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Control Systems
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1
GATE ECE 2024
MCQ (More than One Correct Answer)
+2
-0

Consider a system $S$ represented in state space as

$$\frac{dx}{dt} = \begin{bmatrix} 0 & -2 \\ 1 & -3 \end{bmatrix}x + \begin{bmatrix} 1 \\ 0 \end{bmatrix}r , \quad y = \begin{bmatrix} 2 & -5 \end{bmatrix}x.$$

Which of the state space representations given below has/have the same transfer function as that of $S$?

A

$$\frac{dx}{dt} = \begin{bmatrix} 0 & 1 \\ -2 & -3 \end{bmatrix}x + \begin{bmatrix} 0 \\ 1 \end{bmatrix}r , \quad y = \begin{bmatrix} 1 & 2 \end{bmatrix}x.$$

B

$$\frac{dx}{dt} = \begin{bmatrix} 0 & 1 \\ -2 & -3 \end{bmatrix}x + \begin{bmatrix} 1 \\ 0 \end{bmatrix}r , \quad y = \begin{bmatrix} 0 & 2 \end{bmatrix}x.$$

C

$$\frac{dx}{dt} = \begin{bmatrix} -1 & 0 \\ 0 & -2 \end{bmatrix}x + \begin{bmatrix} -1 \\ 3 \end{bmatrix}r , \quad y = \begin{bmatrix} 1 & 1 \end{bmatrix}x.$$

D

$$\frac{dx}{dt} = \begin{bmatrix} -1 & 0 \\ 0 & -2 \end{bmatrix}x + \begin{bmatrix} 1 \\ 1 \end{bmatrix}r , \quad y = \begin{bmatrix} 1 & 2 \end{bmatrix}x.$$

2
GATE ECE 2018
MCQ (Single Correct Answer)
+2
-0.67
The state equation and the output equation of a control system are given below:

$$\mathop x\limits^. = \left[ {\matrix{ { - 4} & { - 1.5} \cr 4 & 0 \cr } } \right]x + \left[ {\matrix{ 2 \cr 0 \cr } } \right]u,$$

$$y = \left[ {\matrix{ {1.5} & {0.625} \cr } } \right]x.$$

The transfer function representation of the system is
A
$${{3s + 5} \over {{s^2} + 4s + 6}}$$
B
$${{3s - 1.875} \over {{s^2} + 4s + 6}}$$
C
$${{4s + 1.5} \over {{s^2} + 4s + 6}}$$
D
$${{6s + 5} \over {{s^2} + 4s + 6}}$$
3
GATE ECE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
A second order LTI system is described by the following state equation. $$$\eqalign{ & {d \over {dt}}{x_1}\left( t \right) - {x_2}\left( t \right) = 0 \cr & {d \over {dt}}{x_2}\left( t \right) + 2{x_1}\left( t \right) + 3{x_2}\left( t \right) = r\left( t \right) \cr} $$$

When x1(t) and x2(t) are the two state variables and r(t) denotes the input. The output c(t)=X1(t). The systyem is

A
undamped (oscillatory)
B
under damped
C
critically damped
D
over damped
4
GATE ECE 2016 Set 3
MCQ (Single Correct Answer)
+2
-0.6
A second-order linear time-invariant system is described by the following state equations $$$\eqalign{& {d \over {dt}}{x_1}\left( t \right) + 2{x_1}\left( t \right) = 3u\left( t \right) \cr & {d \over {dt}}{x_2}\left( t \right) + {x_2}\left( t \right) = u\left( t \right) \cr} $$$

Where x1(t), then the system is

A
controllable but not observable
B
observable but not controllable
C
both controllable and observable
D
neither controllable nor observable
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GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics