1
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s=-2 and s=-4, and one simple zero at s=-1. A unit step u(t) is applied at the input of the system. At steady state, the output has constant value of 1. The impulse response of this system is
A
[exp(-2t) + exp(-4t)]u(t)
B
[-4exp(-2t) + 12exp(-4t) - exp(-t)]u(t)
C
[-4exp(-2t) + 12exp(-4t)]u(t)
D
[-0.5exp(-2t) + 1.5exp(-4t)]u(t)
2
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
The number of open right half plane poles of $$$G\left(s\right)\;=\;\frac{10}{s^5\;+2s^4\;+3s^3\;+6s^2\;+5s\;+3}\;is$$$
A
$$0$$
B
1
C
2
D
3
3
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
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

Group I $$$P=\frac{25}{s^2+25}\;\;\;\;\;Q=\frac{36}{s^2+20s+36}$$$ $$$R=\frac{36}{s^2+12s+36}\;\;\;\;\;S=\frac{49}{s^2+7s+49}$$$

Group II GATE ECE 2008 Control Systems - Time Response Analysis Question 11 English 1 GATE ECE 2008 Control Systems - Time Response Analysis Question 11 English 2 GATE ECE 2008 Control Systems - Time Response Analysis Question 11 English 3 GATE ECE 2008 Control Systems - Time Response Analysis Question 11 English 4

A
$$\begin{array}{l}P\;\;\;\;Q\;\;\;\;R\;\;\;\;S\\3\;\;\;\;\;1\;\;\;\;\;4\;\;\;\;\;2\end{array}$$
B
$$\begin{array}{l}P\;\;\;\;Q\;\;\;\;R\;\;\;\;S\\3\;\;\;\;\;2\;\;\;\;\;4\;\;\;\;\;1\end{array}$$
C
$$\begin{array}{l}P\;\;\;\;Q\;\;\;\;R\;\;\;\;S\\2\;\;\;\;\;1\;\;\;\;\;4\;\;\;\;\;3\end{array}$$
D
$$\begin{array}{l}P\;\;\;\;Q\;\;\;\;R\;\;\;\;S\\3\;\;\;\;\;4\;\;\;\;\;1\;\;\;\;\;2\end{array}$$
4
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
A certain system has transfer function $$G\left(s\right)=\frac{s+8}{s^2+\alpha s-4}$$, where $$\alpha$$ is a parameter. Consider the standard negative unity feedback configuration as shown below GATE ECE 2008 Control Systems - Stability Question 12 English Which of the following statements is true?
A
The closed loop system is never stable for any value of $$\alpha$$
B
For some positive values of $$\alpha$$, the closed loop system is stable, but not for all positive values
C
For all positive values of $$\alpha$$, the closed loop system is stable
D
The closed loop system is stable for all values of $$\alpha$$, both positive and negative
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