ECSE-4760
Real-Time Applications in Control & Communications
Spring 2014
Exam #2
Monday 5/12 12:00 PM JEC-6314
Name ________________________
Section 1: MR 1:30
(Grades will be posted on SIS when they are completed.)
This exam is open book, open notes, etc. with calculators, but NO laptops, Internet connections, cell phones, …,
and no sharing materials. You need your own copies of everything, including lab reports. If you didn’t bring
your own hardcopies, you will be penalized.
Answer questions in only 5 out of the 8 sets corresponding to each of the experiments in the lab. You do not
need to choose the experiments you performed but you will probably wish to do so. If you answer more than 5
sets, the first 5 will be graded. Each set is worth 20 points (max) with the breakdown shown by the questions.
If you are missing any grades on RPILMS, make sure you bring the reports to me (JEC-6028) before the end of
the day today to get your records corrected.
I Digital Logic ______
II Voice Processing ______
III Binary Communications ______
IV Digital Filter ______
V Interactive Graphics ______
VI Hybrid Control ______
VII DC Motor ______
VIII Optimal Control ______
TOTAL ______
I Digital Logic
2014
Name _________________________
1. (2 pt) What is the dual of (A  B C)(A D  BE )BCE  C ?
2. (6 pt) For the following K-map find 2 equally reduced forms of the output function F. (Don’t care = d.)
AB\CD
00
01
11
10
00
d
0
0
d
01
0
1
1
0
11
0
1
d
0
10
d
0
1
d
3. Given the state transition flow diagram below:
a. (5 pt) Can any state(s) be removed and still maintain the original functionality? If so, redraw the diagram with
the state(s) removed
0/0
1/0
0/0
1/0
A
B
0/0
C
1/1
D
1/1
0/0
b. (2 pt) What is the fewest number of flip-flops necessary to implement the (reduced if applicable) system?
c. (5 pt) Find the (reduced if applicable) system’s next state and output tables.
II Voice Processing
2014
Name _________________________
4
x 10
1.5
1
0.5
0
-0.5
-1
1900
2000
2100
2200
2300
2400
2500
2600
1a. (3 pt) In the speech signal shown above, for the numbered samples from 1800 to 2400, what is the most
likely sound?
i) Soft “S” sound
ii) “SH” sound
iii) Short “A” sound
iv) Unvoiced “TH” sound
b. (5pt) If the sample frequency fs = 8.192kHz, what is the pitch Period and pitch frequency?
c. (2pt) Assuming the peaks in the signal above were all close to 1 volt, which would have a higher crest factor,
the voice signal above or a sine wave whose frequency is the pitch frequency and whose amplitude is 1 volt?
II Voice Processing
2014
Name _________________________
2. Two identical signals are illustrated below, and they are to be transmitted over two channels using two
different delta modulators but both with a sample frequency of 1 kHz. Assume there is no D.C. blocking.
a. (4 pt) For each modulator, draw the input/output characteristics on the axes below and include scale values.
Delta Modulator 1: B = 0.5, A = C = D = 0
Delta Modulator 2: A = 0.5, B = 1.0, C = 0.2, D = 1.0
Modulator 1
Vout
Modulator 2
Vout
Vin
Vin
b. (6 pt) On each of the input signals, sketch the appropriate receiver outputs. Use a starting output value of 0 V
at t = 0, held for one sample.
Delta Modulator 1
Volt s
3
2
1
2
4
6
8
10
12
time
(msec.)
2
4
6
8
10
12
time
(msec.)
Delta Modulator 2
Volt s
3
2
1
III Binary Communications
2014
Name _________________________
1. The following plot shows the output signal quality vs. in-channel noise.
a. (2 pt) Indicate which curve corresponds to PAM and which to PCM.
b. (4 pt) The input source can be expressed as Vinput (t) = 10 cos (30 t + 3/4) Volts and the PCM pulse
amplitude is 10 Volts. Both modulations are using RZ. What is the Signal-to-noise ratio (in dB) at the dotted
line in the plot above for just the PCM signal?
c. (3 pt) Explain why the rate of change is large at point “a” when compared to the straight-line curve.
2. (5 pt) A (7,4) Hamming code similar to the one in the lab receives the word 1001111. It is known that the
code received has 2 bit errors. There are several legal codewords that can lead to this with double errors. Find 2
of these codewords.
III Binary Communications
2014
Name _________________________
3. While some code words are transmitted from a transmitter to a receiver, Gaussian noise is being added to the
channel. As a result errors are seen at the receiver side as shown below.
TRAN SMITTER
RECEIVER
NOISE
Code word #1
Code word #2
Code word #3
Code word #4
Code word #5
Code word #6
Code word #7
Code word #8
Sender
000001
110001
111101
111110
110010
101010
010101
111000
Received code words
000001
100001 (1 error)
111101
111110
110011 (1 error)
101010
111101 (2 errors)
111000
a. (2 pt) It has been shown that the minimum hamming distance is 2. What is the maximum hamming distance
between any to words of this code (assume there are only 8 valid code words as shown)?
b. (2 pt) How many errors can be detected by this code?
c. (2 pt) How many errors can be corrected by this code?
IV Digital Filter
2014
Name _________________________
s2
1
4
 1

:
2
s  3s  2
s 1 s 2
a. (5 pt) Using a (scaled) bilinear transformation with T=0.10 s, find the cut-off frequency for the digital filter
H(z) given the analog filter’s cut-off frequency, which may be taken to be 2 radian/sec here.
1.Given a second order HPF H(s) 

b. (7 pt) Find the impulse invariant transformation of H(s) in a. with T = 0.10.
IV Digital Filter
2014
Name _________________________
2. A causal high order digital filter H(z) has 4 zeros located at z=1, z=j, z=-1, and z=-j and all the poles at z=0.
a. (3 pt) Find H(z) in ratio of polynomial form (not factored form).
b. (3 pt) Sketch the plot of H (z) z e j  for 0    2 . Assume the filter’s gain is normalized for unity peak gain.
c. (2 pt) If the sample frequency is 20 kHz, what is the frequency of the first peak in the spectrum (closest to 0
Hz)?
V Interactive Graphics
2014
Name _________________________
A(s  p)
, what values of  will guarantee that G(s) is a lag controller?
(s  p)
iii)   1
iv)   1
v) none of these
1. (3 pt) For the controller G(s) 
i)   0
ii)   0

3.986
8.2369

(the model of the new D.C. motor system) with negative
s(4839s  1) s(s  2.0664)
unity feedback what is the form of the time domain impulse response of the feedback system? It is not
necessary to solve completely if it can be shown how the magnitude A, , , or  can be evaluated.
2. (7 pt) For G p (s) 


V Interactive Graphics
2014
Name _________________________
3. For the given signals whose statistical parameters are (assuming the noise is zero mean Gaussian):
Signal #1
Signal #2
X0
4
0
Y0
4
4
1
2
X
2
1
Y
0
0

Probability
3/4
1/4
Cost
1
1
a. (7 pt) Sketch the approximate decision boundary on the axes below. The exact x-position is not critical, but
the correct curve shape and y-position is important. Draw the standard deviation contour and label the regions
for signals #1 and #2.
b. (3 pt) If the relative probabilities above are changed to 1/2 and 1/2, the width of Signal #1’s region would:
i) decrease
ii) remain unchanged
iii) increase
iv) can’t be determined
VI Hybrid Control
2014
Name _________________________
ANSWER ANY COMBINATION OF QUESTIONS THAT ADD UP TO 20 POINTS. 10-POINT
QUESTIONS MUST BE FULLY ANSWERED.
1. (5 pt) TRUE or FALSE: An ideal finite settling time (ripple free) controller with no limits on the range of the
output control voltage, is able to control both the overshoot and settling time of the feedback system's output
with proper values of the coefficients and sample period.
2. (5 pt) TRUE or FALSE: In a digital approximation to a continuous controller, setting the sampling period to
half the shortest time constant of the GP(s) will result in a near optimal controller.
3. (10 pt) Using the Graham-Lathrop method, find the gain values for a PI controller applied to the following
1
plant: Gp (s) 
(4s  1)(12s  1)
VI Hybrid Control
2014
Name _________________________
4. (10 pt) Given a set of pole placement gains, kc1 and kc2, determine the following closed loop system
characteristics: damping ratio, natural frequency, and pole locations.
Kc1 = 6.422
Kc2 = 1.478

 0
1 
Ac  

0.75 1.75
0
Bc   
4
Hybrid Control (cont.)
2014
Name _________________________
5. (20 pt) Someone has designed an FST controller for a second order process without a time delay. Using the
given set of gains, find the transfer function of the original plant in the following form:
1
(T1s + 1)(T2 s + 1)
Ts=3.5 sec.
Ke0=4.23
Ke1=-3.71
Ke2=0.59
Ku1=0.669
Ku2=0.332
Gp (s) 
VII DC Motor Control
2014
Name _________________________
4z  0.75
,
3z  0.25
a. (3 pt) Find the difference equation for this discrete controller.
1. Consider D(z) 
b. (8 pt) Suppose that the controller in a. has been obtained from an analog design using the Tustin
approximation with a sampling period of 0.5 second. Find the original, continuous transfer function, Gc(s).
VII DC Motor Control
2014
Name _________________________
2. (9 pt) A PD controller, Gc(s), is used in conjunction with a plant, Gp(s), and it lies in the negative feedback
path. If an overshoot of 3% and a settling time of 0.5 seconds is desired, find the appropriate values for K p and
Kd. Set up all the equations necessary to find a solution, but do not solve them. Note the plant has no deadband.
(Hint: you may want to use the characteristic equation for the closed-loop system.)
503
Gp (s) 
Gc (s)  K p  K d s
s(s  71)
VIII Optimal Control
2014
Name _________________________
1. (10 pt) Given a system equation x’(t) = 4x(t) + 5u(t), y(t) = 2x(t) – u(t), state penalty matrix Q = [3], and
control penalty matrix R = [0.5], find the solutions to the Riccati equation and the optimal feedback gain matrix
G.
2. (8 pt) For a discrete system with:
 0
0 
4 0 0
0
1 


 


A   0
1
1 ,B  0 ,C  1 0 2,D  0,Q  0 2 0,R  0.75 and Ricatti solution



40 15 30

25

0 0 1

5.92 1.18 1.41 
0.125 1 1




P = 1.18 7.39 6.08 
You are given ( A)1  0.625 1 0


1.41 6.08 13.57

0.025 0 0

find only the optimal feedback gain for the first state, g1 of G = [g1 g2 g3].

3. (6 pt) Which of the following matrices are Positive Definite?
4 5
4 5
4 5
5 2
5 2
5 2
4 5
5 2
4 5
5 2