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Benha UniversityFaculty of Engineering at ShoubraMechanical
Engineering DepartmentFourth Year (Production)
Final Term ExamDate: Sunday 24/1/2016Advanced Automatic Control
&Industrial Control ProcessDuration: 3 hours
Attempt all the following questions, and assume any
missing data when necessary.
The exam. Consists of 4 questions on two page
Total counted marks: 80
Question (1) (20 marks)
The electro-mechanical position control system shown in Fig. 1
controls the angular displacement θ2 by
selectingthe desired reference input (r).
Write the governing equation of the whole system in time
and s-domain. [10 marks
Draw the block diagram consider r(t) is the input and
θ2(t) is the output. [6 marks
Determine the transfer function θ2(s) / R(s). [4
marks
Figure 1
Question (2) (25 marks)
1. The hydraulic tank, shown in Fig. 2, is initially
filled with 0.2 m of water. If
the valve resistance is 0.1 s/m2 and tank area is 1 m2. If
tank is subjected to
constant input flow rate equal to 2 m3/s, determine the total
response h(t) of
the system and plot it roughly, then calculate steady state
error. [5 marks] 2. A block diagram model of a
DC-position servomechanism system used to
adjust the rotation angle shown in figure (2).
a. Find an expression for the overall transfer function;
[3 marks]
b. Obtain θo(t) if θi(t) is a unit-step input, assume T1=0,
T2=0.04, K1=80,
K2=0.5, K3=1; [8 marks]
c. Calculate also the maximum overshoot, rise time, peak
time and settling time then sketch roughly the system
response. [4 marks
3. Use Routh stability criterion to check the stability of
the system in problem shown in Fig. 3 and determine its
sustained oscillation. [5 marks
Figure 2
+
-
K 1 ϴo(s)ϴi(s)
K 3
+
-
Figure 3
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Question (3) (15 marks)
1. For the mechanical system shown in Fig. 4, obtain the
state space system that describe all the states of th
system. [9 marks]
2. Obtain the transfer function for the following state
space system described by:
[ ̇ ̇ ] = − 4 − 13 −1 + 11 = 1 0
[6 marks]Question (4) (25 marks)
1. For the following state space system, it is required to
study the Stability, Controllability and observability
̇ ̇ ̇ = 0 1 00 0 1− 2 − 4 − 6 + 0
00 11 0
= 1 0 00 1 0
[7 marks]2. Consider the control system shown in
Fig. 5 in which a PID controller is used to control the system.
The
PID controller has the transfer function () = (1 +
+ ). Using Ziegler – Nichols
tuning rule, iis require to determine the values of the parameters
, and . [10 marks]
3. Consider the regulator system shown in Fig.6. The plant
is given by ̇ = + Where; = 0 1 00 0 1− 1 − 5
− 6 , =
001. The system uses the state feedback control = −. Let
us choose the desiredclosed loop poles at = −2 + 4, = −2 − 4
and = −10. Determine the state feedback gain matrixK. [8 marks
Figure 4
Figure 5
Figure 6
