ECSE-4760
Real-Time Applications in Control & Communications
Spring 2016
Exam #2
Wednesday 5/18 11:30 a.m. Walker-6113
Name ______________________________
Section 1: MR 1:30
(Grades will be posted on SIS when they are available.)
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
Input
P.S.
000
001
010
011
100
101
110
111
2016
0
1
001
010
011
011
000
000
000
000
100
100
100
100
101
111
111
111
Input
P.S.
000
001
010
011
100
101
110
111
Name _________________________
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1. (2pt) Given the state machine with Next State Table and Output Table above, which state will not be entered
during normal operation?
2. (6pt) An input stream starting in state 001 outputs 0 0 0 0 0 0 and ends up back in 001 without repeating any
states in the sequence. Find a sequence of inputs and the states that could be traversed to produce this output
stream.
3. (6pt) Find the simplified expression for the output of the above state machine.
I Digital Logic
2016
Name _________________________
4. (2pt) If the system above was modified to have two inputs (and several more entries in the Next State Table),
how many variables would be needed in finding the input functions for an implementation using D flip-flops?
5. (4pt) 4. (4pt) Show that the following two expressions are NOT equivalent:
F1 = C(D + /ABD) + A/CD
F2 = /ACD + BCD + A(CD + /BD) + /ABCD
II Voice Processing
2016
Name _________________________
1. (2pt) For a quantizer that has a quantization noise SNRdB = 34dB, about how many more bits of resolution will
be needed to increase the SNRdB to at least 62dB?
2.(4pt) For the two waveforms shown, which set of parameters will produce the given delta modulator outputs?
Match up a set below to each plot.
In: 20Hz sin, Out: 2-bit delta modulation (fs=160Hz)
0.6
In: 20Hz sin, Out: 2-bit delta modulation (fs=160Hz)
0.6
0.4
0.4
0.2
0.2
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
a) A = 0.1, B = 0.2, C = 0.07, D = 0.15
c) A = 0.1, B = 0.2, C = 0.0, D = 0.15
0.16
0.18
0.2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
b) A = 0.1, B = 0.3, C = .07, D = 0.17
d) A = 0.1, B = 0.3, C = 0.0, D = 0.17
3. (4pt) Assuming that the waveform below spans ~7.5ms, if the PCM system is sampling the signal at 120kHz
with 1 bit/sample (2’s complement ADC, pulse amplitude is 0.2 V), sketch the modulated output on the plot
from points 250 to 400.
II Voice Processing
2016
Name _________________________
4. (4pt) A modulator below is made by combining 2 modulators. Find a set of the values W, X, Y, and Z that
will result in a modulator whose q(t) vs. e(t) has the characteristics shown below.
Z
-Y
Y
-Z
W
-X
X
-W
ADD
TO
PREVIOUS
Desired q vs. e plot.
5. (3pt) TRUE or FALSE: For the same SNR an LPC system may achieve a 50 times reduction in the bit rate
over a simple digital PCM sampling system.
6. (3pt) TRUE or FALSE: Companding using µ-law is a form of logarithmic compression.
III Binary Communications
2016
Name _________________________
1. (4pt) What is the minimum Hamming distance for a code that can correct double bit errors and
simultaneously detect up to 3 more bit errors
2a. (4pt) For the following variation of a Hamming code:
m1
c1
m2
c1 = m1 
c2 = m2 
c3 = m1 
c4 = m1 
c2
m2 
m3 
m2 
m3 
m3
m3 
m4 
m4 
m4 
c3
m4
c4
m5
m4
m5
m5
m5
assuming less than 3 bit errors, what word was sent if 0 0 0 0 1 0 0 1 1 is received.
2b. (2pt) What is the minimum distance between code words?
2c. (2pt) What is the efficiency of this code?
2d. (2pt) What actions in terms of autocorrection/detection can this code take if 2 bits are received in error?
3. (3pt) For a Hamming code to achieve a Pe of 10-4, approximately what must the S/N ratio be?
a) 1.5 b) 1.5dB c) 4.5
d) 4.5dB e) 6.5
f) 6.5dB
4. (3pt) What is the approximate digital signal power for a NRZ output with PAM if the input sine wave has a
20Vp-p amplitude of sufficiently low frequency (>20 samples per cycle) and 8-bit resolution?
IV Digital Filter
2016
Name _________________________
1. (2pt) A 4th order Butterworth analog filter used to remove noise spikes is being modeled as a digital filter for
simulations. Which transformation will produce the most accurate responses to the actual analog signals?
2a. (4pt) Which pole-zero plot corresponds to the magnitude plot shown below?
a)
c)
e) None of these
b)
d)
2b. (6pt) Label each of the 4 pole-zero diagrams as to the type of filter they represent (LPF, HPF, BPF, or BSF
& Butterworth, Elliptic, Chebyshev I, or Chebyshev II) and specify the order of the filter.
a)
b)
c)
d)
2c. (1pt) Given the frequency scale in the magnitude plot in 2a, what is fs? (The wide vertical bar on the plot
corresponds to z = -1.)
IV Digital Filter
2016
3
Name _________________________
𝑧
3. (4pt) For 𝐻(𝑠) = 𝑠+3 whose impulse invariant transformation (with a different gain) is 𝐻(𝑧) = 𝑧−0.905, find
the sampling frequency for this transformation.
4. (3pt) A BPF (analog) is needed that has a stop band roll off of at least 35dB/decade on both sides. If a
Butterworth design is used, what is the minimum filter order that will meet these specifications?
V Interactive Graphics
2016
Name _________________________
8
1a. (4pt) Using the approximate transfer function of just the DC motor 𝐺𝑝 (𝑠) = 𝑠(𝑠+2), find the characteristic
equation in factored form if the closed loop system is configured with negative feedback gain = 10.
1b. (2pt) Classify the time response for this system (under damped, over damped, critically damped, etc.).
2. (3pt) TRUE/FALSE: All the root loci of continuous phase lead compensators combined with the double pole
DC motor system have poles approaching infinity along lines parallel to the imaginary axis.
3a. (7pt) Given 2 Gaussian pdfs with parameters below with equal costs and a priori probabilities, find 2 points
on the y-axis that are on the decision boundary.
f1(x,y)
f2(x,y)
x
√2
1
y
1
√2

0
0
x0
0
0
y0
0
4
3b. (4pt) Sketch the approximate decision boundary for these 2 pdfs.
VI Hybrid Control
2016
Name _________________________
ANSWER ANY COMBINATION OF QUESTIONS THAT ADD UP TO 20 POINTS.
1. (4pt)
1a. (2pt) Which parameter or factor in a PID controller will introduce a steady-state error between the input and
output when the feedback controller is applied to a Type 0 system?
i) KP
ii) KI
iii) KD
iv) the presence of a free integrator in the plant Gp(s)
1b. (2pt) TRUE or FALSE: Modifying a Ziegler-Nichols P controller to include an I term always decreases the
original feedback gain.
2. (16pt)
0
1
0
] , 𝐵 ′ = [ ] , and 𝐶𝑐′ = [2 4]. If kc1 = 2.5,
−0.6 −0.8 𝑐
1
kc2 = 1.5, and g = 5, find the Ac, Bc, and Cc of the original plant.
2a. (7pt) A pole placement controlled system has 𝐴′𝑐 = [
2b. (2pt) How does the gain g affect the system’s characteristic equation as the gain goes from 1 to 100?
2c. (2pt) Does g = 5 give the controlled system a zero steady state error?
2d. (5pt) Draw the simulation diagram with integrators, gains, and summing junctions for the controlled system.
VI Hybrid Control
2016
Name _________________________
3. (4pt)
3a. (2pt) TRUE or FALSE: For controlled systems higher than 2nd order using the Graham-Lathrop standard
forms all the poles have the same (negative) real component?
3b. (2pt) TRUE or FALSE: The Graham-Lathrop PI controller minimizes the integrated time absolute error for
a Type 0 system.
10
4. (16pt) For 𝐺𝑃 = (𝑠+1)(𝑠+4) find the Gallier-Otto PI controller gains and state how the P and I gains change
(i.e. increases by a factor of ~X, decreases by a factor of ~X, remain unchanged) if the controller is changed to a
PID controller.
VII DC Motor Control
2016
Name _________________________
𝑧+0.5
1a. (6pt) A compensator has a transfer function obtained by a Tustin approximation 10
. What was the
𝑧−0.5
original transfer function? Assume fs = 10Hz.
1b. (2pt) Is the continuous compensator a phase lead or phase lag compensator?
1c. (4pt) What is the peak contribution of the phase shift (either max or min)?
𝑠
𝑠+3
2. (6pt) For the plant 𝐺𝑝 (𝑠) = 𝑠(𝑠+3+𝑗5)(𝑠+3−𝑗5) and compensator 𝐺𝑐 (𝑠) = 𝐾 𝑠+30 , classify the position error
constant, the velocity error constant, and the acceleration error constant. Circle the appropriate choice.
The position error constant is: 0 finite infinite indeterminate
The velocity error constant is: 0 finite infinite indeterminate
The acceleration error constant is: 0 finite infinite indeterminate
3. (2pt) TRUE or FALSE: The digital model for the DC Motor used in the Ripple Free Compensator assumes
the transformation z = esT and a zero order hold.
VIII Optimal Control
2016
Name _________________________
1. (2pt) How many positive definite solutions exist to the Riccati equation for a 3rd order discrete system?
2. (2pt) TRUE or FALSE: The optimal Riccati state feedback gains only work for driving the system to a zero
state and would not optimize the response to a step input.
3. (4pt) Find the positive definite Riccati equation solution for 𝐴𝑐 = [−2], 𝐵𝑐 = [5], and state penalty matrix =
[1], control penalty matrix = [0.5] with no terminal state penalty.
4. (5pt) Find the discrete state matrices for the continuous system in 3. when T = 0.01
5a. (4pt) Assuming values for Ad of [0.9] and Bd of [0.1] with the same penalty matrices as in 3. find the
solution to the Ricatti equation (that may be used to calculate the optimal control gains).
5b. (3pt) Find the feedback gain for these conditions.