GATE 2023 - Important Concepts, Short cuts, Complete Solutions, Examples and Practice Problems

GATE 2007 ECE Control Systems - Complete Video Solutions with Answers

GATE 2007

1. If the closed loop transfer function of a control system is given as T(s) = (s – 5)/[(s + 2)(s + 3)], then it is

a) an unstable system

b) an uncontrollable system

c) a minimum phase system

d) a non-minimum phase system

Solution : https://www.youtube.com/watch?v=4soEmuGvfcI

2. If the Laplace Transform of a signal y(t) is Y(s) = 1/[s(s – 1)], then its final value is:

a) – 1

b) 0

c) 1

d) unbounded

Solution : https://www.youtube.com/watch?v=cvCDerivzj0

3. A control system with a PD controller is shown in the figure.

If the velocity error constant K_v = 1000 and the damping ratio ξ = 0.5, then the values of K_p and K_D are

a) K_p = 100, K_D = 0.09

b) K_p = 100, K_D = 0.9

c) K_p = 10, K_D = 0.09

d) K_p = 10, K_D = 0.9

Solution : https://www.youtube.com/watch?v=vxHx4zTs5vg

4. The transfer function of a plant is T(s) = 5/[(s + 5)(s² + s + 1)]. The second order approximation of T(s) using dominant pole concept is

Solution : https://www.youtube.com/watch?v=y1BxLLTHJOI

5. The open loop transfer function of a plant is given as G(s) = 1/(s² – 1). If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is

Solution : https://www.youtube.com/watch?v=HJ09FtxcO-I

6. A unity feedback control system has an open loop transfer function G(s) = – K/[s(s² + 7s + 12)]. The gain k for which s = –1+j1 will lie on the root locus of this system is

a) 4

b) 5.5

c) 6.5

d) 10

Solution : https://www.youtube.com/watch?v=ppJqQhOp_xk

7. The asymptotic Bode plot of a transfer function is as shown in figure. The transfer function G(s) corresponding to this Bode plot is

Solution : https://www.youtube.com/watch?v=fpM5ezwr90c

8. The state space representation of a separately excited DC servo motor dynamics is given as

where ω is the speed of the motor, i_a is the armature current and u is the armature voltage. The transfer function of the motor is

Solution : https://www.youtube.com/watch?v=jTt-sWQZS0Y

Statement for Linked Answer Questions 9 & 10:

9. The eigen value and eigen vector pairs (λ_i, v_i) for the system are

Solution :

10. The system matrix A is

Solution :

GATE 2008 ECE Control Systems - Complete Video Solutions with Answers

GATE 2008

1. The pole-zero plot given below corresponds to a

a) Low pass filter

b) High pass filter

c) band pass filter

d) Notch filter

Solution : https://www.youtube.com/watch?v=ZaDLLdETZPs

2. Step response of a set of three second order under damped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems?

Solution : https://www.youtube.com/watch?v=X0RUYGCL8P4

3. Group – I lists a set of four transfer functions. Group – II gives a list of possible step responses y(t). Match the step responses with the corresponding transfer functions.

a) P - 3, Q - 1, R - 4, S - 2

b) P - 3, Q - 2, R - 4, S - 1

c) P - 2, Q - 1, R - 4, S - 3

d) P - 3, Q - 4, R - 1, S – 2

Solution : https://www.youtube.com/watch?v=jXGZriqlb1c

4. A certain system has transfer function G(s) = (s + 8)/(s² + αs – 4 ), where α is a parameter. Consider the standard negative unity feedback configuration shown below.

Which of the following statements is true?

a) The closed loop system is never stable for any value of α

b) For some positive values of α, the closed loop system is stable, but not for all positive values

c) For all positive values of α, the closed loop system is stable

d) The closed loop system is stable for all values of α, both positive and negative

Solution : https://www.youtube.com/watch?v=lgA_id_ATbY

5. A signal flow graph of a system is given below.

The set of equations that correspond to this signal flow graph is

Solution : https://www.youtube.com/watch?v=cxlX8Rpj9cs

6. The number of open right half plane poles of G(s) = 10 / (s⁵ + 2s⁴ + 3s³ + 6s² + 5s + 3) is

a) 0

b) 1

c) 2

d) 3

Solution : https://www.youtube.com/watch?v=Seaj7dcM1yk

7. The magnitude of frequency response of an under damped second order system is 5 at 0 rad/sec and peaks to 10/√3 at 5√2 rad/sec. The transfer function of the system is

Solution : https://www.youtube.com/watch?v=3a4n-8XUFCg

8. Group – I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the condition R₂C₂>R₁C₁. The transfer function V_o/V₁ represents a kind of controller. Match the impedance's in Group – I with the types of controllers in Group – II.

a) Q – 1, R – 2

b) Q – 1, R – 3

c) Q – 2, R – 3

d) Q – 3, R – 2

Solution : https://www.youtube.com/watch?v=Q3O1G2CU5Xw

GATE 2009 ECE Control Systems - Complete Video Solutions with Answers

2009

1. The magnitude plot of a rational transfer function G(s) with real coefficients is shown below. Which of the following compensator has such a magnitude plot?

a) Lead compensator

b) Lag compensator

c) PID compensator

d) Lead – Lag compensator

Solution : https://www.youtube.com/watch?v=JVBUSrYEb7Q

2. If the transfer function of the following circuit is V_o(s)/V_i(s) = 1/(2+sCR), then the value of the load resistor R_L is

a) R/4

b) R/2

c) R

d) 2R

Solution : https://www.youtube.com/watch?v=0bJX_BCy6bc

3. consider the system,

where p and q are arbitrary real numbers, which one of the following statements about the controllability of the system is TRUE?

a) the system is completely state controllable for any non zero values of p and q

b) only p=0 and q=0 result in controllability

c) the system is uncontrollable for all values of p and q

d) we cannot conclude about controllability from the given data

Solution : https://www.youtube.com/watch?v=MvBkDRPjIcY

4. the feedback configuration and the pole-zero locations of G(s) = (s² – 2s + 2)/(s² + 2s +2), are shown below.

The root locus for negative values of k, i.e. for –∞ < k < 0, has break away/break in points and angle of departure at pole P (w.r.t. the positive real axis) equal to

a) ± √2 and 0^o

b) ± √2 and 45^o

c) ± √3 and 0^o

d) ± √3 and 45^o

Solution : https://www.youtube.com/watch?v=uagcsFAoEB0

5. The unit step response of an under damped second order system has steady state value of – 2. Which of the following transfer functions has these properties?

Solution : https://www.youtube.com/watch?v=FVflQ49wsF8

Common Data Questions: (6 & 7)

The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed loop system in the feedback configuration shown.

6. Which of the following statements is TRUE?

a) G(s) is an all pass filter

b) G(s) has a zero in the right half plane

c) G(s) is the impedance of a passive network

d) G(s) is marginally stable

Solution : https://www.youtube.com/watch?v=2t0EyW64kfI

7. The gain and phase margin of G(s) for closed loop stability are

a) 6 dB and 180^o

b) 3 dB and 180^o

c) 6 dB and 90^o

d) 3 dB and 90^o

Solution : https://www.youtube.com/watch?v=RlFKoEWXgw8

GATE 2010 ECE Control Systems - Complete Video Solutions with Answers

2010

1. The transfer function Y(s)/R(s) of the system shown is

Answer:B

Solution : https://www.youtube.com/watch?v=ORTP8lmNl44

2. A system with transfer function Y(s)/X(s) = s/(s + p) has an output y(t) = cos(2t – π/3) for the input signal x(t) = p cos(2t – π/2). Then, the system parameter 'p' is

a) √3

b) 2/√3

c) 1

d) √3/2

Answer:B

Solution : https://www.youtube.com/watch?v=3WAIkGRRes4

3. For the asymptotic bode magnitude plot shown below, the system transfer function can be

Solution : https://www.youtube.com/watch?v=Tt58Wfn-dsQ

4. Given f(t) = L^–1[(3s + 1) / (s³ + 4s² + (k-3)s)]. If Lim_{t
-> ∞} f(t) = 1, then the value of k is

a) 1

b) 2

c) 3

d) 4

Solution : https://www.youtube.com/watch?v=q65ZfJH4Ww0

5. A unity negative feedback closed loop system has a plant with the transfer function G(s) = 1/(s² + 2s + 2) and a controller G_c(s) in the feed forward path. For a unit step input, the tranfer function of the controller that gives minimum steady state error is