Digital Control Systems (CSCT4108)
Computer Science - COS
Semester: First Semester
Level: 400
Year: 2016
EXERCISE I: 25 Marks
The system with e(t) as input and s(t) as output is established by the differential equation
( )
+
( )
= ( ) Where is the time
constant and the static gain.
Note: the initial value of the system is 0
Show that, if ( ) is the Laplace transform of ( ), therefore, the Laplace transform of
( )
is given by
( )
− (0).
Calculate the transmittance of the system
( )
=
( )
( )
Impulsion response: if
( )
= ( ), where is Dirac impulsion, calculate and draw ( )
Indice response: if
( )
= 1, calculate and draw ( ), the conclude
Supposing that the input is purely sinusoidal = ,
Show that
( )
= where is to be determine.
Draw the Bode, Black and Nyquist plot of this system
Exercise II: 45 marks
The system beside is to be
controlled, R1 =R2=47K, the
operational amplifiers U1A and
U1B are ideal. R3=R4=10K,
C1=C2=10nF.
1- Calculate the transfer
function at open
( )
=
( )
( )
and
draw its Bode diagram
2- If
( )
= ( ), calculate
s(t)
3- The system studied above
is now at unity feedback,
i) draw the block diagram and calculate the transfer function at close loop
( )
=
( )
( )
ii) give the order of this system and deduce the parameters (m and w0)
iii) draw the Black and the Nyquist diagram
MINISTRY OF HIGHER EDUCATION
UNIVERSITY OF BAMENDA
HIGHER TECHNICAL TEACHER TRAINING
COLLEGE
DEPARTMENT OF COMPUTER SCIENCE
LEVEL 300/FUNDAMENTAL
REPUBLIC OF CAMEROUN
PEACE – WORK – FATHERLAND
DIGITAL CONTROLLED SYSTEM: END OF FIRST SEMESTER EVALUATION
DURATION: 2HOURS; NO DOCUMENT IS ALLOWED
EXERCISE I: 25 Marks
The system with e(t) as input and s(t) as output is established by the differential equation
( )
+
( )
= ( ) Where is the time
constant and the static gain.
Note: the initial value of the system is 0
Show that, if ( ) is the Laplace transform of ( ), therefore, the Laplace transform of
( )
is given by
( )
− (0).
Calculate the transmittance of the system
( )
=
( )
( )
Impulsion response: if
( )
= ( ), where is Dirac impulsion, calculate and draw ( )
Indice response: if
( )
= 1, calculate and draw ( ), the conclude
Supposing that the input is purely sinusoidal = ,
Show that
( )
= where is to be determine.
Draw the Bode, Black and Nyquist plot of this system
Exercise II: 45 marks
The system beside is to be
controlled, R1 =R2=47K, the
operational amplifiers U1A and
U1B are ideal. R3=R4=10K,
C1=C2=10nF.
1- Calculate the transfer
function at open
( )
=
( )
( )
and
draw its Bode diagram
2- If
( )
= ( ), calculate
s(t)
3- The system studied above
is now at unity feedback,
i) draw the block diagram and calculate the transfer function at close loop
( )
=
( )
( )
ii) give the order of this system and deduce the parameters (m and w0)
iii) draw the Black and the Nyquist diagram
MINISTRY OF HIGHER EDUCATION
UNIVERSITY OF BAMENDA
HIGHER TECHNICAL TEACHER TRAINING
COLLEGE
DEPARTMENT OF COMPUTER SCIENCE
LEVEL 300/FUNDAMENTAL
REPUBLIC OF CAMEROUN
PEACE – WORK – FATHERLAND
DIGITAL CONTROLLED SYSTEM: END OF FIRST SEMESTER EVALUATION
DURATION: 2HOURS; NO DOCUMENT IS ALLOWED
EXERCISE I: 25 Marks
The system with e(t) as input and s(t) as output is established by the differential equation
( )
+
( )
= ( ) Where is the time
constant and the static gain.
Note: the initial value of the system is 0
Show that, if ( ) is the Laplace transform of ( ), therefore, the Laplace transform of
( )
is given by
( )
− (0).
Calculate the transmittance of the system
( )
=
( )
( )
Impulsion response: if
( )
= ( ), where is Dirac impulsion, calculate and draw ( )
Indice response: if
( )
= 1, calculate and draw ( ), the conclude
Supposing that the input is purely sinusoidal = ,
Show that
( )
= where is to be determine.
Draw the Bode, Black and Nyquist plot of this system
Exercise II: 45 marks
The system beside is to be
controlled, R1 =R2=47K, the
operational amplifiers U1A and
U1B are ideal. R3=R4=10K,
C1=C2=10nF.
1- Calculate the transfer
function at open
( )
=
( )
( )
and
draw its Bode diagram
2- If
( )
= ( ), calculate
s(t)
3- The system studied above
is now at unity feedback,
i) draw the block diagram and calculate the transfer function at close loop
( )
=
( )
( )
ii) give the order of this system and deduce the parameters (m and w0)
iii) draw the Black and the Nyquist diagram
MINISTRY OF HIGHER EDUCATION
UNIVERSITY OF BAMENDA
HIGHER TECHNICAL TEACHER TRAINING
COLLEGE
DEPARTMENT OF COMPUTER SCIENCE
LEVEL 300/FUNDAMENTAL
REPUBLIC OF CAMEROUN
PEACE – WORK – FATHERLAND
DIGITAL CONTROLLED SYSTEM: END OF FIRST SEMESTER EVALUATION
DURATION: 2HOURS; NO DOCUMENT IS ALLOWED
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