ECSE-4760
Real-Time Applications in Control & Communications
Spring 2008
Exam #2
Thursday 5/8 11:30 a.m. Low-3045
Name:
Section: MR 1:30___
MR 6:30___
(Grades will be posted on SIS when they are available.)
This exam is open book, open notes, etc. but no laptops; only calculators
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 break-down shown by the questions.
If you are missing any grades on RPILMS, make sure you bring the reports to me (CII-6219) 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 ______
‘08
I Digital Logic
Name _________________________
2
Given the following state machine, with flip-flops from right to left labeled Q3, Q2, Q1, & Q0, the initial states
respectively are 0, 0, 0, & 1. The gate is an XOR (exclusive OR) and behaves as an OR gate except it outputs a
0 when both inputs are 1. (Assume the CLR & PRE lines have been properly wired for operation.)
3
10
CLK Q
5
12
6
11
D
PRE
3
Q
CLR
8
D
Q
CLK Q
9
8
13
2
PRE
4
CLK Q
9
CLR
11
Q
1
6
D
PRE
12
CLR
5
13
DSTM1
Q
CLK Q
1
3
D
CLR
2
PRE
4
10
1
CLK
1. (4pt) Find the sequence of the states Q3Q2Q1Q0 starting with 0001 until the pattern repeats. (HINT: there are
more than 10 states.) Please check your answers carefully since other answers depend on it.
2. (2pt) How many unique states does this machine have?
3. (5pt) Treating this as a random state counter, create a next state table. Order the current states from low to
high as a 4-bit binary number starting with 0001.
I Digital Logic
‘08
Name _________________________
4. (7pt) This state machine is to be redesigned using T flip-flops. Find the input equation for T0, the low bit in
the new implementation and simplify it using a Karnaugh map.
5. (2pt) How many input equations are needed to be found to implement a JK flip-flop version of a similar D
flip-flop state machine that has 63 unique states before repeating the pattern?
‘08
II Voice Processing
Name _________________________
1. (6pt) A sampling system has an incorrect value for the antialiasing and reconstruction filter’s cutoff
frequency. The input is a single 12kHz sine wave. If the reconstruction is an ideal 15kHz LPF, what frequencies
will be present in the reconstructed signal.
Antialias
Filter
fco =15kHz
Ideal
Sampler
fs = 20kHz
Ideal LPF
Reconstruction
fco =15kHz
2a. (2pt) What is the value of the crest factor for a triangle wave? (HINT: the average of a 1V triangle wave
squared is 1/3.)
2b. (4pt) Given a sine wave and Gaussian white noise with equal power, which has the highest crest factor?
3a. (4pt) For a delta modulator output shown below with a sawtooth wave input, given C = 0.4V and D = 1.4V,
find the values of A and B.
QuickTime™ and a
decompressor
are needed to see this picture.
3b. (2pt) Could these values of A, B, C, & D be implemented in on the lab voice/delta modulator DSP
hardware?
4. (2pt) TRUE or FALSE: With 2 bits of resolution and sampling at 48kHz, spoken voice can be understood but
the speaker cannot be identified.
III Binary Communications
‘08
Name _________________________
1. (7pt) For a Hamming distance of 5, what are all the possible operational modes, i.e. combinations for a code
trading off between the number of errors corrected and the number of errors detected?
2. (3pt) In the laboratory Hamming system, if m1m2m3m4 = 0101 and the system is set for single error
correction, find all the possible received codewords that would be able to correctly determine the message bits?
3. (2pt) TRUE or FALSE: A parity code with perfect retransmission will correct a 3-bit error transmitted word.
4. (5pt) Using RTZ (RZ) square pulses (50% duty cycle) in a PCM system sampling at 50kHz and 12 bits per
sample, what is the approximate bandwidth of the channel where the spectrum of the pulses is down by about
20dB from its maximum value?
5. (3pt) What probability of bit error, Pe, is necessary to guarantee that an 8-bit word (assuming independent bit
errors) is received error free 99.92% of the time?
‘08
IV Digital Filter
Name _________________________
1. (5pt) A 6th order filter was designed with fcutoff = 3kHz and fs = 18kHz. When it was downloaded to the
Hyperception DSP board and executed, the measured fcutoff was found to be 8kHz. It was suspected that the
sampling frequency was set incorrectly. What actual sampling frequency on the running filter would yield this
cutoff frequency?
2. (6pt) Two digital filters, H1 (z ) 
z  0.5
z
,
and H 2 (z ) 
z
z 1
are combined in parallel. What are the poles and
zeros of the combined filters?

3. (3pt) For a 6th order Butterworth LPF or Chebyshev I LPF (don’t care about unity gain at DC) what is the
numerator of H(z)?
4a. (2pt) What type of filter and what order is represented by the pole-zero diagram (LPF, HPF, etc.)?
j
z
X
X
(2 zeros)
-1
O
-.5
(2 zeros)
O
1
.5
X
X
-j
B
4b. (4pt) If fs = 18kHz, at what frequency is the magnitude of the output maximized?
‘08
V Interactive Graphics
Name _________________________
5000
, is it possible to place the poles of the
s2
compensated system at s = -2 ± j2 with a purely proportional H(s)? Why or why not?
1a. (4pt) Using the transfer function of just the DC motor G(s) 

1b. (4pt) If the compensated feedback system in 1a. had poles at s = -2 ± j2, its stability would be classified as
i) overdamped
ii) underdamped iii) marginally stable iv) unstable
2a. (4pt) Given a Gaussian pdf f1 (x ,y ) 
f 2 (x, y) 
regions?

1 x 2 y 2 

exp   2 
, and a second Gaussian pdf

4  x
4 
 2  x

1
1(x  4) 2 y 2 
1
exp  
 , what range of values for x will divide the x-y plane into 3 distinct
6
9 
 2  1

2b. (2pt) What are the values of  and 2 in f1 and f2?

3. (6pt) Given a Gaussian pdf f1 (x, y) 
1x 2 y 2 
1
exp    , and a second Gaussian pdf
8
4 
 2  4
1(x  4) 2 y 2 
1
f 2 (x, y) 
exp  
 , determine the probability of the points (2,2) & (-4,0) belonging to f1.
6
9 
 2  1

‘08
VI Hybrid Control
Name _________________________
ANSWER ANY COMBINATION OF QUESTIONS THAT ADD UP TO 20 POINTS.
1. (10pt) Given the following open loop step response, design a Ziegler-Nichols PID controller and give its
transfer function, Gc(s). The input is 3.5ustep(t) (note: input is not normalized and this must be considered).
volts
4
input
3
output
2
1
1
2
3
4
5
t (sec)
2. (5pt) If a Gallier-Otto controller was designed for the plant in 1. above instead of the Ziegler-Nichols, the
controlled system would be expected to have
i) more overshoot ii) less overshoot iii) a much longer settling time iv) a much shorter settling time
v) a steady-state error
3. (5pt) For the following system find a single value of K where the system becomes unstable.
+
K
-
(s+5)(s+15)
4. (5pt) Will a digital approximation to a Gallier-Otto PID controller, with no limits on the range of the control
voltage applied as input to the plant, used in the experiment be expected to perform the same if the sample
period is increased from 0.1s to 2.0s? Why or why not?
‘08
VI Hybrid Control
Name _________________________
5. (5pt) An FST controller on an ideal 2nd order system will reach and hold the desired value after 2 sample
periods. The same controller on a 1st order system will do the same after a single sample period. Given a system
whose output to a step input x(t) = Austep(t) is y(t) = A(1 – e-t), with T = 0.1 s find the values of the FST
controller u(k), k = 0, 1 that will drive the output to 1 and hold it there. Note that u(k) = u(1) for all k > 1.
0
0
1 
 and Bc   , find the location of the controlled system’s poles with
1 3
2
6. (5pt) Given a system with Ac  
pole placement gains kc1 = 1.5 and kc2 = 2.


7. (5pt) What expression or value is minimized by a Gallier-Otto controller? Give the name and equation.
‘08
VII DC Motor Control
Name _________________________
1. (4pt) Which of the following must be a phase lead compensator?
(s  z )
(s  2 p)
(s  z )
i). Gc (s )  2
ii) Gc (s)  0.5
iii) Gc (s )  
(s  2z )


2a. (6pt) For the plant G p (s ) 
(s  z )
(s  p)

123s  11
s 2  3s  8
iv) Gc (s )  5
(s  2)
(s 10)
v) none of these

and compensator GC (s )  7
s 2
,
s 10
what is the value of the acceleration
error constant Ka and the steady-state error, ess, to a parabola input?


2b. (2pt) If the Dead Zone for the system in degrees is defined as
10
, what must be added to the compensator
Kv
Gc(s) in 2a. to control the system with a finite steady-state error to a ramp input?

3. (5pt) Find the Tustin approximation to an analog integrator with sampling time T = 1s. Give the difference
equation in terms of output y(k) and input x(k).
4. (3pt) TRUE or FALSE: A minimal prototype controller will result in a lower order controller than a ripple
free controller.
‘08
VIII Optimal Control
Name _________________________
1. (2pt) TRUE or FALSE: Assuming the lab system would still behave properly with larger voltages applied,
inputting a 20V square pulse for 150ms would have the same effect of driving the output to 0.
2. (4pt) An optimal LQR controller is applied to a hypothetical system. The state responses for the controlled
1 0
system are x1(t) and x2(t) for an input u(t) when R = 0.75, Q =  , H = 0, and tf = ∞. Set up the equation to
0 2
be solved to calculate the performance index J and simplify by removing the matrices from the equation.

 0
1 
2
3a. (4pt) For a continuous optimal LQR system with A = 
, B =  , C = 3 0.5 , D = 9,
7 3
1
5 10
1.5
.5 
5
Q = 
, R = 2, P = 
, and x0 =  , give the uncontrolled system state and output matrix equations.
0 2 
.5 1.2
0 






3b. (2pt) Why doesn’t the optimally controlled system change if C and D are given new values?
4. (4pt) Which of the following matrix (matrices) is (are) Positive Definite?
4
3
i) P =  
3 3

2
3
ii) P = 

3 1 

8
3 
iii) P = 

3 1

4
6
iv) P = 

6 10 

4
6 
v) P = 

 6 10 

5. (4pt) For an initial set of Q and R coefficients, the system response is shown below left. For a modified set of
Q and R the response is shown below right. What was most likely done to Q and R to change the response?
i) R was increased ii) R was decreased iii) q22 was decreased iv) q22 was increased v) i & iii vi) ii & iv
vii) i & iv viii) ii & iii
volts
volts
2
x1
2
x1
x2
x2
5
t
(sec)
5
t
(sec)