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This document contains exam questions from Benha University's Electrical Engineering Department regarding automatic control systems. It asks students to determine differential equations and state space representations for various mechanical and electrical systems based on diagrams. It also asks students to derive transfer functions from state space representations, draw signal flow graphs from transfer functions, and represent a transfer function in controllable and observable canonical forms.

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33 views7 pages

Sheet

This document contains exam questions from Benha University's Electrical Engineering Department regarding automatic control systems. It asks students to determine differential equations and state space representations for various mechanical and electrical systems based on diagrams. It also asks students to derive transfer functions from state space representations, draw signal flow graphs from transfer functions, and represent a transfer function in controllable and observable canonical forms.

Uploaded by

knowledge engineering
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Benha University 1st Semester, 2021-2022

Faculty of Engineering at Shoubra Electrical Power


Electrical Engineering Department Automatic Control

Sheet (4)
Question (1)
For the following mechanical systems, determine:
(a) Differential system equations describing each system.
(b) State space representation.

Consider the input is (u) and the output is (x1 and x2).
Figure (1)

Consider the input is f(t) and the output is (x2).


Figure (2)

1
Benha University 1st Semester, 2021-2022
Faculty of Engineering at Shoubra Electrical Power
Electrical Engineering Department Automatic Control

Consider the input is f(t) and the output is (y2).


Figure (3)

Consider the input is f(t) and the output is (x1 and x2).
Figure (4)

2
Benha University 1st Semester, 2021-2022
Faculty of Engineering at Shoubra Electrical Power
Electrical Engineering Department Automatic Control

Consider the input is T(t) and the output is (θ1 and θ2).
Figure (5)

Question (2)
For the following electrical systems, determine:
(a) Differential system equations describing each system.
(b) State space representation.

Consider the input is (ei) and the output is (eo).


Figure (1)

3
Benha University 1st Semester, 2021-2022
Faculty of Engineering at Shoubra Electrical Power
Electrical Engineering Department Automatic Control

Consider the input is v(t) and the output is (VC).

Figure (2)

Consider the input is (ea(t) and TL) and the output (𝜽𝒎 , and 𝝎𝒎 ).
Figure (3)

4
Benha University 1st Semester, 2021-2022
Faculty of Engineering at Shoubra Electrical Power
Electrical Engineering Department Automatic Control

Consider the input is (ei) and the output is (eo)


Figure (4)

Consider the input is (V) and the output is (x1 and x2)
Figure (5)

5
Benha University 1st Semester, 2021-2022
Faculty of Engineering at Shoubra Electrical Power
Electrical Engineering Department Automatic Control

Question (3)
Given the following state space representation, determine the transfer function.
a- System (1)

−1 2 1
𝐴=[ ] , 𝐵 = [ ] , 𝐶 = [1 0], 𝐷 = [0]
3 −4 0

b- System (2)

−1 5 8 2
𝐴 = [−1 −2 1 ] , 𝐵 = [ 0] , 𝐶 = [1 2 3], 𝐷 = [0]
−2 5 −1 0

Question (4)
Use the following transfer functions to draw a state diagram (signal flow graph) and
derive the dynamic equations using phase variable (direct) decomposition, cascaded
decomposition, and parallel decomposition.
𝐶(𝑠) 𝑠+1
a- =
𝑅(𝑠) 𝑠 3 +9𝑠 2 +26𝑠+24

𝐶(𝑠) 10𝑠+10
b- =(
𝑅(𝑠) 𝑠+2)2 (𝑠+5)

𝐶(𝑠) 24(𝑠+1)(𝑠+2)
c- =
𝑅(𝑠) (𝑠+4)(𝑠+5)(𝑠+6)

6
Benha University 1st Semester, 2021-2022
Faculty of Engineering at Shoubra Electrical Power
Electrical Engineering Department Automatic Control
d-

Find the transfer function

Question (5)
Use the following transfer function to draw a state diagram (signal flow graph) and
derive the dynamic equations using the controllable and observable canonical form
representation.

𝐶(𝑠) 𝑠 2 + 4𝑠 + 5
= 3
𝑅(𝑠) 𝑠 + 3𝑠 2 + 6𝑠 + 18

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