s a s G 1 ab d G 2 a r e c o n n e c t e d i n p a ra l l e l . T h e ir r e s u l t ant w i l l b e( a) G 1 +G 2 ( b ) G 1 o r G 2 w h i ch e ve r i s h i g h e r ( c ) G 1 o r G 2 w h i ch e ve r i s l owe r ( d ) G 1 G 2

9 . T h e p r o d u c t of t h e b r a n ch ga i n s e n c o u nt e r e d i n t r ave r s i n g a p at h i s( a) l o op ga i n ( b ) p a th ga i n ( c ) Fo r war d p at h g ai n ( d ) f e e d b a ck p at h g a i n

1 0. N a tu r a l f r e q u e n c y of a u n i ty f e e d b a ck c o nt r ol s y s t e m o f tr a n s f e r f u n c t i on G ( s ) = 1 0/s ( s + 1 ) i s( a) 4 . 16 r a d /s e c ( b ) 0 . 5 ra d / s e c ( c ) 4 . 6 ra d / s e c ( d ) 3 . 16 r a d /s e c

1 1. T h e ty p e - 2 s y s t e m h a s ( a) s i m p l e p o l e a t t h e o r i gi n ( b ) two p ol e s a t t h e o r i gi n ( c ) n et p ol e at t h e or i g i n ( d ) n o n e t p ol e at t h e or i g i n

1 2. I n c ont r ol s y s t e m e xc e s s i ve b a n d w i d t h s h o u l d b e avo i d e d b a c au s e( a) i t l e a d s to l ow r e l a t i ve s t ab i l i ty ( b ) n o i s e i s p r op or t i on a l t o b a n d w i d t h ( c ) i t l e a d sto s l ow s p e e d of r e s p o n s e ( d ) i t l e a d s to h i g h s p e e d o f re s p o n s e

1 3. I n a s t ab l e c o nt r ol s y s t e m b a ck l as h c a n c a u s e w h i ch o f t h e f ol l ow i n g ?( a) l ow l e ve l o s c i l l a t i on s ( b ) u n d e r d a mp i n g ( c ) p o o r s t ab i l i ty a t r e d u c e d va lu e s o f o pe n l o op ga i n ( d ) ove r d a m pi n g

1 4. T h e p o s i t i on e rr o r c o e ffi e c i e nt f or a u n i ty f e e d b ack s y s t e m i s d e fi n e d a s( a) L i m S * G ( s ) s ? 0 ( b ) L i m G (s ) s ? 0 ( c ) L i m G (s )/ s s ? 0 ( d ) L i m S 2 G ( s ) s ? 0



1 5. T h e e rr o r s i gn a l p r o d u c e d i n a c o nt r ol s y s t e m i s Q r= a +b t . i f o n l y p ro p o r ti o n al ac t i on i s u s e d , t h e i n p u t i s gi ve n t o t h e fi n a l c o nt ro l e l e m e nt w h e n P I D a c t i on i s u s e d , w i l l b e( a) - ( K a + K 1b t + K 2 a+ K 2 b t) ( b ) ( ( K a+ K 1 ( a+ b t )+ K 2 (a t +b t 2 ) ) ( c ) - K (a + b tK 1( a t+ b t 2K2 b ) ) ) ( d ) ( ( K a+ K 1 ( a+ b t )+ K 2 (a t +b t 2 ) )

1 6. t h e t r a n s f e r f u n c ti o n o f a u n ity f e e d b ack s y s t e m i s G ( s ) = K / s ( s + s ) ( s +5 ) . th e r an g eof K f or s ta b l e o p e r a t i on i s( a) 0 < K < 3 0 ( b ) K = 0 ( c ) K = 10 ( d ) K > 4 0

1 7. G i ve n , G ( s ) = ( 1- s ) /( s ( s + 2) ) . T h e s y s t e m w i t h t h e t r a n s f e r f u n c ti o n i s op e ra t e d i n aC l os e d - l o op w i th u n i ty f e e d b ack . T h e c l os e d - l o op s y s t e m i s ( a) s t a b l e ( b ) m a rg i n a l ly st ab l e ( c ) u n s t a b l e ( d ) c o n d i t i on a l l y s t ab l e

1 8. w h i ch of t he f o l l ow i n g s ta t e m e nt s i s n ot tr u e f o r r o o t l o c u s te ch n i qu e( a) i t p r ov i d e s t h e p a t te rn of m ove m e nt o f c l os e d - l o op p ol e s w h e n o p e n - l o o p g ai n var i e s (b ) c a n t t e l l f r o m t h e op t i o ns g i ve n ( c ) i t i s m os t u s e f u l f or s i n gl e - i n p u t a n d s i n g l e - o ut p u t s y s t e m ( d ) i t i s u s e d to o b t ai n c l os e d - l o o p p o l e c o n fi g u ra t i on f r om op e n - l o op p ol es a n d z e ro s

1 9. T h e t ra n s f e r f u n c t i on i s K /( s + 1) ( s + 2) ( s + 3) th e n , t h e b r e a k away p o i nt w i l l b e b e twe en( a) - 2 a n d - 3 ( b ) 0 a n d - 1 ( c ) - 1 a n d - 2 ( d ) B e yo n d - 3

2 0. T h e e ff e c t of ad d i n g p ol e s a nd z e r o s c a n b e d e t e r m i n e d qu i ck l y by w h i ch of t h e f o l l ow in g( a) b o d e p l ot ( b ) N i ch o l as ch ar t ( c ) r o ot l o c u s ( d ) ny qu i s t p l ot

1 . A t e m p e r at u r e c o nt ro l s ys te m i s kn ow n a s( a) C a s c a d e c o nt ro l s ys te m s ( b ) P r o c e s s c o ntr o l s y s t e m ( c ) O u tp u t C ont r ol s y s t e m ( d )S e r vom e ch a n i s m

2 . T h e op e n l o op t ra n s f e r f u n c t i on of a u n i ty f e e d b a ck s y s t e m i s G ( s ) = K S ( 1 + S T ) t h ech a r ac t e r i s t i c e q u at i o n o f t h e c l os e d l o o p s y s t e m i s( a) s 2 + k= 0 ( b ) S + K = 0 ( c ) s 2 + s T + K ( d ) s 2 + s T = 0

3 . W i t h f e e d b a ck s y s t e m ( a) t h e t r a ns i e nt r e s p o n s e d e c ay s m or e qu i ck l y ( b ) t h e t r a nsi e nt r e s p o n s e d e c ay s at a c on s t a nt r at e ( c ) t h e t r a ns i e nt r e s p o n s e ge t s m ag n i fi e d ( d ) t he t r a ns i e nt r e s p o n s e d e c ay s s l ow l y

4 . T h e l i n e ar e q u at i o n d e s c ri b i n g t h e m ot i o n of p e n d u l u m f o r s m al l va l u e s of d i s p l a c em e nt ( t h e t a) i s g i ve n by( a) d 2 ? / d t 2 + ( l /g ) s i n ? = 0 ( b ) d 2 ? / d t 2 + ( l /g ) ? = 0 ( c ) d 2 ? / d t 2 + ( g/ l ) ? = 0 ( d ) d 2 ? /d t 2 + ( g/ l ) s i n ? = 0

5 . I n f or c e - vol t ag e an a l og y, m as s i s an a l og ou s t o( a) r e s i s t a n c e ( b ) c u r r e nt ( c ) i n d u c t a nc e ( d ) vol t a ge

6 . T h e s e r vo m ot or d i ff e r s f ro m o t h e r m o to r s i n t h e s e ns e t h a t i t h a s( a) e nt i r e l y d i ff e r e nt c o n s t r u c t i on ( b ) h i g h i n e r t i a an d h i gh to r qu e ( c ) l ow i n e r t i a an dl ow to r qu e ( d ) l ow i n e r t i a an d h i gh to r qu e

7 . T h e tr a n s f e r f u nc ti o n o f a s i m p l e R- C n e twor k f u n c t i o n i n g as a c ont ro l l e r i s G ( s ) = ( s+Z 1) / ( s +P 1) . T h e c on d i t i o n f o r R - C n e two r k t o ac t as a p h as e l e a d c o nt ro l l e r i s ( a) P 1 = Z1 ( b ) P 1 = 0 ( c ) P 1 < Z 1 ( d ) P 1 > Z 1



8 . T wo b l o ck s h avi n g r e s p e c t i ve f u n c t i o n s a s G 1 an d G 2 a re c o n n e c t e d i n s e r i e s c a s c a de . T h e i r re s u l ta nt w i l l b e( a) G 1 /G 2 ( b ) G 2 /G 1 ( c ) G 1 + G 2 ( d ) G 1 G 2

9 . l o op s w h i ch do n o t h ave a c om m o n n o d e ar e s ai d t o b e( a) s e l f l o op s ( b ) f o r war d l o o p s ( c ) t ou ch i n g l o o p s ( d ) n o n t ou ch i n g l o o p s

1 0. T h e ch ar a c t e r i s t i c e q u a t i on o f th e s e c on d or d e r s ys te m i s g i ve n by s 2 + 2 c w 0 s +w 0 2 =0 . I f c =1 , t h e s y s t e m i s( a) ove r d a m p e d ( b ) u n d e r d a m p e d ( c ) a b s ol u t e l y da m p e d

1 1. T h e ch ar a c t e r i s t i c e q u a t i on o f th e s e c on d or d e r s ys te m i s g i ve n by s 2 + 2c w 0s + w 0 2 =0 . I f ? = 0 1 , t h e p o l e s a r e

( a) + o r - j c w 0 ( b ) + o r - j c w 0 2 ( c ) + o r - j w 0 2 ( d ) + o r - j w 0

1 2. A s e c o n d o r d e r s y s t e m w i t h n o z e r os h a s i t s p o l e s l o c at e d at - 3+ j 4 a n d - 3- j 4 i n th e s - pl an e t h e un d a m p e d n at u r a l f r e q u e n c y a n d t h e d am p i n g f a c t o r of t h e s ys te m ar e r e s p e cti ve l y( a) 5 ra d / s e c an d 0 . 6 0 ( b ) 4 ra d / s e c a nd 0. 7 5 ( c ) 3 ra d / s e c a nd 0. 6 0 ( d ) 5 ra d / s e c an d 0 . 8 0

1 3. I n a s t ab l e c o nt r ol s y s t e m b a ck l as h c a n c a u s e w h i ch o f t h e f ol l ow i n g ?( a) u n d e r d a mp i n g ( b ) l ow l e ve l o s c i l l a t i on s ( c ) ove r d a m pi n g ( d ) p o o r s t ab i l i ty a t r e du c e d val u e s o f o p e n l o op ga i n

1 4. I n a c ont r ol s y s t e m i nt e g ra l e rr o r c o m p e n s a t i on s t e a d y s t a te e r r or( a) d o e s n ot h ave any e ff e c t o n ( b ) n o th i n g c a n t e l l ( c ) i n c r e a s e s ( d ) d e c r e a s e s

1 5. T h e e rr o r s i gn a l p r o d u c e d i n a c ont r ol s y s t e m i s Q r= a +b t . i f o n l y p ro p o rt i o n al a c t i on i s u s e d , t h e i n p u t i s gi ve n t o t h e fi n a l c o nt ro l e l e m e nt w h e n P I D a c t i on i s u s e d , w i l l b e

( a) ( ( K a+ K 1 ( a+ b t )+ K 2 (a t +b t 2 ) ) ( b ) - K (a + b tK 1( a t+ b t 2K 2 b ) ) ) ( c ) ( ( K a+ K 1 ( a+ b t )+ K2 (a t +b t 2 ) ) ( d ) - ( K a + K 1b t + K 2 a+ K 2 b t)

1 6. a t t h e p o i nt w h e r e 18 0 0 l o c u s c r os s e s t h e j - a x i s , th e s y s t e m i s( a) ove r d a m p e d ( b ) a b s ol u t e l y s t ab l e ( c ) a b s ol u t e l y un s ta b l e ( d ) u n d e r d a m p e d

1 7. A s te p f u n c t i o n i s ap p l i e d t o th e i n p u t o f s y s t e m an d ou t p u t i s of t h e f or m y = t, t h e s y s te m i s( a) s t a b l e ( b ) u n s t a b l e ( c ) c o n d i t i on a l l y s t ab l e ( d ) n o t n e c e s s ar i l y s ta b l e

1 8. A s ys te m h a s l o o p g ai n a s G ( s ) H ( s ) = K /s (s +1 ) (s +2 ) (s +3 ) . t h e nu mb e r of p ol e s a n d z e ro sre s p e c t i ve l y a re( a) 1 , 3 ( b ) 4 , 0 ( c ) 2 , 2 ( d ) 1 , 4

1 9. T h e t ra n s f e r f u n c t i on i s K /( s + 1) ( s + 2) ( s + 3) t h e n , t h e b r e a k away p o i nt w i l l b e b e twe en( a) 0 a n d - 1 ( b ) - 1 a n d - 2 ( c ) B e yo n d - 3 ( d ) - 2 a n d 3

2 0. A d d i n g i n t h e z e r os i n t h e t ra n s f e r f u n c t i on c a u s e s ( a) l e a d - l a g c om p e n s a ti o n ( b )l a g- c om p e n s at i o n ( c ) l e a d c o m p e n s a t i on ( d ) n o c o m p e n s a t i on



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