ECSE-4760
Real-Time Applications in Control & Communications
Spring 2015
Exam #2
Thursday 5/21 11:30 AM Troy-2018
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. No softcopies are allowed!
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. It
is more important to set up the equations for the solutions than to solve them completely. You may go back if
you have time at the end to do so.
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
2015
Name _________________________
1. (6 pt) Find the reduced SOP expression for (𝐴 + 𝐵̅ 𝐶)(𝐴̅𝐷 + 𝐵𝐸̅ )𝐵̅ 𝐶𝐸̅ + 𝐶̅ ?
̅ + 𝐴𝐵𝐶 + 𝐴𝐶𝐷
̅ + 𝐴̅𝐵̅ 𝐷
̅ + 𝐵𝐶𝐷
̅ + 𝐴̅𝐵̅ 𝐶̅ 𝐷
̅ using K- maps.
2. (4 pt) Reduce the expression 𝐹 = 𝐵𝐷 + 𝐴𝐵̅ 𝐶𝐷
3. Given the state transition flow diagram below for a system with inputs and output:
01/1
00/0
11/0
A
10/0
00/1
10/1
B
01/0
11/0 00/1
C
11/0
01/1
D
10/1
11/0
10/0
00/1
01/1
a. (2 pt) Is it possible for a set of inputs to get to state D from state A only outputting 0s? If so, what set of inputs
will do it?
b. (8 pt) Find the system’s next state and output tables.
II Voice Processing
2015
Name _________________________
1. (6 pt) Match each speech signal shown below (the sample frequency fs = 8.192kHz) with a choice below.
i) Soft “S” sound
ii) Voiced “TH” sound as in “this”
iii) Long “O” sound
iv) End “T” sound as in “left”
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
0
200
400
600
800
0.025
1000
1200
1400
1600
1800
0.5
0.02
0.4
0.015
0.3
0.01
0.2
0.005
0
0.1
-0.005
0
-0.01
-0.1
-0.015
-0.2
-0.02
-0.025
0
50
100
150
200
250
300
350
400
450
500
-0.3
0
100
200
300
400
500
600
700
800
900
2a. (2pt) Rate the following signals in order from lowest to highest crest factor: 2sin(2π4000t), a 1Vpp triangle
wave at 500 Hz, a 2Vpp square wave at 100 Hz, a comb function (.1V spikes lasting 0.1ms and repeating every
2ms.?
b. (2pt) What is the lowest possible value for a crest factor that any signal can have?
II Voice Processing (cont.)
2015
Name _________________________
3. Two identical signals are illustrated below, that have been transmitted over two channels using two different
delta modulators but both with a sample frequency of 320Hz. Assume there is no D.C. blocking or LPF.
a. (7 pt) Find the A, B, C, & D parameters for each delta modulator that will produce the corresponding output.
Note that the y-axis scales are not the same in each plot.
b. (3 pt) For each modulator, draw the input/output characteristics on the axes below and include scale values.
Modulator 1
Vout
Modulator 2
Vout
Vin
Vin
In: 20Hz sin, Out: 2-bit delta modulation (fs=160Hz)
In: 20Hz sin, Out: 2-bit delta modulation (fs=160Hz)
0.8
0.5
0.4
0.6
0.3
0.4
0.2
0.1
0.2
0
0
-0.1
-0.2
-0.2
-0.3
-0.4
-0.4
-0.6
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2 -0.5
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
III Binary Communications
2015
Name _________________________
1a. (3 pt).If the SNR = 10.46dB for a PCM digital signal with 100% Duty Cycle and 5V amplitude pulses, what
is the RMS voltage of the noise?
b. (3 pt) What would the SNR be in 1a. if the Duty Cycle were reduced to 25%?
2. (2 pt) TRUE/FALSE: In-phase signaling alone (without any quadrature components) cannot use carrier
modulated pulses.
3. A (7,4) Hamming code can be extended to (8,4) by adding a parity bit to the full 7-bit string:
c1 c2 m1 c3 m2 m3 m4 p with
c1 = m1  m2  m4,
c2 = m1  m3  m4,
c3 = m2  m3  m4, and
p = c1  c2  m1  c3  m2  m3  m4
a. (2 pt) What is the efficiency of this code?
b. (2 pt) What is the minimum hamming distance of the code? (Assume it can maximally detect one more bit
error than the (7,4) code.)
c. (4 pt) What are the possible modes for error corrections and/or simultaneous error detection given the
possibility of 1 bit error, 2 bit errors, 3 bit errors, etc.?
d. (4 pt) If the received codeword is 00110100 and it is known to have at least 1 bit error, determine how many
bit errors it contains and if it is correctable, find the corrected codeword.
IV Digital Filter
2015
Name _________________________
1. A second order HPF is designed to have a cutoff frequency of 60Hz with a sampling frequency of 10kHz. The
coefficients are entered into a DSP correctly, but instead of a setting the sampling frequency to 10kHz it is
mistakenly set to 10krad/s. What is the end effect on the filter's operation?
a. (1 pt) What is its sample period?
b. (4 pt) What is its effective cutoff frequency in Hz?
c. (1 pt) Will it still behave as a HPF or will it be transformed into a LPF?
2. (8 pt) The impulse invariant transformation of H(s) is 𝐻(𝑧) =
s = -4, find H(s).
0.6𝑧−0.134
𝑧−0.67
. Assuming there is at least one pole at
IV Digital Filter (cont.)
2015
Name _________________________
3. A digital filter with fs = 18kHz has the following pole-zero diagram (top half only).
a. (1 pt) What type is it?
i) LPF ii) BPF ii)BSF
iv) HPF
v) All Pass Filter (only changes phase)
b. (1 pt) What is the order of the filter? (None of the poles shown are repeated poles.)
4. (4 pt) What is/are the cutoff frequency(ies)?
V Interactive Graphics
2015
Name _________________________
1. (3 pt) How far apart must the pole and zero be in a lead compensator for the maximum phase to approach 20?
3.986
8.2369
(the model of the new D.C. motor system) what purely

s(4839s  1) s(s  2.0664)
proportional feedback gain will result in repeated poles?
2. (5 pt) For G p (s) 

V Interactive Graphics (cont.)
2015
Name _________________________
3. For the given signals whose statistical parameters are (assuming the noise is zero mean Gaussian):
Signal #1
Signal #2
Mean x0
1
0
1
2

Probability
3/4
1/4
Cost
C
1
a. (8 pt) Find the linear or quadratic equation that can be solved to give the decision boundary in terms of Signal
#1’s cost C.
b. (4 pt) If the a priori probabilities above are changed to ½ and ½ and both functions have the same standard
deviation, while increasing C, the width of Signal #1’s region would (select all that apply):
i) decrease ii) remain unchanged iii) increase iv) move to the left v) move to the right iv) can’t be
determined
VI Hybrid Control
2015
Name _________________________
ANSWER ANY COMBINATION OF QUESTIONS THAT ADD UP TO 20 POINTS. 10-POINT
QUESTIONS MUST BE FULLY ANSWERED.
1. Assuming the 2.5V step input is applied at t = 0, the following step response for a system is observed.
2.5
0
1
2
3
4
a. (7 pt) Find the Ziegler-Nichols L and R values and the PID feedback control gains.
b. (3 pt) If L doubles but R remains the same, find the new values for the PID gains.
5 time (s)
VI Hybrid Control (cont.)
2015
Name _________________________
2
2a. (7 pt) Use the Graham-Lathrop method to find the PID gains for plant 𝐺𝑃 (𝑠) = (𝑠+3)2 with ω0 = 1.5.
b. (3 pt) Find the PD controller gains for the above plant?
VI Hybrid Control (cont.)
2015
Name _________________________
3. (10 pt) For a system x’(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t), if the pole placement gains are kc1 = 4.5 and
kc2 = 1.5 for a response with ζ = 0.707 and ωn = 4, determine the A and B matrices (assume canonic form and
that a1/a2 = 3.29).
VI Hybrid Control (cont.)
4. (10 pt) For 𝐺𝑃 =
𝑒 −0.064𝑠
(𝑠+1)(𝑠+5)
2015
Name _________________________
find the Gallier-Otto PID controller gains.
VII DC Motor Control
2015
Name _________________________
1a. (6 pt) Find D(z), the minimal prototype compensator for the lab D.C. motor system when the sampling period
is 150ms.
b. (3 pt) If the D.C. motor system in a. is hardwired with an amplifier whose gain is 10 and considered to be part
of the new system, how would D(z) change?
2. (3 pt) Given 𝐺𝐶 (𝑠) =
constant for the system.
7(𝑠+10)
𝑠+20
50
𝑎𝑛𝑑 𝐺𝑃 (𝑠) = 𝑠(𝑠+0.5), find the velocity error constant and the acceleration error
VII DC Motor Control (cont.)
2015
Name _________________________
3. (8 pt) An FST controller for a 1st order system requires a control output of 100V at t = 0 when the sample
period T is set to 1.0ms What must the sample period be increased to in order for the control output to be
reduced to 10V at t = 0. Remember, the form of the output for a 1st order system is A(1-e-t), assuming a unity
time constant.
VIII Optimal Control
2015
Name _________________________
1. (1 pt) How many positive solutions exist to the Riccati equation for a 1st order digital system.
2. (3 pt) TRUE/FALSE: The state feedback gains determined by the Riccati solution are completely independent
of the output equation coefficients but not the initial state of the system.
3. (3 pt) TRUE/FALSE: The calculations of the feedback gain vector G for the continuous optimal LQR does not
depend on the system’s A matrix.
3
3
2
4. (6 pt) Given the gain is calculated by 𝐺 = − (4) (2) (2) (3 √3 − 1), find the matrix equation for the original
system of x as a function the states and input u and the values of Q and R.
0
0
1
0
(
5. (7 pt) For the system: 𝑥̇ 𝑡) = [ 0
𝑦(𝑡) = [−1.5 √2 9]𝑥(𝑡) + √3𝑢(𝑡)
1
0 ] 𝑥(𝑡) + [5] 𝑢(𝑡)
−2 −5 −8
4
∞
1
0
0
1
𝐽(𝑡) = ∫ {𝑥 ′ (𝑡) [0 3 0] 𝑥(𝑡) + 𝑢′ (𝑡)8𝑢(𝑡)} 𝑑𝑡
𝑤𝑖𝑡ℎ 𝑅𝑖𝑐𝑐𝑎𝑡𝑖 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠 (𝑟𝑜𝑢𝑛𝑑𝑒𝑑):
2 0
0 0 1
−1.7 −0.4 0.2
1.7 −0.4 0.2
𝑃 = [−0.4 1.6 −0.1] , [−0.4 1.6 −0.1], find the optimal feedback gain vector G.
0.2 −0.1 −0.1
0.2 −0.1 0.1