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EE351 – Control Systems and Instrumentation
Tutorial (2)
Modeling in the Time Domain
EE351- Control Systems and
Instrumentation
Dr. Mohamed Trabelsi
Tutorial
2
Objectives
•
Find a state-space representation, for a linear, time-invariant system.
•
Model electrical systems in state space.
•
Convert a transfer function to state space.
•
Convert a state-space representation to a transfer function.
1. Problem (1)
Represent the electrical network shown below in state space, where vo(t) is the output, and R = 3 Ω, L = 1 H, and C =
0.5 F.
L
iL
+
i
+ C
vC
C
–
u(t)
R
vo(t)
–
2. Problem (2)
Represent the electrical network shown below in state space, where iR(t) is the output.
3Ω
vi(t) +-
v1(t)
3F
Control Systems and Instrumentation – (EE351), Kuwait College of Science and Technology
2H
4v1(t)
3Ω
iR(t)
Page | 2
Tutorial
2
3. Problem (3)
Represent the electrical network shown below in state space, if the output is ( )
4. Problem (4)
Find the state-space representation in phase-variable form for each of the transfer functions shown below:
5. Problem (5)
Find the state-space representation in phase-variable form for each of the transfer functions shown below:
(a) ( ) = 2
25
+2 +1
(b) ( ) = 3
1
+6 2 +11 +6
Control Systems and Instrumentation – (EE351), Kuwait College of Science and Technology
Page | 3
EE351 – Control Systems and Instrumentation
Homework (1)
Name: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
EE351 – Control Systems and Instrumentation
KCST ID No: _ _ _ _ _ _ _ _ _ _ _ _
Dr. Mohamed Trabelsi
Homework
1
1. Problem (1)
Represent the electrical network shown below in state space, if the output is ( )
2. Problem (2)
Find the state-space representation for the phase-variable representation of the below transfer function:
3. Problem (3)
Convert the below state-space representation to a transfer function.:
EE351 – Control Systems and Instrumentation
Page | 2
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