Previous Year Questions- Mathematical Models of Physical Systems - 1 | Control Systems - Electrical Engineering (EE) PDF Download

Q1: For the block-diagram shown in the figure, the transfer function C(s)/R(s) is  (2024)
(a)
(b)
(c)
(d)
Ans: (d)
Sol: Transfer function

Q2: The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is  (2023)
(a) 2.51e^{−0.032 s}
(b)
(c) 1.04e^{−2.514 s}  
(d) 2.51e^{−1.047 s} 
Ans: (d)
Sol: Transfer function of transportation lag system,
T(s) = Ke^−STTd
From magnitude plot,
From angle plot,
at ω = 1rad/sec.,θ = −60°
We have,

Q3: A continuous-time system that is initially at rest is described by
where x(t) is the input voltage and y(t) is the output voltage. The impulse response of the system is  (2023)
(a) $3e-2t$3e^−2t
(b) (1/3) e^−2t u(t)
(c) 2e^−3t u(t)
(d) 2e^−3t
Ans: (c)
Sol: Given :
Taking Laplace transform,
We have impulse response
= L⁻¹ (Transfer function)
So, taking inverse Laplace transform,
y(t) = 2e^−3tu(t)  

Q4: For the block diagrm shown in the figure, the transfer function Y(s)/R(s) is  (2023)
(a)
(b)
(c)
(d)
Ans: (b)
Sol: Signal flow graph:
Forward paths,
Using Masson's graph formula,

Q5: For the closed-loop system shown, the transfer function  is  (2021)
(a)
(b)
(c)
(d)
Ans: (c)
Sol: 
Q6: Which of the options is an equivalent representation of the signal flow graph shown here?  (2020)
(a) (b) (c) (d) Ans: (c)
Sol: Simplifying given signal flow graph

Q7: For a system having transfer function  a unit step input is applied at time t = 0. The value of the response of the system at t = 1.5 sec is __________.  (SET-1(2017))
(a) 0.5
(b) 1
(c) 1.5
(d) 2.5
Ans: (a)
Sol: 
Q8: In the system whose signal flow graph is shown in the figure, U₁(s) and U₂(s) are inputs. The transfer function Y(s)/U₁(s) is  (SET-1 (2017))
(a)
(b)
(c)
(d)
Ans: (a)
Sol: Transfer function,

Q9: Let a causal LTI system be characterized by the following differential equation, with initial rest condition
 Where x(t) and y(t) are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)  (SET-1 (2017))
(a) $2e-2tu\left(t\right)-7e-5tu\left(t\right)$2e^−2tu(t) − 7e^−5tu(t)
(b) −2e^−2tu(t) + 7e^−5tu(t)
(c) $7e-2tu\left(t\right)-2e-5tu\left(t\right)$7e^−2tu(t) − 2e^−5tu(t)
(d) −7e^−2tu(t) + 2e^−5tu(t)
Ans: (b)
Sol: Impulse response = L⁻¹(Transfer function)

Q10: For the system governed by the set of equations:
dx₁/dt = 2x₁ + x₂ + u
dx₂/dt = −2x₁ + u
y = 3x₁
the transfer function Y(s)/U(s) is given by  (SET-2(2015)
(a) $3(s+1)/(s2-2s+2)$3(s + 1)/(s² − 2s + 2)
(b) 3(2s + 1)/(s² − 2s + 1)
(c) $(s+1)/(s2-2s+2)$(s + 1)/(s² − 2s + 2)
(d) $3(2s+1)/(s2-2s+2)$3(2s + 1)/(s² − 2s + 2)
Ans: (a)
Sol: From equation (i),

Q11: Find the transfer function Y(s)/X(s) of the system given below.  (SET-1 (2015))
(a)
(b)
(c)
(d)
Ans: (c)
Sol: 
Q12: For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function   (SET-1 (2015))(a)
(b)
(c)
(d)
Ans: (b)
Sol: 
Q13: The signal flow graph of a system is shown below. U(s) is the input and C(s) is the output
Assuming h₁ = b₁ and h₀ = b₀ − b₁a₁, the input-output transfer function  of the system is given by  (SET-3 (2014))
(a)
(b)
(c)
(d)
Ans: (c)
Sol: Using Mason's gain fomlula,
Transfer function,
Non-touching loops=zero

Q14: The signal flow graph for a system is given below. The transfer function Y(s)/U(s) for this system is  (2013)
(a)
(b)
(c)
(d)
Ans: (a)
Sol: Using mason's gain formula,
Δ = 1−[−2s⁻¹−2s⁻²−4−4s⁻¹]

Q15: The transfer function V₂(s)/V₁(s) of the circuit shown below is  (2013)
(a)
(b)
(c)
(d)
Ans: (d)
Sol: