136. In the given system, (Q. 56) if a = 0.1, then steady state error to unity ramp input will be______ .

1. 1. 0.35

   
   
   

   2. 35

   
   
   

   3. 3.5

   
   
   

   4. 350

   
   
   

---

1. View Hint View Answer Discuss in Forum

   
   

   G(s) =	8
   	s2 + (2 + 8a)s

   
   

   =	8
   	s2 + 2.8 s

   
   
   

   ∴ ess =	1	=	2.8	= 0.35
   	Kv		8

   
   

   Correct Option: A

   
   

   G(s) =	8
   	s2 + (2 + 8a)s

   
   

   =	8
   	s2 + 2.8 s

   
   
   

   ∴ ess =	1	=	2.8	= 0.35
   	Kv		8

   
   

---

137. In the system shown in the figure, r(t) = sin ωt
     
     The steady-stat e response c(t) will exhibit a resonance peak at a frequency of_______ rad/sec

1. 1. 2 √2

   
   
   

   2. √2

   
   
   

   3. 2

   
   
   

   4. None of these

   
   
   

---

1. View Hint View Answer Discuss in Forum

   ∴	C(s)	=		16		=	8
   				s(s + 4)
   	R(s)		1 +	16	× 1		16 + s(s + 4)
   				s(s + 4)

   
   

   C(jω)	=	16	=	16
   R(jω)		16 + jω(jω + 4)		16 - ω² + 4jω

   
   

   =	16	∠ -tan-1	4ω
   	√(16 - ω)² + (4ω)²		(16 - ω²)

   
   For resonance to occur
   

   	d	√(16 - ω)² + (4ω)² = 0
   	dω

   
   F(ω) = (16 - ω²)² + (4 ω)²
   = ω⁴ + 256 - 32 ω² + 16ω²
   = ω⁴ - 16 ω² + 256
   

   ∴	dF(ω)	= 4ω3 - 32 ω = 0
   	dω

   
   ⇒ ω = √8 = 2 √2 rad / sec

   Correct Option: A

   ∴	C(s)	=		16		=	8
   				s(s + 4)
   	R(s)		1 +	16	× 1		16 + s(s + 4)
   				s(s + 4)

   
   

   C(jω)	=	16	=	16
   R(jω)		16 + jω(jω + 4)		16 - ω² + 4jω

   
   

   =	16	∠ -tan-1	4ω
   	√(16 - ω)² + (4ω)²		(16 - ω²)

   
   For resonance to occur
   

   	d	√(16 - ω)² + (4ω)² = 0
   	dω

   
   F(ω) = (16 - ω²)² + (4 ω)²
   = ω⁴ + 256 - 32 ω² + 16ω²
   = ω⁴ - 16 ω² + 256
   

   ∴	dF(ω)	= 4ω3 - 32 ω = 0
   	dω

   
   ⇒ ω = √8 = 2 √2 rad / sec

---

---

138. The unit step error coefficient of a system G(s) =	1
     	(s + 6)(s + 1)

     
     with unity feedback is _______

1. 1. 6

   
   
   

   2. 5/6

   
   
   

   3. 1/6

   
   
   

   4. 5

   
   
   

---

1. View Hint View Answer Discuss in Forum

   
   

   Correct Option: C

   
   

---

139. The value of k for a unity feedback system with G(s) =	k
     	s(1 + s)

     
     to have a peak overshoot of 50% is _______

1. 1. 53

   
   
   

   2. 0.53

   
   
   

   3. 5.3

   
   
   

   4. None of the above

   
   
   

---

1. View Hint View Answer Discuss in Forum

   T(s) =	k
   	s2 + s + k

   
   2 ξ ω_n = 1 , ω_n = √k
   

   ξ =	0.5
   	√k

   
   

   Mp = 0.50 = exp		-π ξ
   		√1 - ξ²

   
   

   ⇒	0.5	= 0.16
   	√1 - ξ²

   
   ξ = 0.15
   k = 5.3

   Correct Option: B

   T(s) =	k
   	s2 + s + k

   
   2 ξ ω_n = 1 , ω_n = √k
   

   ξ =	0.5
   	√k

   
   

   Mp = 0.50 = exp		-π ξ
   		√1 - ξ²

   
   

   ⇒	0.5	= 0.16
   	√1 - ξ²

   
   ξ = 0.15
   k = 5.3

---

---

140. A unity-feedback control system has the open-loop transfer function
     

     G(s) =	4(1 + 2s)
     	s2 (s + 2)

     
     If input to the system is a unit ramp, then steadystate error will be_______

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 2

   
   
   

   4. 3

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Open loop transfer function =	4(1 + 2s)
   	s2 (s + 2)

   
   unit ramp
   Type 2.
   Steady state error = 0

   Correct Option: A

   Open loop transfer function =	4(1 + 2s)
   	s2 (s + 2)

   
   unit ramp
   Type 2.
   Steady state error = 0

---