Final Exam (Part 2)

bustlingdivisionElectronics - Devices

Nov 15, 2013 (3 years and 8 months ago)

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Digital Control Systems

Final Exam (Part 2)

Instruction



The e
xam in

this part contains

3 problems,
each of which has 15 points.
Do only 2 problems.



All the problems are solvable by hand computation. However,
some problems can also be solved
by MATLAB.



If you solve a
problem using MATLAB
,
you are required to list all MATLAB commands used in
the problem, and to attach

all
numerical and
/or

grap
hical
results obtain
ed

from MATLAB

in
your solution sheets.



Problem 1

We are given the continuous time plant

10( 1)
( ).
5
s
G s
s
 



First,
suppose that the plant
( )
G s
is controlled by a

gain

K

(
both negative and positive
)
in
the closed
-
loop system below
:


a)

Let
max
K

and
min
K

be
t
he maximum
and minimum
possible value
s
, respectively,
of the
gain
K
for
which the above system is stable. Compute
min
K
and
max
K
. (4 points)


Now consider t
he digital control system below:



b)

Let
max
K

and
min
K

be
t
he maximum
and minimum
possible value
s
, respectively,
of the
gain
K
for
which the digital control

sy
stem
is stable.

Express
min
K
and
max
K
in terms of the sampling period
T
.

(5 points)

c)

C
alculate
min
K
and
max
K
in p
roblem 1b)
when
0.1.
T s


(2 points)

Now consid
er the closed
-
loop system below. Note that there is one sample delay in the feedback path
.
The sampling period is assumed to be 0.1

sec.


d)

Let
max
K

and
min
K

be
t
he maximum
and minimum
possible value
s
, respectively,
of the
gain
K
for
w
hich the above

sy
stem
is stable.

Calculate
min
K
and
max
K
, and then
discuss the differences betwee
n
this answer and

those of p
roblems
1a) and 1c). (4 points)