EEE NOTES

POWER PLANT  ENGINEERING NOTES

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B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2010 Fourth Semester Electrical and Electronics Engineering EE2252 — POWER PLANT ENGINEERING (Regulation 2008) Time: Three hours : 100 Marks Answer ALL Questions
PART A — (10 × 2 = 20 Marks) 1. Mention the various modern ash handling systems. 2. What are the factors affecting cooling of water in cooling tower? 3. Enumerate advantages and disadvantages of hydropower plants. 4. What is a surge tank? 5. What are the requirements of fission process? 6. What are the essential components of a nuclear reactor? 7. State the merits and demerits of closed cycle gas turbine over open cycle gas turbine power plant. 8. State the applications of diesel power plant. 9. What is a fuel cell? 10. What are the advantages and limitations of tidal power plant? PART B — (5 × 16 = 80 Marks) 11. (a) Give the layout of a modern steam power plant and explain it briefly.[Marks 16] Or (b) How are cooling towers classified? Explain any one of them with a neat sketch.[Marks 16] 12. (a) Explain with a neat sketch a pumped storage power plant.[Marks 16] Or (b) What is the function of a hydraulic turbine? How are the turbines classified? Explain any one with a suitable sketch.[Marks 16] 13. (a) With the help of a sketch show all the important part of nuclear reactor. Describe briefly the functions of each part.[Marks 16] Or (b) Explain the following terms: (i) Fission of nuclear fuel (ii) Distribution of fission energy (iii) The chain reaction. [Marks 16] 14. (a) Discuss briefly the methods employed for improvement of thermal efficiency of open gas
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turbine power plant.[Marks 16]
Or
(b) List the essential components of a diesel power plant and explain them briefly.[Marks 16]
15. (a) Explain with a neat diagram of wind electric generating power plant.[Marks 16]
Or
(b) Describe open cycle MHD system with suitable sketch.[Marks 16]

DLC NOTES

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EEE – Digital Logic Circuits
Unit – 1
1) Define binary logic?
Binary logic consists of binary variables and logical operations. The
variables are designated by the alphabets such as A, B, C, x, y, z, etc., with each
variable having only two distinct values: 1 and 0. There ar e thr ee basic logic
operations: AND, OR, and NOT.
2) Write the names of basic logical operators.
1. NOT / INVERT
2. AND
3. OR
3) What are basic properties of Boolean algebra?
The basic properties of Boolean algebra are commutative property,
associative property and distributive property.
4) State the associative property of boolean algebra.
The associative property of Boolean algebra states that the OR ing of
sever al variables results in the same regardless of the grouping of the variables.
The associative property is stated as follows:
A+ (B+C) = (A+B) +C
5) State the commutat ive property of Boolean algebra.
The commutative property states that the order in which the variables
are OR ed makes no difference. The commutative property is:
A+B=B+A
6) State the dist ributive property of Boolean algebra.
The distributive property states that AND ing several variables and
OR ing the result with a single var iable is equivalent to OR ing the single variable
with each of the several variables and then AND ing the sums. The distributive
property is: A+BC= (A+B) (A+C)
7) State the absorption law of Boolean algebra.
The absorption law of Boolean algebra is given by X+XY=X, X(X+Y) =X.
8) Simplify the f ollowing using De Morgan's theorem [((AB) 'C)'' D]'
[(( AB)'C)'' D]' = ((AB)'C)'' + D' [(AB)' = A' + B']
= (AB)' C + D'
= (A' + B‟) C + D'
9) State De Morgan's theorem.
De Morgan suggested two theorems that form important part of
Boolean algebra. They are,
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1) The complement of a product is equal to the sum of the complements.
(AB)' = A' + B'
2) The complement of a sum term is equal to the product of the complements.
(A + B)' = A'B'
10) Reduce A.A'C
A.A'C = 0.C [A.A' = 1]
= 0
11) Reduce A ( A + B)
A (A + B) = AA + AB
= A (1 + B) [1 + B = 1]
= A.
12) Reduce A'B'C' + A'BC' + A'BC
A'B'C' + A'BC' + A'BC = A'C'(B' + B) + A'B'C
= A'C' + A'BC [A + A' = 1]
= A'(C' + BC)
= A'(C' + B) [A + A'B = A + B]
13) Reduce AB + (AC)' + AB’C (AB + C)
AB + (AC)' + AB‟C (AB + C) = AB + (AC)' + AAB'BC + AB'CC
= AB + (AC) ' + AB'CC [A.A' = 0]
= AB + (AC) ' + AB'C [A.A = 1]
= AB + A' + C' =AB'C [(AB)' = A' + B']
= A' + B + C' + AB'C [A + AB' = A + B]
= A' + B'C + B + C' [A + A'B = A + B]
= A' + B + C' + B'C
=A' + B + C' + B'
=A' + C' + 1
= 1 [A + 1 =1]
14) Simplify the following expression Y = (A + B)(A + C' )(B' + C'
)
Y = (A + B)(A + C' )( B' + C' )
= (AA' + AC +A'B +BC) (B' + C') [A.A' = 0]
= (AC + A'B + BC) (B' + C‟)
= AB'C + ACC' + A'BB' + A'BC' + BB'C + BCC'
= AB'C + A'BC'
15) Show that (X + Y' + XY) (X + Y') (X'Y) = 0
(X + Y' + XY)(X + Y')(X'Y) = (X + Y' + X) (X + Y‟) (X' + Y) [A + A'B = A + B]
= (X + Y‟) (X + Y‟) (X'Y) [A + A = 1]
= (X + Y‟) (X'Y) [A.A = 1]
= X.X' + Y'.X'.Y
= 0 [A.A' = 0]
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16) Prove that ABC + ABC' + AB'C + A'BC = AB + AC + BC
ABC + ABC' + AB'C + A'BC=AB( C + C') + AB'C + A'BC
=AB + AB'C + A'BC
=A (B + B'C) + A'BC
=A (B + C) + A'BC
=AB + AC + A'BC
=B (A + C) + AC
=AB + BC + AC
=AB + AC +BC ...Proved
17) Convert the given expression in canonical SOP form Y = AC + AB + BC
Y = AC + AB + BC
=AC (B + B‟) + AB (C + C‟) + (A + A') BC
=ABC + ABC' + AB'C + AB'C' + ABC + ABC' + ABC
=ABC + ABC' +AB'C + AB'C' [A + A =1]
18) Define duality property.
Duality property states that every algebraic expression deducible from
the postulates of Boolean algebra remains valid if the operators and identity
elements are interchanged. If the dual of an algebraic expression is desired, we
simply interchange OR and AND operators and replace 1's by 0's and 0's by 1's.
19) Find t he complement of the functions
F1 = x'yz' + x'y'z and F2 = x (y'z' + yz). By applying De-Morgan's theorem.
F1' = (x'yz' + x'y'z)' = (x'yz') '(x'y'z)' = (x + y' + z)(x + y +z')
F2' = [x(y'z' + yz)]' = x' + (y'z' + yz)'
= x' + (y'z')'(yz)'
= x' + (y + z)(y' + z')
20) Simplify the following expression
Y = (A + B) (A = C) (B + C)
= (A A + A C + A B + B C) (B + C)
= (A C + A B + B C) (B + C)
= A B C + A C C + A B B + A B C + B B C + B C C
= A B C
Unit – II
1. What are the classifications of sequential circuit s?
The sequential circuits are classified on the basis of timing of their
signals into two types. They ar e, 1) Synchronous sequential circuit. 2)
Asynchronous sequential circuit.
.
2. Define Flip flop
The basic unit for storage is flip flop. A flip-flop maintains its output
state either at 1 or 0 until directed by an input signal to change its
state.
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3. What are the different types of flip-flop?
There are various types of flip flops. Some of them are mentioned
below they ar e,
RS flip-flop
SR flip-flop
D flip-flop
JK flip-flop
T flip-flop
4. What is t he operat ion of RS f lip- flop?
When R input is low and S input is high the Q output of flip-flop is
set.
When R input is high and S input is low the Q output of flip-flop is
reset.
When both the inputs R and S are low the output does not change
When both the inputs R and S are high the output is unpredictable.
5.
What is t he operat ion of SR f lip- flop?
When R input is low and S input is high the Q output of flip-flop is
set.
When R input is high and S input is low the Q output of flip-flop is
reset.
When both the inputs R and S are low the output does not change.
When both the inputs R and S are high the output is unpredictable.
6. What is t he operat ion of D flip-flop?
In D flip-flop during the occurrence of clock pulse if D=1, the
output Q is set and if D=0, the output is reset.
7. What is the operation of JK flip-flop?
When K input is low and J input is high the Q output of flip-flop is
set.
When K input is high and J input is low the Q output of flip-flop is
reset.
When both the inputs K and J are low the output does not change
When both the inputs K and J are high it is possible
to set or reset the flip-flop (ie) the output toggle on the next positive
clock edge.
8. What is the operation of T flip-flop?
T flip-flop is also known as Toggle flip- flop.
When T=0 there is no change in the output.
When T=1 the output switch to the complement state (ie) the output
toggles.
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9. Define race around condition.
In JK flip-flop output is fed back to the input. Therefor e change in the
output results change in the input. Due to this in the positive half of the
clock pulse if both J and K are high then output toggles continuously.
This condition is called „race around condition‟.
10. What is edge-triggered f lip- flop?
The problem of race around condition can solved by edge triggering
flip flop. The term edge triggering means that the flip-flop changes
state either at the positive edge or negative edge of the clock pulse
and it is sensitive to its inputs only at this transition of the clock.
11. What is a master-slave flip-flop?
A master-slave flip-flop consists of two flip-flops where one circuit
serves as a master and the other as a slave.
12. Define rise time.
The time required to change the voltage level from 10% to 90% is
known as rise time(tr).
13. Define fall time.
The time required to change the voltage level from 90% to 10% is
known as fall time (tf) .
14. Define propagation delay.
A propagation delay is the time required to change the output after the
application of the input.
15. Explain the f lip- flop excitation tables for RS FF.
In RS flip-flop there are four possible transitions fr om the present state
to the next state. They are,
00 transition: This can happen either when R=S=0 or when R=1 and S=0.
01 transition: This can happen only when S=1 and R=0.
10 transition: This can happen only when S=0 and R=1.
11 transition: This can happen either when S=1 and R=0 or S=0 and R=0.
16. Explain the f lip- flop excitation tables for JK flip-flop
In JK flip-flop also there are four possible transitions from present state
to next state. They are,
00 transition: This can happen when J=0 and K=1 or K=0.
01 transition: This can happen either when J=1 and K=0 or when J=K=1.
10 transition: This can happen either when J=0 and K=1 or when J=K=1.
11 transition: This can happen when K=0 and J=0 or J=1.
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17. Explain the f lip- flop excitation tables for D flip-f lop
In D flip-flop the next state is always equal to the D input and it is
independent of the present state. Therefore D must be 0 if Qn+1 have
to 0, and if Qn+1 has to be 1 regardless the value of Qn.
18. Explain the f lip- flop excitation tables for T flip-flop
When input T=1 the state of the flip- flop is complemented; when
T=0,the state of the flip-flop remains unchanged. Therefore, for 0_0
and 1_1 transitions T must be 0 and for 0 1 and 1 0 transitions must be
1.
19. Define sequential circuit?
In sequential circuits the output variables dependent not only on the
present input variables but they also depend up on the past history of
these input variables.
20. Give the comparison between combinational circuits and sequential
circuits.
Combinational circuits Sequential circuits
Memory unit is not required Memory unity is required
Parallel adder is a combinational circuit Serial adder is a sequential
circuit
Unit III
1. What are secondary variables?
Present state variables in asynchronous sequential circuits
2. What are excitation variables?
Next state variables in asynchronous sequential circuits
3. What is fundamental mode sequential circuit?
-input variables changes if the circuit is stable
-inputs are levels, not pulses
-only one input can change at a given time
4. What is pulse mode circuit?
-inputs are pulses
-widths of pulses are long for circuit to respond to the input
-pulse width must not be so long that it is still pr esent after the new
state is reached
5. What is the significance of state assignment?
In synchronous circuits-state assignments are made with the objective
of circuit reduction In Asynchronous circuits-its objective is to avoid
critical r aces
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6. When does race condit ion occur?
Two or more binary state variables change their value in r esponse to
the change in i/p variable
7. What is non critical race?
-final stable state does not depend on the order in which the
state variable changes
-race condition is not har mful
8. What is critical race?
-final stable state depends on the order in which the
state variable changes
-race condition is harmful
9. When does a cycle occur?
Asynchronous circuit makes a transition through a series of unstable
state
10. What are the different techniques used in state assignment?
-shared row state assignment
-One hot state assignment
11. What are the steps for the design of asynchronous sequential
circuit?
-construction of primitive flow table
-reduction of flow table
-state assignment is made
-realization of primitive flow table
12. What is flow t able?
State table of a synchr onous sequential network
13. What is primitive flow chart?
One stable state per row
14. What is combinational circuit?
Output depends on the given input. It has no storage element.
15. What is state equivalence theorem?
Two states SA and SB are equivalent if and only if for every possible
input X sequence, the outputs are the same and the next states are
equivalent i.e., if SA ( t + 1) = SB (t + 1) and ZA = ZB then SA = SB.
16. What do you mean by distinguishing sequences?
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Two states, SA and SB of sequential machine ar e distinguishable if
and only if their exists at least one finite input sequence. Which, when
applied to sequential machine causes different output sequences
depending on whether SA or SB is the initial state.
17. Prove t hat the equivalence partit ion is unique
Consider that ther e are two equivalence partitions exist: PA and PB,
and PA) PB. This states that, there exist 2 states Si & Sj which are in
the same block of one partition and not in the same block of the other.
If Si & Sj are in different blocks of say PB, there exists atleast on input
sequence which distinguishes Si & Sj and therefore, they cannot be in
the same block of PA.
18. Define merger graph.
The merger graph is defined as follows. It contains the same number
of vertices as the state table contains states. A line drawn between the
two state vertices indicates each compatible state pair. It two states
are incompatible no connecting line is drawn.
19. Explain the procedure for state minimization.
a. Partition the states into subsets such that all states in the same
subsets are 1 -equivalent.
b. Partition the states into subsets such that all states in the same
subsets are 2 -equivalent.
c. Partition the states into subsets such that all states in the same
subsets are 3 -equivalent.
20. Define closed covering
A Set of compatibles is said to be closed if, for every compatible
contained in the set, all its implied compatibles are also contained in
the set. A closed set of compatibles, which contains all the states of M,
is called a closed covering.
Unit – IV
1. What is a Logic gate?
Logic gates are the basic elements that make up a digital system. The
electr onic gate is a circuit that is able to operate on a number of binary
inputs in order to perform a particular logical function.
2. Give the classification of logic families
1. Bipolar Unipolar
2. Saturated Non Saturated PMOS
3. NMOS
4. CMOS
5. RTL Schottky TTL
6. ECL DTL
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7. TTL
8. I I C
3. What are the basic digital logic gates?
The three basic logic gates are
AND gate
OR gate
NOT gate
4. Classify the logic family by operation?
The Bipolar logic family is classified into
Saturated logic, Unsaturated logic.
The RTL, DTL, TTL, I2L, HTL logic comes under
the saturated logic family.
The Schottky TTL, and ECL logic comes under
the unsaturated logic family.
5. State the classifications of FET devices.
FET is classified as
Junction Field Effect Transistor (JFET)
Metal oxide semiconductor family (MOS).
6. Mention the classification of saturated bipolar logic families.
The bipolar logic family is classified as follows:
1. RTL- Resistor Transistor Logic
2. DTL- Diode Transistor logic
3. I2L- Integrated Injection Logic
4. TTL- Transistor Transistor Logic
5. ECL- Emitter Coupled Logic
7. Mention the important characteristics of digital IC’s?
1. Fan out
2. Power dissipation
3. Propagation Delay
4. Noise Margin
5. Fan In
6. Operating temperature
7. Power supply requirements
8. Def ine Fan-out?
Fan out specifies the number of standard loads that the output of the
gate can drive with out impairment of its normal operation.
9. Def ine power dissipation?
Power dissipation is measur e of power consumed by the gate when
fully driven by all its inputs.
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10. What is propagation delay?
Propagation delay is the average transition delay time for the signal to
propagate from input to output when the signals change in value. It is
expressed in ns.
11. Def ine noise margin?
It is the maximum noise voltage added to an input signal of a digital
circuit that does not cause an undesirable change in the circuit output.
It is expressed in volts.
12. Def ine fan in?
Fan in is the number of inputs connected to the gate without any
degradation in the voltage level.
13. What is Operating temperature?
All the gates or semiconductor devices are temperatur e sensitive in
nature. The temperature in which the performance of the IC is effective
is called as operating temperature. Operating temper ature of the IC
vary from 00 C to 700 c.
14. What is High Threshold Logic?
Some digital circuits operate in environments, which produce very high
noise signals. For operation in such surroundings there is available a
type of DTL gate which possesses a high threshold to noise immunity.
This type of gate is called HTL logic or High Threshold Logic.
15. What are the t ypes of TTL logic?
1. Open collector output
2. Totem-Pole Output
3. Tri-state output.
16. What is depletion mode operation MOS?
If the channel is initially doped lightly with p-type impurity a conducting
channel exists at zero gate voltage and the device is said to operate in
depletion mode.
17. What is enhancement mode operation of MOS?
If the region beneath the gate is left initially uncharged the gate field
must induce a channel before current can flow. Thus the gate voltage
enhances the channel current and such a device is said to operate in
the enhancement mode.
18. Mention the characteristics of MOS transist or?
The n- channel MOS conducts when its gate- to- source
voltage is positive.
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The p- channel MOS conducts when its gate- to- source
voltage is negative
Either type of device is turned of if its gate- to- source voltage is zero.
19. How Schottky transistors are formed and state its use?
A schottky diode is formed by the combination of metal and
semiconductor. The pr esence of Schottky diode between the base and
the collector prevents the transistor fr om going into satur ation. The
resulting transistor is called as schottky transistor. The use of schottky
transistor in TTL decr eases the pr opagation delay without a sacrifice of
power dissipation.
20. List the different versions of TTL
1. TTL (Std.TTL) 2.LTTL (Low Power TTL)
3. HTTL (High Speed TTL) 4.STTL (Schottky TTL)
5. LSTTL (Low power Schottky TTL)
UNIT V
1. List basic types of programmable logic devices.
a. Read only memor y
b. Progr ammable logic Array
c. Progr ammable Array Logic
2. Define ROM
A read only memory is a device that includes both the decoder and the
OR gates within a single IC package.
3. Define address and word:
In a ROM, each bit combination of the input variable is called on
address. Each bit combination that comes out of the output lines is
called a word.
4. What are the types of ROM
a. Masked ROM.
b. Progr ammable Read only Memory
c. Erasable Programmable Read only memory.
d. Electrically Erasable Programmable Read only Memory.
5. What is programmable logic array? How it differs f rom ROM?
In some cases the number of don‟t care conditions is excessive, it is
more economical to use a second type of LSI component called a PLA
A PLA is similar to a ROM in concept; however it does not provide full
decoding of the variables and does not generates all the minterms as
in the ROM
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6. What is mask - programmable?
With a mask programmable PLA, the user must submit a PLA program
table to the manufacturer.
7. What is field programmable gate array?
The second type of PLA is called a field programmable gate array. The
EPLA can be progr ammed by the user by means of certain
recommended procedures.
8. Give the comparison between prom and PLA.
PROM PLA
1.And array is fixed and OR Both AND and OR arrays are
array is pr ogrammable. Programmable.
2. Cheaper and simple to use. Costliest and complex than PROMS
9. Define PROM.
PROM is Programmable Read Only Memory. It consists of a set of
fixed AND gates connected to a decoder and a programmable OR
array.
10. Define PLA
PLA is Programmable Logic Array (PLA). The PLA is a PLD that
consists of a programmable AND array and a programmable OR array.
11. Define PAL
PAL is Programmable Array Logic. PAL consists of a programmable
AND array and a fixed OR array with output logic.
12. Why was PAL developed?
It is a PLD that was developed to overcome cer tain disadvantages of
PLA, such as longer delays due to additional fusible links that result
from using two programmable arrays and more circuit complexity.
13. Why the input variables to a PAL are buffered
The input variables to a PAL are buffered to prevent loading by the
large number of AND gate inputs to which available or its complement
can be connected.
14. What does PAL 10L8 specify?
PAL - Programmable Logic Array
10 - Ten inputs
L - Active LOW Output
8 - Eight Outputs
15. Why totem pole outputs cannot be connected together.
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Totem pole outputs cannot be connected together because such a
connection might produce excessive current and may result in damage
to the devices.
16. State advantages and disadvantages of TTL
Adv:
Easily compatible with other ICs
Low output impedance
Disadv:
Wired output capability is possible only with tristate and
open collector types
Special circuits in Circuit layout and system design are requir ed.
17. When does t he noise margin allow digital circuit s to function
properly?
When noise voltages ar e within the limits of VNA(High State Noise
Margin) and VNK for a particular logic family.
18.
Define state table.
For the design of sequential counters we have to relate present states
and next states. The table, which represents the relationship between
present states and next states, is called state table.
19. Define total state
The combination of level signals that appear at the inputs and the
outputs of the delays define what is called the total state of the circuit.
20. What are the steps for the design of asynchronous sequential
circuit?
1. Construction of a primitive flow table from the problem statement.
2. Primitive flow table is reduced by eliminating redundant states
using the state reduction
3. State assignment is made
4. The primitive flow table is r ealized using appropriate logic elements.
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Part – B
Unit-I
1) Construct a Truth Table for the Boolean equation and Draw the logic
gate diagram for t he Boolean equation using AND, OR, and NOT
gates. Identif y an appropriate choice of IC chips which may be used
to make this logic circuit.
Q=(A C+B C) (A+C)
· · ·
inputs output
A B C A*C B*C (A*C)+(B*C) A+C Q
0 0 0 0 0 0 0 0
0 0 1 0 0 0 1 0
0 1 0 0 0 0 0 0
0 1 1 0 1 1 1 1
1 0 0 0 0 0 1 0
1 0 1 1 0 1 1 1
1 1 0 0 0 0 1 0
1 1 1 1 1 1 1 1
A B
C
AC
AC+BC
Q
BC
A+C
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2) i)Write out the Boolean equation and construct the truth t able for the
logic gate diagram shown below.
A
B
Q
C
Solution:
Q=(A B +B) C
· ·
inputs Q =
A B C N(A*B)
N(A*B)+B N( N(A*B)+B)*C
0 0 0 1 1 0
0 0 1 1 1 0
0 1 0 1 1 0
0 1 1 1 1 0
1 0 0 1 1 0
1 0 1 1 1 0
1 1 0 0 1 0
1 1 1 0 1 0
Therefore: Q = 0
ii) Using Boolean rules t o show the reduction:
Q=(A B +B) C
· ·
Q=((A +B)+B) C
·
“ Rule 20”
Q=((A +B)+B) C
·
Q=(A +(B+B)) C
·
“Rule 12”
Q=(A +(B+B)) C
·
Q=(A +1) C
·
“Rule 4”
Q=(A +1) C
·
Q=(1) C
·
= 0 C
·
“Rule 2”
Q = 0 C
·
“Rule 6” Q = 0
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3) What is the logical expression shown by the following gate circuits?
a)
A
B
X
X
= · · ·
A B+B C D
C
D
b)
A
B
C
Y
( )
Y
= + · · · ·
A (B C) (C D) D
D
c)
A
Z
B
Z
=
(
A
·
B
)
·
(
C
·
D
)
·
(
C
+
A
·
B
)
·
(
D
)
C
D
Can you simplify any of these three cir cuits? X: X is simplified
Y: Y can be simplified to Y = 1
Z: Z can be simplified to
Z
=
A
·
B
·
D
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4) Explain all the Logic Gates
Digital Electronics use symbols to repr esent the digital logic or circuitry which are
used to perform these logical operations. These logic gates form the basic
construction tools for digital electronics:
AND Gate: OR Gate: Inverter (NOT gate):
A B A · B A B A + B A
A
0 0 0 0 0 0 0 1
0 1 0 0 1 1 1 0
1 0 0 1 0 1
1 1 1 1 1 1
Other commonly used types of logical operations and electrical logic gates
include:
NAND gate: the combination of an AND gate followed by a NOT.
A B
A B
·
0 0 1
0 1 1
1 0 1
1 1 0
NOR gate: a combination of an OR gate followed by a NOT gate.
A B
A+B
0 0 1
0 1 0
1 0 0
1 1 0
Exclusive OR gate also called XOR: a pair of ANDs with one inverted input into
an OR gate.
or
A B
×
A B
A
A B
A B
·
A B
·
A B+A B
· ·
0 0 0 0 0
B
0 1 0 1 1
1 0 1 0 1
1 1 0 0 0
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Rule 20 of the Boolean logic (DeMorgan Theorem) are statements that show
relationships between NAND and NOR gate structures.
NOR NAND
( )
( )
X+Y =X Y
·
and
X Y =X+Y
·
=
=
Examine the Truth Table for each form of the NOR:
A B
A+B
0 0 1
0 1 0
1 0 0
1 1 0
A B
A B
·
A
B
0 0 1 1 1
0 1 1 0 0
1 0 0 1 0
1 1 0 0 0
A similar r elationship is also true for the NAND gate.
Examine the Truth Table for each form of the NOR:
=
A B
A+B
A B
A
B
0 0 1 1 1 1
0 1 1 1 0 1
1 0 1 0 1 1
1 1 0 0 0 0
A NOR may be created by either A NAND may be created by either
-- inverting the output of an OR gate --inverting the output of an
AND gate
or or
-- inverting all inputs of an AND gate - - inverting all inputs of an OR
gate.
=
=
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There are NAND and NOR (as well as AND and OR) gates which have 3 or more
inputs.
Multiple input NAND gate:
or
A
Q
A
Q
Q
= · · =
A B C A+B+C
B
B
C
C
Multiple input NOR gate:
A
or
A
Q Q
Q
= = · ·
A+B+C A B C
B
B
C
C
NANDs and NORs have a unique and robust ability. If you could only have a
single kind of gate, you'd probably want to have either all NANDs or all NORs.
To understand why, determine the logical results of the circuits below.
A
A A
·
A ?
0 1
1 0
A B
A B
·
A
A B A B
· · ·
0 0 1 0
?
B
0 1 1 0
1 0 1 0
1 1 0 1
A B
A
A A
·
B B
·
A A B B
· · ·
?
0 0 1 1 0
B
0 1 1 0 1
1 0 0 1 1
1 1 0 0 1
What do the results of the above Truth Tables tell you about the NAND gate
Any other kind of logic gate may be set up using only NAND in the right number
and configuration.
It is possible to make any other type of common logic gate or logic gate circuit
out of all NANDs. In other words, you could construct the complete logic circuit
of a computer out of only one type of gate if you wanted to. This is not the most
efficient use of the gates, and this won't produce the most efficient use of
semiconductor density or power usage, but it could be done.
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In the same way, the NOR could also be used to create all other logic gates and
logic circuitry.
In the space below, can you create a logic gate structur e using only NORs which
can be used to replace an AND gate.
A
B
5) State the postulates and theorems of Boolean algebra.
X + 0 = X
X · 1 = X
X + X' = 1
X · X' = 0
X + X = X
X · X = X
X + 1 = 1
X · 0 = 0
(X')' = X
X + Y = Y + X
XY = YX
X + (Y + Z) = ( X + Y) + Z
X (YZ) = (XY) Z
X(Y + Z) = XY + XZ
X + YX = (X + Y) (X + Z)
(X + Y)' = X'Y'
(XY) ' = X' + Y'
X + XY = X
X( X + Y) = X
Unit-II
6) Examine the digit al circuit below and work through the output states
given the Q values shown.
Inputs Output
S R Q
Q
0 1 0 1
0 0 0 1
1 0 1 0
0 0 1 0
0 1 0 1
0 0 0 1
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R
1 0 1 0
Q
1 1 - -
This circuit is known as an SR Flip-
Time
Flop. (S for Set and R for Reset)
Q
The output toggles when the input
S
states undergo certain transitions
from low to high.
Since this device is intended to have complimentary output Q and
, the state
Q
when S=R=1 is called an illegal or invalid state. It also considered unstable. SR
Flip- Flops are not intended be used with this input state.
There are two common versions of the SR Flip- Flop:
Low to High activated SR Flip- Flop.
A flip flop (shown in the figure above) made from two NORs. The output will
latch when an appr opriate Low to High transition is sent to an input.
High to Low activated Flip-Flop:
If a SR Flip-Flop is built out of NAND gates instead of NOR gates. The flip flops
output is latched when a High to Low transition occurs at an input state. While
the circuit is cor rectly shown using the NAND gates, the preferred gate diagram
is to use ORs with inverted inputs indicating that Low levels activate the flip-flop.
Tr y to fill in the table below:
R
Q
S R Q
Q
1 0 1 0
1 1 - -
0 1 0 1
Q
S
Time
1 1 - -
R
Q
1 0 1 0
1 1 - -
0 1 0 1
0 0 0 1
Q
S
When working with digital IC chips, these flip flops are shown using the following
alter nate diagrams:
High-Level activated Low-Level Activated
Flip Flop Flip Flop
Q
S
Q
R
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S Q
R
Q
Timing Char t:
Set Input
Since Flip-Flops are sequential
devices, truth tables are not enough.
The state levels are sometimes
Reset Input
shown by use of timing charts.
It's easier to keep track of the
states using timing charts
Set Output Q
especially for devices
which are triggered by
edge transitions.
Reset Output Q
time
7) Explain D-Flip-Flop:
D Flip- Flops are implemented with a Clock input instead of an Enable.
These ar e devices which latch the output when a transition occurs on the clock
input.
The most common version of the D Flip-Flop uses a clock transition from Low to
High as the enabling transition. Some versions of this flip-flop commonly have
Set and Clear inputs that are primarily used as a way to preset the output to a
known starting state. The symbol used to indicate a clock or edge trigger is the
.
Set
Inputs Outputs
Set Clear Clock D Q
Q
D Q
0 1 X X 1 0
1 0 X X 0 1
Q
0 0 X X 1 1
Clock
1 1 0 1 1 1 0
1 1 0 1 0 0 1
Clear
Use the D Flip-Flop truth table above to complete the following behavior table for
the D Flip-Flop. Observe that the output Q changes to agree with D whenever the
Clock input undergoes a L H transition. Changing D at other times does not
affect the output, Q
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The Set and Clear pins are used to initialize the original state of output and
enable the device. Without these pins, you would not know what the or iginal
output state of the device was.
Complete the timing chart for this set of clock transitions.
Assume that Set and Clear are both high (1) and that the output state Q starts
low (0).
D-Flip Flop Timing Diagram
D
time
Clock
Q
Q
8) Explain the operation of counter
A counter is used to r ecord the number of pulses or events. Depending upon the
configuration of the gates, they can be wired to count up or down in binary or
decimal, asynchronously or synchronously. Below is an example of an
asynchronous circuit which counts upward through the octal values. Notice that
this str ucture is using a slightly different D flip-flop than was used in the previous
examples. It is triggered by a High Low tr ansition. How can you tell? This type
of circuit is also called a ripple counter.
Outputs
b
b
b
1
0
2
D Q
D Q
D Q
1
1
1
Pulses to
Clk
Clk
Clk
be counted
Q
Q
Q
1
1
1
Octal value in binary = b2 b
b
1
0
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clock
b
0
b
1
b
2
b
b
b
000
001
010
011
100
101
110
111
000
repeat
2
2
2
2
2
2
2
2
2
2
1
0
Process timer:
Used in combination with a line decoder, a counting circuit like this could be used
to implement a process stepper . As the D flip-flops counts down through a
binary 4 count, the complement of the output is sent to
EN
the decoder which enables one and only one of the output
lines (enabled Low). The truth table for the decoder is
P0
given on the table below.
P1
A1
P2
P3
A0
2 to 4 line decod er
Q
1
74LS139
A
A
P
P
P
P
D Q
D Q
0
1
1
0
0
1
2
3
Q
Q
Clock
Clk
0 0 0 1 1 1
Clk
0
1
0 1 1 0 1 1
4 down ripple counter
1 0 1 1 0 1
using 74LS74
1 1 1 1 1 0
9) Explain the Debouncing circuit:
Real switches often do not make a nice clean tr ansition from one state to
another. The signal given off by a simple contact switch from one line to another
might give behavior similar to that shown by the diagram below.
V
V
cc
cc
A
B
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Line A
Line B
No
contact
Bounce as
during
Switch in
Bounce as
switch is
switch
Switch in
po sition A
switch is
transition
position B
opened at A
closed at B
Since there are many cases where the switch bounce will be recorded as a
number of individual pulses or transitions, there is a need to debounce the signal
that occurs during switching. Use of flip-flops is one simple way to accomplish a
nice clean signal change.
Any of the following digital flip flops will debounce a contact switch.
Output
Output
Set
Output
D Q
Clk
Q
Clear
10) Example of the octal ripple count ers using the JK flip-flop:
This performs an upward asynchrous 8 count. A counter is used to record the
number of pulses or events. Depending upon the configuration of the gates, they
can be wired to count up or down in binary or decimal, asynchronously or
synchr onously. Below is an example of an asynchronous circuit which counts
upward through the octal values. Notice that this structur e is using a slightly
different D flip-flop than was used in the previous examples. It is triggered by a
High Low transition. How can you tell? This type of circuit is also called a
ripple counter.
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The logic of the JK flip-flop can be summarized by the table below:
Set
Inputs Outputs
Set Clear J K Clock Q
J Q
Q
0 1 X X X 1 0
1 0 X X X 0 1
Clock
0 0 X X X Illegal
Q
1 1 0 0 1 0 Latched
K
1 1 0 1 1 0 0 H
1 1 1 0 1 0 1 0
Clear
1 1 1 1 1 0 Toggle
Outputs
all J=K=1
J Q
J Q
J Q
1
1
1
Pulses to
Clk
Clk
Clk
be counted
Q
Q
Q
1
1
1
K
K
K
Clear
Unit -III
11) J-K Flip-Flop.
A JK flip-flop is similar to the SR Flip- Flop with one exception; If two High inputs
occur simultaneously, the JK Flip- Flop output will toggle (reverse their output
states)when the clock performs a high-to-low transition.. This eliminates the
undefined output state (H-H) found in the SR flip-flop.
The logic of the JK flip-flop can be summarized by the table below:
Set
Inputs Outputs
Set Clear J K Clock Q
Q
J Q
0 1 X X X 1 0
1 0 X X X 0 1
Clock
0 0 X X X Illegal
Q
1 1 0 0 1 0 Latched
K
1 1 0 1 1 0 0 H
1 1 1 0 1 0 1 0
Clear
1 1 1 1 1 0 Toggle
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Use the JK flip-flop truth table shown above or the demo in the logicdemo.m
program to understand its behavior. (let 1 = High and 0 = Low)
Inputs Outputs
Clear Set J K Clock Q
Q
H H H L L-H-L
H H L L
Respond to
H H L H
J & K
H H L L
H H H L
H H L H
Time
H H H L
L H H L
Held in
L H L L
Clear
L H L H
L H L L
H L L L
Held in Set
H L H L
(or Preset)
H L L L
H L L H
H H H H
H H H H
Toggle
H H H H
H H H H L-H-L
12) Explain Digital IC chips:
Up until now, we've been talking about these logic gates as useful but vague
logical or graphical abstractions.
Each of the logic gates discussed is available
as an easy to use integrated circuit (such as in the
DIP (Dual Inline Package) chip shown to the right).
There are two common families of chip
TTL --transistor-transistor logic
and
CMOS – complimentary metal oxide semiconductor
Some of the commonly available TTL chips include:
7400 Quad 2-Input NAND Gate
7402 Quad 2-Input NOR Gate
7404 Hex Inverter (NOT Gate)
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7408 Quad 2-Input AND Gate
7410 Triple 3-Input NAND Gate
7411 Triple 3-Input AND Gate
7420 Dual 4-Input NAND Gate
7421 Dual 4-Input AND Gate
7427 Triple 3-Input NOR Gate
7430 8-Input NAND Gate
7432 Quad 2-Input OR Gate
7442 BCD to Decimal 4 to 10 Line Decoder
7446 BCD to 7 Segment Decoder/Driver
7454 4-wide AND-OR- Invert Gate
7473 Dual J-K Flip-Flops with Clear
7474 Dual D Flip-Flop with Clear and Preset
7486 Quad 2-Input XOR Gate
7489 64 bit Read/Write Memories
7490 Decade Counters
7491 8-bit Shift Registers
7493 4-bit Binary Counters
74138 3 to 8 Line Decoder/Multiplexer
13) Explain PLD
Programmable logic device
A programmable logic device or PLD is an electronic component
used to build reconfigurable digital circuits. Unlike a logic gate, which has a fixed
function, a PLD has an undefined function at the time of manufacture. Before the
PLD can be used in a circuit it must be programmed, that is, reconfigured.
Using a ROM as a PLD
Before PLDs were invented, read-only memory (ROM) chips
were used to create ar bitrary combinational logic functions of a number of inputs.
Consider a ROM with m inputs (the address lines) and n outputs (the data lines).
When used as a memory, the ROM contains 2
words of n bits each. Now
m
imagine that the inputs are driven not by an m-bit addr ess, but by m independent
logic signals. Theoretically, ther e are 2
possible Boolean functions of these m
m
signals, but the structure of the ROM allows just 2
of these functions to be
n
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produced at the output pins. The ROM therefore becomes equivalent to n
separate logic circuits, each of which generates a chosen function of the m
inputs.
The advantage of using a ROM in this way is that any conceivable
function of the m inputs can be made to appear at any of the n outputs, making
this the most general-purpose combinatorial logic device available. Also, PROMs
(programmable ROMs), EPROMs (ultr aviolet-erasable PROMs) and EPROM‟s
(electrically erasable PROMs) are available that can be programmed using a
standard PROM programmer without r equiring specialized har dware or software.
However, there ar e several disadvantages:
they are usually much slower than dedicated logic circuits,
•
they cannot necessarily provide safe "covers" for asynchronous logic
•
transitions so the PROM's outputs may glitch as the inputs switch,
they consume more power,
•
They are often more expensive than programmable logic, especially if high speed
FPGAs use a grid of logic gates, similar to that of an ordinar y gate array, but the
programming is done by the customer, not by the manufacturer. The term "field-
programmable" means the array is done outside the factory, or "in the field."
FPGAs are usually progr ammed after being soldered down to the circuit board, in
a manner similar to that of lar ger CPLDs. In larger FPGAs the configuration is
volatile, and must be re-loaded into the device whenever power is applied or
different functionality is required. The main difference between FPGAs and
CPLDs is that FPGAs have a volatile memory, thus it requires to be pr ogrammed
after power up. CPLDs do not. Also, FPGAs usually consume more power than
CPLDs due to their SRAM nature. Finally, CPLDs do not have as many registers
or memory storage as FPGAs. In gener al CPLDs are a good choice for wide
combinatorial logic applications while FPGAs are more suitable for large state
machines (i.e. microprocessors).
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Other variants
PLDs are being sold now that contain a microprocessor with a fixed function (the
so-called core) surrounded by programmable logic These devices let designers
concentrate on adding new features to designs without having to worry about
making the microprocessor work.
How PLDs retain their configuration
A PLD is a combination of a logic device and a memory device. The memory is
used to store the pattern that was given to the chip during programming. Most of
the methods for storing data in an integrated circuit have been adapted for use in
PLDs.
SRAM, or static RAM, is a volatile type of memory, meaning that its contents are
lost each time the power is switched off. SRAM-based PLDs therefore have to be
programmed every time the circuit is switched on. This is usually done
automatically by another part of the circuit.
Flash memory is non-volatile, retaining its contents even when the power is
switched off. It can be erased and reprogrammed as required. This makes it
useful for PLD memory.
As of 2005, most CPLDs are electrically programmable and er asable, and non-
volatile. This is because they ar e too small to justify the inconvenience of
programming internal SRAM cells every time they start up, and EPROM cells are
more expensive due to their ceramic package with a quartz window.
14) Explain EPROM realizat ion.
An EPROM, or erasable programmable read only memory, is a type of
memory chip that retains its data when its power supply is switched off. In other
words, it is non-volatile. It is an array of floating-gate tr ansistor s individually
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programmed by an electronic device that supplies higher voltages than those
nor mally used in digital circuits. Once programmed, an EPROM can be erased
only by exposing it to strong ultraviolet light. That UV light usually has a
wavelength of 253.7nm (for optimum er asure time) and belongs to the UVC
range of UV light. EPROM‟s are easily recognizable by the transparent fused
quartz window in the top of the package, through which the silicon chip is visible,
and which permits exposure to UV light during erasing.
Operation
Development of the EPROM memory cell started with investigation of faulty
integrated circuits where the gate connections of transistors had broken. Stored
char ge on these isolated gates changed their properties. The EPROM was
invented by Israeli engineer Dov Frohman of Intel in 1971
EPROM sizes and types
EPROM‟s come in several sizes both in physical packaging as well and storage
capacity. While par ts of the same type number fr om different manufacturers are
compatible as long as they'r e only being r ead, there are subtle differences in the
programming process.
Most EPROMS could be identified by the programmer through "signature mode"
by forcing 12V on pin A9 and reading out two bytes of data. However, as this was
not universal, programmer software also would allow manual setting of the
manufacturer and device type of the chip to ensur e proper programming.
15) Compare the digital logic families characteristics
There are a number of commonly- available electronic logic families, as
summarized in (NIM logic is a special case included for completeness. It will be
considered mor e fully in the section on particle counting.) As you can see, the
types differ in their elementary function and in whether they respond to current or
voltage signals. Fan-out refer s to the ability of an
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output to drive more than one subsequent input, but this is not usually a problem.
Fr om a design perspective, the speed of operation is often a deciding factor,
along with cost and the ability to construct very complex single-chip circuits (Very
Lar ge Scale Integration).
You should also be aware that there ar e many ready-made functions
available in each of the commercial logic families. These typically include multi-
input gates, flip-flops, and adder circuits
Summary of Gate Characteristics
Gate Type
Charac TTL ECL CMOS NIM(neg) NIM(pos)
Basic func. NAND OR,NOR NOR - -
Connection Current Voltage Voltage Current Voltage
Logic 0
0.0 ® 0.8V
-0.9V
0 ® 2V
+1 ® -2mA
1.5 ® -2V
1
2.5 ® 5.0V
-1.8V
7 ® 10V
4 ® 12mA
3 ® 12V
Fan-out 10 25 10-20 1 1-2
Gate delay 15ns 3ns 70ns 10ns 500ns
Advantages Standard
Fast Low power
Modules
Modules
Cheap
Very cheap
Flexible
Flexible
Noise
VLSI
Z=50W
immunity
Disadv Can‟t drive
Noise
Slow
Costly
Costly
cable
immunity
Static-
Bulky
Bulky
sensitive
Fan-out
and even complete CPUs. Ther e are also compatible interface circuits, such as
display drivers, transmission line drivers, analog to digital converters and so on.
For reasons of simplicity and reliability, you should make use of specialized units
whenever possible. It is highly unlikely that you will ever need to build a logic
function out of discrete tr ansistor s, resistors etc., so for the present we will treat
the circuits as black boxes. If you do a lot of digital design you should gain at
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least a rough idea of how the functions are carried out bythe internal circuitr y,
since that will help you use the building blocks more effectively.
Unit-IV
16) With apt diagrams explain PAL and PLA.
The term Programmable Arr ay Logic (PAL) is used to describe a family of
programmable logic device semiconductors used to implement logic functions
in digital circuits introduced by Monolithic Memories, Inc.
PAL devices consisted of a small PROM (programmable read-only
memory) core and additional output logic used to implement particular desired
logic functions with few components.Using specialized machines, PAL devices
were "field-pr ogrammable". Each PAL device was "one-time programmable"
(OTP), meaning that it could not be updated and reused after its initial
programming. (MMI also offered a similar family called HAL, or "hard array logic",
which were like PAL devices except that they were mask- programmed at the
factory.)
The original 20 and 24-pin PALs were described by MMI as medium-scale
integration (MSI) devices.
PAL architecture
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The programmable elements (shown as a fuse) connect both the true and
complemented inputs to the AND gates. These AND gates, also known as
product terms, are ORed together to form a sum-of-products logic array.
The PAL architecture consists of two main components: a logic plane and output
logic macro cells.
Progr ammable logic plane
The programmable logic plane is a programmable read-only memory (PROM)
array that allows the signals present on the devices pins (or the logical
complements of those signals) to be routed to an output logic macrocell.
PAL devices have arrays of transistor cells arranged in a "fixed-OR,
programmable-AND" plane used to implement "sum-of-products" binary logic
equations for each of the outputs in terms of the inputs and either synchronous or
asynchronous feedback fr om the outputs.
Output logic
The early 20-pin PALs had 10 inputs and 8 outputs. The outputs were active low
and could be registered or combinational. Members of the PAL family were
available with various output str uctures called "output logic macro cells" or
OLMCs. Prior to the introduction of the "V" (for "variable") series, the types of
OLMCs available in each PAL were fixed at the time of manufactur e. (The
PAL16L8 had 8 combinational outputs and the PAL16R8 had 8 registered
outputs. The PAL16R6 had 6 registered and 2 combinational while the PAL16R4
had 4 of each.) Each output could have up to 8 product terms (effectively AND
gates), however the combinational outputs used one of the terms to control a
bidirectional output buffer. There were other combinations that had fewer outputs
with more product term per output and were available with active high outputs.
The 16X8 family or registered devices had an XOR gate before the register.
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This fixed output structur e often frustrated designers attempting to optimize the
utility of PAL devices because output structures of different types were often
required by their applications
Though some engineers pr ogrammed PAL devices by manually editing files
containing the binary fuse pattern data, most opted to design their logic using a
har dware description language (HDL)
17) Design a simple microprocessor:
Many times the most practical method to solve a system design problem
is to use a standard microprocessor. Ther e are many single chip
micr oprocessors with built in RAM and EPROM / EPROM available.
The PIC family of processor fr om microchip offers a wide r ange
of clock speeds, memory sizes, and analog I/O capability (ADCS)
Microprocessors provide great flexibility because Systems can
be upgraded in the field through software patches. Do not under estimate the
cost of softwar e development for microprocessor based systems.
Programmable Logic:
A variety of programmable chips are available that can be more efficient
than general purpose microprocessors.
1. Chips with programmable logic arrays
2. Chips with programmable inter connect
3. Chips with reprogrammable logic and interconnect.
The System designer s should be familiar with these options for reasons.
•
First it allows the designer to completely assess a particular
system requirement for an IC and r ecommend a solution given
the system complexity, speed of operation etc.
•
Second it is familiarizes the IC designer with methods of mailing
any chip reprogrammable at the hardware level and hence both
more useful and of under spread use.
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Progr ammable Logic Devices:
A PLA consists of an AND plane and an OR plane to
compute any function expressed as a sum of products. Each transistor in the
AND and OR array plane must be capable of being
Progr ammed to be pr esent or not. This can be achieved by truly populating the
AND and OR plane with a NOR structure at each PLA location. Each node is
programmed with a floating gate transistor and a fusible link.
18) Explain the commonly available TTL sequential logic digit al IC chips
:
7474 Dual D Flip-Flop 7475 Quad Latch
With Preset and Clear:
7473 Dual Master Slave 7476 Dual Master-Slave J-K
J- K Flip-Flop with Clear Flip-Flop with Clear and Preset
19) Explain the VHDL description of combinational networks with example
The Synopsys tools to synthesize combinational logic circuits inot
standard-cell circuit designs using Verilog as an input language.
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1. Background
Logic synthesis tools allow designers to compile high-level descriptions of a
circuit into standard-cell implementations that can be converted into chip layouts
using placement and routing tools.
2. Describing Combinational Logic using Verilog HDL
As discussed in class, the basic construct used to describe hardware in Verilog is
the module. Modules describe the interface of a circuit element - its inputs and
outputs, and either the structure or function or of the module. Structure is
described using module instantiation - the creation of submodules which are
connected together to implement a desired function. Function can be described
using either assign statements or always blocks. The assign statement is
preferr red for specifying simple logic, while the always block is needed for more
complex functions. In this experiement, we will use an always block to describe
the function of a binary decoder.
The general structur e of a module description with an always block is shown
below:
module myLogic(i1, i2, ..., o1, o2, ...);
input i1, i2, ...;
output o1, o2, ...;
reg o1, o2
always @(i1, i2, ...)
begin
... statements that operate on i1, i2, ...
o1 = ...;
...
o2 = ...;
...
o3 = ...;
end
endmodule
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Here the combination of the always and @() operators specify a block of logic
that activates during simulation when one of the inputs i1, i2, ... changes. When
simulating, the model waits for an input to change, then executes the code in the
"begin ... end" block, change any outputs for which there are assignment
operators, and then loops back to the @() operator to wait for another input
change. when synthesizing combinational logic, keep in mind that your
Verilogger input is a specifiction of a set of outputs that are combinational
functions of its inputs. This is a key differ ence from a software pr ogram written in
a language like C.
Progr amming constructs like for loops can be used to make this description more
concise, but they do not imply any sequential or procedural behavior. Instead, the
Design Compiler expands or "unrolls" loop constructs to form a combinational
logic function. The one exception to this rule is when an ouput is not specified for
all possible values of the inputs. For example, this can occur when an if-then
statement that assigns a value to an uninitialized variable without a
corresponding assignment in the else statement. In this case, the Design
Compiler will insert a latch to hold the previous value, since the previous value
must be preserved if a new value is not specified.
The design compiler works in two steps. In the first step, it translates the Verilog
into hardware that implements the logic functions in a straightforward way without
regard to cost. In the second step, it optimizes this logic and maps it cells in the
MSU SCMOS standard cell library that we are using in our design projects.
A major part of the Design Compiler's capabilities are directed toward optimizing
logic under timing constraints. It contains a built-in timing analyzer that finds the
longest paths in the synthesized logic network and compares their delay against
timing constraints specified by the user. If the constraints are not met, it attempts
to modify the design and notifies the user about whether or not the constraints
were successfully met. Although this part of the Design Compiler is heavily used
in "industrial strength" designs, we will not use it in this lab.
3. Prelab
A skeleton of a 2-4 binary decoder is shown below. Complete this description by
adding appropriate entries to the case statement. Write these entries down on a
piece of paper and br ing these to lab with you.
module dec2_4(d_in, d_out);
input [1:0] d_in;
output [3:0] d_out;
reg [3:0] d_out;
always @(d_in)
begin
case (d_in)
2'b00 : d_out = 4'b0001;
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/* add additonal cases here */
...
default : d_out = 4'bxxxx;
endcase
end
endmodule
20) Explain Full adder and write the program in structural Description (
Behavioral modeling )
Full adder is used for adding more than two numbers. It
contains 3 inputs and one sum and one carry part.
Progr am for Full adder
Module FA(a, b, c)
Input a;
Input b;
Input c;
Output sum;
Output carry;
Wire s1, c1,c2, c3;
Xor
X1 (s1, a, b);
X2 ( sum, s1, c);
And
a1 (c1, a, b);
a2 (c2, a, c);
a3 (c3, b, c);
or
b1 (carry , c1, c2, c3) ;
end module
Unit -V
21) Explain the compilat ion and simulation of VHDL code
1. Compilation Process:
Compilation is a process that translates the design that are
described by various methods of data entry to an
inter mediate for mat.
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The Different Stages of Compiler are
1. Analysis
2. Generic hardware Generation
3. Logic Optimization
4. Binding
Analysis
The Syntax for the VHDL code is checked after that the design is converted in to
uniform representation means that implementation of the design depends on how
we configure the macro cells using mux array.
Generic Hardware Generation:
This will generate the hardware for the uniform representation of the design given
by the analysis block.
Binding:
Binding means conversion of circuit according to the target device.
Routing And Placement:
The routing and placement of FPLD cells
Timing Analysis:
This will help us to decide the clocking speed of the circuit.
SIMULATION
This simulation software verifies the functionality of the design.
Two kinds of simulation
1. Pre Simulation
2. Post Simulation
1. Pre Synthsis Simulation:
By giving test data to the simulation.
The simulation part doesnot include the delays introduced by the gates
and wires.
2. Post Synthsis Simulation:
The compilation part with delay is given to the post simulation.
This method is based on the net list file and timing file , the simulation will
generate output waveform
22) Explain VHDL operators
1. Arithmetic Oper ator
2. Logical Operator
3. Bitwise Operator
4. Conditional Operator
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5. Relational Oper ator
6. Equality Operator
7. Reduction Operator
8. Shift Operator
1. Arithmetic Operator :
+ ( Unary & Binary Operator)
-
( Uanry minus)
* Mulitiply
/ Divide
% modulo
2. Logical Operator:
&& (Logical and)
|| (Logical or)
! (Logical Not
3. Bitwise Operator:
| (binary or)
& (Binary and)
4. Conditional Operator:
Synatax:
Con – exp?exp1:exp2
5. Relational Oper ator:
> (greater than)
< (less than)
>= (greater than or equal to)
<= (less than or equal to)
6. Equality Operator:
= =(logical Equality)
= = = (case Equality)
= (Logical in equaloity)
7. Reduction Operator:
& (reduction AND)
| (reduction OR)
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8. Shift Operator:
<< (left shift)
>> (right shift)
23) Design a Binary Mult iplier
A multiplier for unsigned binary numbers. When we form the
product A X B the first operand (A) is called the multiplicand and
the second operand ( B) is called the multiplier.
Example 13 x 11 in binary
1101 (13)
1011 (11) we can get 143.
Operation:
1.A multiplication two 4 bit binary numbers required a 4 bit
mulitiplicand register, a 4 bit multiplier register pr oduct,
2.If the multiplicand were shifted left each time before it was
added to the accumulator.
3.The 4 bit from the accumulator and 4 bit fr om the
multiplicand register re connected to the accumulator .
4.The sum 4 bit and the carry output from the adder are
connected back to the accumulator.
5.An extra bit at the left end of the product register temporarily
stores any carry that is generated when the multiplicand is added to
the accumulator.
6.The control cicuit puts out the proper sequence of add and
shift signal after a start signal(st=1)has been received.
BEHAVIORAL Model For 4 x 4 binary multiplier
Library BITLIB;
Use BITLIB, bit_pack_all
Enitity mult 4 x 4 is
Port(clk,st: inbit;mplier,mcand:inbit_vector ,Done: outbit);
End mult 4 x 4;
Architectural behavioral of 4 x 4 is
Signal state: integer r ange 0 to 9;
Signal acc bitvector (8 down to 0):
Alias: bit is acc( 0);
Begin
Process
Begin
Wait until clk=‟ 1‟;
Case state is
When 0 =>
If state „1‟ then
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Acc(8 down to 4) <=”0000”
Acc(3 downto 0) <= mplier;
State <=1;
End if
When 1/3/5/7=>
If m=1 then
Acc (8 downto 4)
State <=state+1;
Else
Acc <+ „0‟ & acc(8 downto 0);
State<=state+2;
End if
When 2/4/6/8=>
Acc,=‟0‟ 4 acc(8 downto 1);
state =state+1;
end case
end processdone <=‟1‟ when state =9 else 0;
end behavioral
Model FLIPFLOP using VHDL process
Progr am for D flip-flop (Positive Edge Trigger ing)
Module DFF(q.qbar, d, clk);
Input d,clk;
Output q.qbar;
Reg q.qbar ;
Always @ (pos edge clk)
Begin
Q=d;
Qbar= ~d;
End
end module
Progr am for D-Flip-flop (Negative Edge Triggering)
Module dff(q.qbar, d, clk);
Input d,clk;
Output q.qbar;
Reg q.qbar ;
Always @(neg edge clk)
Begin
Q=d;
Qbar= ~d;
End
End module
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24) Explain Behavioral Description using example
This is the third style of modeling in verilog HDL. RTL modeling
concentrates on specifying the movement at data among hardware sections. RTL
specification is viewed as being the link between purely abstract modeling and
har dware design.
Procedural Costraint:
1. Intial Statement
2. Always Statement
1. Intial Statement:
Syntax:
Initial[timing control]procedural statement
Eg:
Reg count
.
.
.
.
initial
count=2;
2. Always Statement:
Syntax:
Always
[timing contr ol]procedur al statement
eg:
always
clock = ~ clock;
Timing Controls:
1. delay control
2. event contr ol
1.Delay control:
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syntax:
# delay procedur al statement;
eg
# 3 count= 2;
3. Event Control;
1.Edge triggering control
2.Level Triggering control
1. Edgetriggering event control
Syntax:
Event procedural statement;
2. Block Statement:
Sequential Block:
Syntax:
Begin
[: block id{declaration}]
procedur al statements
end;
Parallel Block
Syntax:
Fork
[: block id{declaration}]
procedural statements
join;
4. Procedure Statement
It is an assignment statement with in the initial statement or an always
statement.
Only register data types areassigned in this type
Eg:
Reg[1:2] temp, a, b;
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.
.
.
.
.
#2 temp = a & b;
5. IF statement
Syntax:
If(condition)
Procedural statement;
Else(condition)
Procedural statement;
End;
6. Case statement:
Syntax:
Case(expression)_
Procedural statement;
End case;
Eg:
Case(operation)
Add : z=a+b;
Sub :z= a-b;
Mul : z=a*b;
End case
25) Explain about adder:
Entity Declaration
The entity declaration defines the NAME of the entity and lists the input and
output ports. The general form is as follows,
entity NAME_OF_ENTITY is [ generic generic_declarations);]
port (signal_names: mode type;
signal_names: mode type;
:
signal_names: mode type);
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end [NAME_OF_ENTITY] ;
Structural modeling of design lends itself to hierarchical design, in which one can
define components of units that are used over and over again. Once these
components are defined they can be used as blocks, cells or macros in a higher
level entity. This can significantly reduce the complexity of large designs.
Hierarchical design approaches are always prefer red over flat designs. We will
illustrate the use of a hierarchical design approach for a 4-bit adder, shown in
Figure 4 below. Each full adder can be described by the Boolean expressions for
the sum and carry out signals,
sum = (A
B)
C
carry = AB + C(A
B)
In the VHDL file, we have defined a component for the full adder first. We used
sever al instantiations of the full adder to build the structure of the 4-bit adder. We
have included the libr ary and use clause as well as the entity declarations.
Structural description
The circuit of can also be described using a structural model that specifies what
gates are used and how they are interconnected. The following example
illustrates it.
architecture structural of BUZZER is
-- Declarations
component AND2
por t (in1, in2: in std_logic;
out1: out std_logic);
end component;
component OR2
por t (in1, in2: in std_logic;
out1: out std_logic);
end component;
component NOT1
por t (in1: in std_logic;
out1: out std_logic);
end component;
-- declaration of signals used to interconnect gates
signal DOOR_NOT, SBELT_NOT, B1, B2: std_logic;
begin
-- Component instantiations statements
U0: NOT1 port map (DOOR, DOOR_NOT);
U1: NOT1 port map (SBELT, SBELT_NOT);
U2: AND2 port map (IGNITION, DOOR_NOT, B1);
U3: AND2 port map (IGNITION, SBELT_NOT, B2);
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U4: OR2 port map (B1, B2, WARNING);
end structural;
Architecture body
The architecture body specifies how the circuit operates and how it is
implemented. As discussed earlier, an entity or circuit can be specified in a
variety of ways, such as behavioral, structural (interconnected components), or a
combination of the above.
The architecture body looks as follows,
architecture architecture_name of NAME_OF_ENTITY is
-- Declarations
-- components declarations
-- signal declarations
-- constant declarations
-- function declar ations
-- procedure declar ations
-- type declarations
:
begin
-- Statements
:
end architecture_name;
One can add other libraries and packages. The syntax to declare a package is
as follows:
-- Package declaration
Package name_of_package is
package declarations
end package nam e_of_package;
-- Package body declarations
package body nam e_of_package is
package body declarations
end package body name_of_package;

CONTROL SYSTEM



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CONTROL SYSTEMS
EEE
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Two Marks Questions and answers
1.What is frequency response?
A frequency response is the steady state response of a system when the input to the system is
a sinusoidal signal.
2.List out the different frequency domain specifications?
The frequency domain specification are i)Resonant peak. ii)Resonant frequency.
3.Define –resonant Peak (
)?
r
The maximum value of the magnitude of closed loop transfer function is Called resonant peak.
4.Define –Resonant frequency( f)?
The frequency at which resonant peak occurs is called resonant frequency.
5.What is bandwidth?
The bandwidth is the range of frequencies for which the system gain Is more than 3 dbB.The
bandwidth is a measure of the ability of a feedback system to reproduce the input signal ,noise
rejection characteristics and rise time.
6.Define Cut-off rate?
The slope of the log-magnitude curve near the cut-off is called cut-off rate. The cut-off rate
indicates the ability to distinguish the signal from noise.
7.Define –Gain Margin?
The gain margin,kg is defined as the reciprocal of the magnitude of the open loop transfer
function at phase cross over frequency.
Gain margin kg = 1 /
|
G(j
pc)
|
.
8.Define Phase cross over?
The frequency at which, the phase of open loop transfer functions is called phase cross over
frequency
.
pc
9.What is phase margin?
The phase margin ,
is the amount of phase lag at the gain cross over Frequency required to
bring system to the verge of instability.
10.What is a compensator?
A device inserted into the system for the purpose of satisfying the specifications is called as a
compensator.
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11.Define Gain cross over?
The gain cross over frequency
is the frequency at which the magnitude of the open loop
gc
transfer function is unity.
12.What is Bode plot?
The Bode plot is the frequency response plot of the transfer function of a system. A Bode plot
consists of two graphs. One is the plot of magnitude of sinusoidal transfer function versus log
.The other is a plot of the phase angle of a sinusoidal function versus log
.
13.What are the main advantages of Bode plot?
The main advantages are:
i) Multiplication of magnitude can be in to addition.
ii) A simple method for sketching an approximate log curve is available.
iii) It is based on asymptotic approximation. Such approximation is sufficient if rough information
on the frequency response characteristic is needed.
iv) The phase angle curves can be easily drawn if a template for the phase angle curve of 1+
j
is available.
14.Define Corner frequency?
The frequency at which the two asymptotic meet in a magnitude plot is Called corner frequency.
15.Define Phase lag and phase lead?
A negative phase angle is called phase lag.
A positive phase angle is called phase lead.
16.What are M circles?
The magnitude of closed loop transfer function with unit feed back can be shown to be in the for
every value if M.These circles are called M circles.
17.What is Nichols chart?
The chart consisting if M & N loci in the log magnitude versus phase diagram is called Nichols
chart.
18.What are two contours of Nichols chart?
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Nichols chart of M and N contours, superimposed on ordinary graph. The M contours are the
magnitude of closed loop system in decibels and the N contours are the phase angle locus of
closed loop system.
19.How is the Resonant Peak(M
), resonant frequency(W
) , and band Width determined
r
r
from Nichols chart?
i) The resonant peak is given by the value of .contour which is tangent to G(j
) locus.
ii) The resonant frequency is given by the frequency of G(j
) at the tangency point.
iii) The bandwidth is given by frequency corresponding to the intersection point of G(j
) and –
3dB M-contour.
20.What are the advantages of Nichols chart?
The advantages are:
i) It is used to find the closed loop frequency response from open loop frequency response.
ii) Frequency domain specifications can be determined from Nichols chart.
iii) The gain of the system can be adjusted to satisfy the given specification.
21.What are the two types of compensation?
i. Cascade or series compensation
ii. Feedback compensation or parallel compensation
22.What are the three types of compensators?
i. Lag compensator
ii. Lead compensator
iii. Lag-Lead compensator
23.What are the uses of lead compensator?
speeds up the transient response ,increases the margin of stability of a system,
increases the system error constant to a limited extent.
24.What is the use of lag compensator?
Improve the steady state behavior of a system, while nearly preserving its transient response.
25.When is lag lead compensator is required?
The lag lead compensator is required when both the transient and steady State response of a
system has to be improved
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26.What is nyquist contour
The contour that encloses entire right half of S plane is called nyquist contour.
27.State Nyquist stability criterion.
If the Nyquist plot of the open loop transfer function G(s) corresponding to The nyquist control in
the S-plane encircles the critical point –1+j0 in the Counter clockwise direction as many times
as the number of right half S-plane poles of G(s),the closed loop system is stable.
28.Define Relative stability
Relative stability is the degree of closeness of the system,it an indication of strength or degree
of stability.
29.What are the two segments of Nyquist contour?
i. An finite line segment C1 along the imaginary axis.
ii. An arc C2 of infinite radius.
30.What are root loci?
The path taken by the roots of the open loop transfer function when the loop gain is varied from
0 to _ are called root loci.
31.What is a dominant pole?
The dominant pole is a air of complex conjugate pair which decides the Transient response of
the system.
32.What are the main significances of root locus?
i. The main root locus technique is used for stability analysis.
ii. Using root locus technique the range of values of K, for as table system can be determined
33.What are the effect of adding a zero to a system?
Adding a zero to a system increases peak overshoot appreciably.
34.What are N circles?
If the phase of closed loop transfer function with unity feedback is _, then tan will be in the form
of circles for every value of _. These circles are called N circles.
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35.What is control system?
A system consists of a number of components connected together to perform a specific
function . In a system when the output quantity is controlled by varying the input quantity then
the system is called control system.
36.What are the two major types of control system?
The two major types of control system are open loop and closed loop
37.Define open loop control system.
The control system in which the output quantity has no effect upon the input quantity are called
open loop control system. This means that the output is not feedback to the input for correction.
38.Define closed loop control system.
The control system in which the output has an effect upon the input quantity so as to maintain
the desired output value are called closed loop control system.
39.What are the components of feedback control system?
The components of feedback control system are plant , feedback path elements, error
detector and controller.
40.Define transfer function.
The T.F of a system is defined as the ratio of the laplace transform of output to laplace
transform of input with zero initial conditions.
41.What are the basic elements used for modeling mechanical translational system.
Mass, spring and dashpot
42.What are the basic elements used for modeling mechanical rotational system?
Moment of inertia J,fdashpo with rotational frictional coefficient B and torsional spring with
stiffness K
43.Name two types of electrical analogous for mechanical system.
The two types of analogies for the mechanical system are Force voltage and force current
analogy
44.What is block diagram?
A block diagram of a system is a pictorial representation of the functions performed by each
component of the system and shows the flow of signals. The basic elements of block diagram
are blocks, branch point and summing point.
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45.What is the basis for framing the rules of block diagram reduction technique?
The rules for block diagram reduction technique are framed such that any modification made on
the diagram does not alter the input output relation.
46.What is a signal flow graph?
A signal flow graph is a diagram that represents a set of simultaneousalgebraic equations .By
taking L.T the time domain differential equations governing a control system can be transferred
to a set of algebraic equations in s-domain.
47. What is transmittance?
The transmittance is the gain acquired by the signal when it travels from one node to another
node in signal flow graph.
48.What is sink and source?
Source is the input node in the signal flow graph and it has only outgoing branches.
Sink is a output node in the signal flow graph and it has only incoming branches.
49.Define non touching loop.
The loops are said to be non touching if they do not have common nodes.
50.Write Masons Gain formula.
Masons Gain formula states that the overall gain of the system is
T = 1/ P
k k
k-no.of forward paths in the signal flow graph.
P
- Forward path gain of k
forward path
t h
k
= 1-[sum of individual loop gains ] +[sum of gain products of all possible
combinations of two non touching loops]-[sum of gain products of all
possible combinations of three non touching loops]+…
= for that part of the graph which is not touching k
forward path.
t h
k
51.Write the analogous electrical elements in force voltage analogy for the elements
of mechanical translational system.
Force-voltage e
Velocity v-current i
Displacement x-charge q
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Frictional coeff B-Resistance R
Mass M- Inductance L
Stiffness K-Inverse of capacitance 1/C
52.Write the analogous electrical elements in force current analogy for the elements
of mechanical translational system.
Force-current i
Velocity v-voltage v
Displacement x-flux_
Frictional coeff B-conductance 1/R
Mass M- capacitance C
Stiffness K-Inverse of inductance 1/L
53.Write the force balance equation of an ideal mass element .
F = M d
x /dt
2
2
54. Write the force balance equation of ideal dashpot element .
F = B dx /dt
55. Write the force balance equation of ideal spring element .
F = Kx
56.Distinguish between open loop and closed loop system
open loop system
closed loop system
1.Innaccurate
accurate
2.Simple and economical
Complex and costlier
3.The changes in output
The changes in output due to external
due to external disturbance
disturbances are corrected automatically
are not corrected
Great efforts are needed to design a
4.They are generally stable
stable System
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57.What is servomechanism?
The servomechanism is a feedback control system in which the output is mechanical
position (or time derivatives of position velocity and acceleration,)
58.Why is negative feedback invariably preferred in closed loop system?
The negative feedback results in better stability in steady state and rejects any disturbance
signals.
59.What is transient response?
The transient response is the response of the system when the system changes from one state
to another.
60.What is steady state response?
The steady state response is the response of the system when it approaches infinity.
61.What is an order of a system?
The order of a system is the order of the differential equation governing the system. The order
of the system can be obtained from the transfer function of the given system.
62.Define Damping ratio.
Damping ratio is defined as the ratio of actual damping to critical damping.
63.List the time domain specifications.
The time domain specifications are
i.Delay time
ii.Rise time
iii.Peak time
iv.Peak overshoot
64.Define Delay time.
The time taken for response to reach 50% of final value for the very first time is delay time.
65.Define Rise time.
The time taken for response to raise from 0% to 100% for the very first time is rise time.
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66.Define peak time.
The time taken for the response to reach the peak value for the first time is peak time.
67.Define peak overshoot.
Peak overshoot is defined as the ratio of maximum peak value measured from the Maxmium
value to final value
68.Define Settling time.
Settling time is defined as the time taken by the response to reach and stay within specified
error.
69.What is the need for a controller?
The controller is provided to modify the error signal for better control action
70.What are the different types of controllers?
Proportional controller, PI controller, PD controller, PID controller
71.What is proportional controller?
It is device that produces a control signal which is proportional to the input error signal.
72.What is PI controller?
It is device that produces a control signal consisting of two terms –one proportional to error
signal and the other proportional to the integral of error signal
73.What is the significance of integral controller and derivative controller in a PID
controller?
The proportional controller stabilizes the gain but produces a steady state error.
The integral control reduces or eliminates the steady state error.
74.Why derivative controller is not used in control systems?
The derivative controller produces a control action based on the rate of change of error signal
and it does not produce corrective measures for any constant error.
75.Define Steady state error.
The steady state error is defined as the value of error as time tends to infinity.
76.What is the drawback of static coefficients?
The main draw back of static coefficient is that it does not show the variation of error with time
and input should be standard input.
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77. What is step signal?
The step signal is a signal whose value changes from zero to A at t= 0 and remains constant at
A for t>0.
78. What is ramp signal?
The ramp signal is a signal whose value increases linearly with time from an initial value of zero
at t=0.the ramp signal resembles a constant velocity.
79.What is a parabolic signal?
The parabolic signal is a signal whose value varies as a square of time from an initial value of
zero at t=0.This parabolic signal represents constant acceleration input to the signal.
80.What are the three constants associated with a steady state error?
Positional error constant
Velocity error constant
Acceleration error constant
81.What are the main advantages of generalized error co-efficients?
i) Steady state is function of time.
ii) Steady state can be determined from any type of input
82. What are the effects of adding a zero to a system?
Adding a zero to a system results in pronounced early peak to system response thereby the
peak overshoot increases appreciably.
83. State-Magnitude criterion.
The magnitude criterion states that s=sa will be a point on root locus if for that value of s ,
| D(s) | = |G(s)H(s) | =1
84.State – Angle criterion.
The Angle criterion states that s=sa will be a point on root locus for that value of s, D(s) =
G(s)H(s) =odd multiple of 180°
85. What is a dominant pole?
The dominant pole is a pair of complex conjugate pair which decides the transient response of
the system.
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86.What is stepper motor?
A stepper motor is a device which transforms electrical pulses into equal increments of rotary
shaft motion called steps.
87.What is servomotor?
The motors used in automatic control systems or in servomechanism are Called servomotors.
They are used to convert electrical signal into angular motion.
88.Name the test signals used in control system
The commonly used test input signals in control system are impulse step ramp acceleration and
sinusoidal signals.
89.Define BIBO stability.
A linear relaxed system is said to have BIBIO stability if every bounded Input results in a
bounded output.
90.What is the necessary condition for stability.
The necessary condition for stability is that all the coefficients of the characteristic polynomial be
positive.
91.What is the necessary and sufficient condition for stability.
The necessary and sufficient condition for stability is that all of the elements in the first column
of the routh array should be positive.
92.What is quadrant symmetry?
The symmetry of roots with respect to both real and imaginary axis called quadrant symmetry.
93.What is limitedly stable system?
For a bounded input signal if the output has constant amplitude oscillations Then the system
may be stable or unstable under some limited constraints such a system is called limitedly
stable system.
94.What is synchros?
A synchros is a device used to convert an angular motion to an electrical signal or vice versa.
95.What is steady state error?
The steady state error is the value of error signal e(t) when t tends to infinity.
96.What are static error constants.
The Kp Kv and Ka are called static error constants.
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97.What is the disadvantage in proportional controller?
The disadvantage in proportional controller is that it produces a constant steady state error.
98.What is the effect of PD controller on system performance?
The effect of PD controller is to increase the damping ratio of the system and so the peak
overshoot is reduced.
99.Why derivative controller is not used in control system?
The derivative controller produces a control action based on rare of change of error signal and it
does not produce corrective measures for any constant error. Hence derivative controller is not
used in control system
100.What is the effect of PI controller on the system performance?
The PI controller increases the order of the system by one, which results in reducing the steady
state error .But the system becomes less stable than the original system.
101. What is PD controller?
PD controller is a proportional plus derivative controller which produces an output signal
consisting of two time -one proportional to error signal and other proportional to the derivative of
the signal.
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1)Write in detail about the control system
A control system is a dynamical system that affects the behaviour of another system. Examples
of control systems can be found all around, and in fact there are very few mechanical or electro-
mechanical systems that do not include some kind of a feedback control device. In
robotics
,
control design algorithms are responsible for the motion of the manipulators. In
flight
applications
, control algorithms are designed for stabilization, altitude regulation and disturbance
rejection.
Cruise control
is an interesting application in which the automobile's speed is set at a
fixed value. In electronic amplifier s feedback is used to reduce the damaging influence of
external noise. In addition, these days control systems can be found in diverse fields ranging
from semiconductor manufacturing to environmental regulation.
This course is intended to present you with the basic pr inciples and techniques for the design of
feedback control systems. At this point in your study you have mastered the pr erequisite topics
such as dynamics and the basic mathematical tools that are needed for their analysis. Control
system design relies on your knowledge in these fields but also requires additional skills in
system interfacing. As you will see from this course, from further electives, or fr om future
exper ience, the design of feedback control systems depends on
1. Knowledge of basic engineering principles such as dynamics, fluid mechanics, thermal
science, electrical and electronic circuits, and materials. These tools are important, as
we will soon see, for designing mathematical models of systems. In addition, thorough
understanding of the underlying physics is very valuable in determining the most suitable
control algorithms and hardware.
2. Knowledge of mathematical tools. In control system design, extensive use is made of
matrices and differential equations, and therefore, you should be very comfortable with
such concepts. Laplace transforms and complex variables are also used in control
applications.
3. Knowledge of simulation techniques. System simulation is essential for verifying the
accuracy of the model and for verifying that the final control design meets the desired
specifications. In this course we will use the software Matlab to perform control design
simulations.
4. Knowledge of control design methodologies, and the basic capabilities and limitations of
each control methodology. This aspect of the control design procedure will be the main
goal of this course.
5. Knowledge of control hardware such as the different commercially available sensors and
actuators. We will cover this part briefly in this course.
6. Knowledge of control software for data acquisition and for the implementation of control
algorithms.
Before we go on discussing the technical aspects of feedback contr ol, we will give a very
short outline of its historical beginnings. The use of feedback mechanisms can be traced
back to devices that were invented by the Greeks such as liquid level control
mechanisms. Early work on the mathematical aspects of feedback and control was
initiated by the physicist Maxwell who developed a technique for determining whether or
not systems which are governed by linear dif ferential equations are stable. Other
prominent mathematicians and physicists, such as Routh and Lyapunov, contributed
greatly to the study of stability theory. Their results now for m much of the backbone for
control design.
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Historical Mechanism for Water Level Control.
The study of electronic feedback amplifiers pr ovided the impetus for much of the
progress of control design during the first part of the 20th century. The wor k of Nyquist
(1932) and Bode (1945) used mathematical methods based on complex analysis for the
analysis of the stability and per formance of electronic amplifiers. These techniques are
still in use in many technological applications as we will see in this course. Such complex
analytic methods are currently called classical control techniques.
During the second world war , advances in control design centered around the use of
stochastic analysis techniques to model noise and the development of new methods for
filter ing and estimation. The MIT mathematician N. Wiener was ver y influential in this
development. Also dur ing that period, research at MIT Radiation Laboratory gave rise to
more systematic design methods for servomechanisms.
During the 1950's a differ ent approach to the analysis and design of control systems was
developed. This approach concentrated on differential equations and dynamical systems
as opposed to complex analytic methods. One advantage of this approach is that it is
intimately related to, physical modeling and can be viewed as a continuation to the
methods of analytical mechanics. In addition, it provided a computationally attractive
methodology for both analysis and design of control systems. Work by Kalman in the
USA and Pontryagin in the USSR laid the foundation to what is curr ently called modern
control.
Recently, research aiming at providing reliable and robust control design algorithms
resulted in a combination of complex analytic methods and dynamical systems methods.
These recent approaches utilize the best features of each method. In this course we will
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develop techniques that are based on each one of these approaches. At that point it will
become clearer what the relative mer its are of these two approaches.
2)Explain the modeling of mechanical system
Spring-mass-damper system.
In this example we model the spring- mass-system shown in Figure (a). The mass,
m
is
subjected to an external for ce
f
. Let's suppose that we ar e interested in controlling the
position of
m
. The way to control the position of the mass is by chossing
f
.
We first identify the input and output.
Input: external force,
f
, output: mass position,
x
.
Figure (a) Diagram of the mechanical system components. (b) Free body diagram of the
mechanical system.
We apply Newton's second law to obtain the differential equation of this mechanical
system. Using the free-body-diagram shown in Figure (b), we have
where,
b
is the damping coeff icient and
k
is the spring stiffness . Equation (2) is the
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differential equation that describes the dynamics of the spring- mass-damper system. Note
that the input and output appear in this equation. If we know the input,
f
then we can
solve equation ( 2) for the output,
x
. The mechanical system described can be represented
the following block diagram:
Block diagr am representation of the mechanical system.
3)Explain with examples the term Stability in detail .
Conceptually, a stable system is one for which the output is small in magnitude whenever the
applied input is small in magnitude. In other words, a stable system will not “blow up” when
bounded inputs are applied to it. Equivalently, a stable system’s output will always decay to zero
when no input is applied to it at all. However, we will need to express these ideas in a more
precise definition.
Stability (asymptotic stability):
A linear system of the form
is a stable system if
Notice that
u(t)
= 0 results in an unforced system:
By the variation of parameters formula, the state
x(t)
for such an unforced system satisfies
In this case, the system output
y(t)
=
Cx(t)
is driven only by the initial conditions.
Example 1
Let us analyze the stability of the scalar linear system:
Let
u(t)
= 0 and use the var iation of parameters formula. We have
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If a < 0, then the system is stable because
x(t)
goes as to zero as
t
goes to infinity for any initial
condition. If a = 0,
x(t)
stays constant at the initial condition and according to our definition of
stability the system is unstable. Finally, if a > 0 then
x(t)
goes to infinity (“blows up”) as
t
goes
to infinity and thus the system is unstable.
Example 2:
Let us analyze the stability of the following unforced linear system
Using the var iation of parameters formula one can see that
Because both exponentials have a negative number multiplying
t ,
for any values of the initial
conditions we have
By the definition of stability given above, this system is stable.
Examples of stable and unstable systems are the spring-mass and spring-mass-damper systems.
These two systems are shown in Figure . The spring-mass system (Figure ( a)) is unstable since if
we pull the mass away from the equilibrium position and r elease, it is going to oscillate forever
(assuming there is no air resistance). Therefore it will not go back to the equilibrium position as
time passes. On the other hand, the spring-mass-damper system (Figure (b)) is stable since for
any initial position and velocity of the mass, the mass will go to the equilibrium position and
stops there when it is left to move on its own.
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Figure (a) Spring-mass system with no damping. (b) Spring- mass-damper system.
Let us analyze the stability of the spring-mass system using mathematical relations. The equation
of motion for the spr ing- mass system shown in Figure 1(a) is written as
Note that there is no damping and external force (
b
= 0 and
f
= 0). Rewriting the above
differential equation in the state space form with the mass position and velocity as state
variables, we get
The solution of this state equation is
We now compute the state transition matrix
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Ther efore, the state variables of the system as a function of time are given as
Note that the two state variables do not go to zero as time goes to infinity for any initial
condition. They instead oscillate around the equilibrium point (x
= 0 and x
= 0). Therefore, the
1
2
system is unstable.Another example that demonstrates the concept of stability is the pendulum
system which is shown in Figure . If air resistance is negelected the pendulum will oscillate
forever and thus the system will be unstable. On the other hand, the mass will always go back
to its equilibrum position if air resistance is taken into account and the system will therefore be
stable.
Figure : Pendulum System.
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4)Give the Input/Output Description of a Dynamical System
We have studied systems of the form:
where
u
is the input,
y
is the output and is the initial condition. Pictorially, the system can be
represented as follows:
Fr om the variation of parameters formula, the state
x(t)
satisf ies:
and therefore the output
y(t)
can be written as:
The first term, , is the unforced response r esulting only from the initial conditions and the
term, , is the forced response due to the input
u(t)
. A state space
description of a system is an internal description because it contains all the information that is
available about the internal oper ation of the system. This information is contained in the state
vector. In an external or input/output representation, this internal system information is lost and
the effect of the input only on the output is considered. In other words, the output represents only
the forced response and the initial conditions ar e assumed to be equal to zero.
Given the following internal descr iption of a dynamical system
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we want to find an input/output relationship in the Laplace domain. We first take the Laplace
transform of the above equations with the initial condition set to zero, we have
Solving for
X(s)
we obtain:
Taking the Laplace transform of the output equation
y = Cx+Du
, we find that
An internal or state space system representation descr ibes the evolution of the system in the time
domain. However, an external or input/output system description is developed in the Laplace
domain. We now consider how an external representation may be obtained from an internal one.
The ter m is called the transfer function of the system and it determines the output
Y( s)
for any given input
U(s)
. Notice that the equation does not
contain any information about the system state or the initial conditions.
Summary:
Given the internal repr esentation of a system:
it straightforward to obtain the transfer function
A transfer function can be represented by the following block diagram:
where
Y(s) = T(s)U(s).
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For a given set of system matrices
A
,
B
,
C
,
D
, there is only one corresponding transfer function
T( s). However, one transfer function may correspond to many different state space
representations. A state space description obtained from a transfer function is known as a
realization and can take on many different forms. We will study a few of these forms such as the
controllable canonical form and the observable canonical form later on in the course.Remember
that in computing a transfer function, the initial conditions ar e set to zero. Therefore, a piece of
infor mation is lost in the transformation from a state space description to a transfer function.
5)Discuss about the block diagram
We will deal with block diagrams of the form shown below. Comparing this diagram with the
one given in the previous lecture we note that the sensor block
S(s)
is missing here. The closed
loop system below is called a unity feedback system since
S(s)
= 1. I n practice this can be easily
achieved by adding an amplifier to the measurement system in order to make the measured and
actual outputs equal in value. The units of two outputs will be usually different.
Fr om the previous lecture the transfer function of the above closed loop (feedback) system is
(with
S(s)
= 1):
The transfer function from the input
R
to the error
E
is equal to
Response of the closed loop syst em
If we know the input signal
r(t),
then the response of the system due to the input signal can be
found as follows
6)Explain the standard input t est signals
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1. Unit step,
2. Step,
3. Ramp,
4. Sine signal,
Refer note
7) Explain Feedback Control Approach
•Establish control objectives
–Qualitative–don’t use too much fuel
–Quantitative
–settling time of step response<3sec
–Typically requires that you understand the process (expected commands and disturbances ) and the over
all goa ls (bandwidths).
–Often requires that you have a strong understanding of the physical dynamics of the systems that you do
not “fight” them in inappropriate (i.e .,inefficient) ways.
•Selectsensors&actuators
–What aspects of the system are to be sensed and controlled?
–Consider sensor noise and linearity as key discrimina tors.
–Cost, reliability ,size,...
•Obtain model
–Analytic(FEM) or from measured data (system ID )
–Evaluationmodel reducesize/complexity D esignmodel
–Accuracy ? Error model ?
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•Design controller –Select technique (SISO,MIMO),(classical , state-space)
–Choose parameters (ROT , optimization)
•Analyz e closed-loop performa nce.
Meet objectives ?
–Analysis, simulation, experimentation,...
–Yes- done, No- iterate...
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8)Find the transfer function of the given mechanical translational system
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9)
Obtain the Bode plot of the system given by the tr ansfer function G(s)= 1
(2s+1)
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10)Explain Polar Plot.
G j
( )
G j
( )
The polar plot of a sinusoidal transfer function
is a plot of the magnitude of
G j
( )
versus the phase angle of
on polar coordinates as
is varied from zero to infinity. An
advantage of using polar plot is that it depicts the frequency response characteristics of a
system over
the entire frequency range in a
single plot.
The polar
plot of
1 1
G j T
( ) tan
= =
is shown in figure below.
-
1
1 1
+ +
j T T
2 2
The polar plot of the transfer function,
1
G j j j T
( ) (1 )
= +
is shown in figure
above.
The plot is asymptotic to the vertical line
passing through the point (-T, 0).
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Polar plots are useful for the stability study of systems. The general shapes of the polar plots of
some important transfer functions are given in figure below.
From the plots above, following observations are made,
1. Addition of a nonzero pole to the transfer function results in further rotation of the polar
8
.
plot through an angle of -90
°
as
2. Addition of a pole at the origin to the transfer function rotates the polar plot at zero and
infinite frequencies by a further angle of -90
°
.
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11) Draw the Bode plot of the transfer function G(s)= 64(s+2)
s(s+0.5)(s
+3.2s+64)
2
64( 2) 4(1 / 2)
s s
+ +
.
G s s s s s s s s s
( ) ( 0.5)( 3.2 64) (1 2 )(1 0.05 / 64)
= =
+ + + + + +
2 2
The sinusoidal transfer function in time-constant form is,
4(1 / 2)
+
j
.
G j
( )
=
2
j j j
(1 2 )(1 0.4 8 8
+ + -
f
Factor
Log-magnitude characteristic Phase angle
c
characteristic
4 /
j
Constant
- Straight line of slope -20 db/decade,
20log4 12
=
passing through
db point
-90
°
at
.
=
1
1/1 2
+
j
<
0 to -90
=
Straight line of 0 db for
,
,
o
1
1
0.5
straight line of slope -20 db/decade for
-
45
at
.
o
>
.
1
1
1 0.5
+
j
<
0 to +90
=
Straight line of 0 db for
,
,
o
2
2
2
straight line of slope +20 db/decade
45
at
.
o
>
for
.
2
2
<
0 to 180
-
=
Straight line of 0 db for
,
o
2
3
1 0.4 8 8
+ -
j
;
3
= =
8, 0.2
8
straight line of slope -40 db/decade for
n
-
90
at
.
o
>
.
3
3
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The phase angle curve may be drawn using the following procedure.
( )
K j
/
1. For the factor
, draw a straight line of -90
°
r.
r
(1 )
+
j T
2. The phase angles of the factor
are
±
1
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±
45 at =1/T
a.
o
±
26.6 at =1/2T
b.
o
±
5.7 at =1/10T
c.
o
±
63.4 at =2/T
d.
o
±
84.3 at =10/T
e.
o
3. The phase angles for the quadratic factor are
a.
-
90 at =
o
n
b. A few points of phase angles are read off from the normalized Bode plot for the
particular
.
12) Construct the root locus for the open-loop transfer function .
The degree of the numerator polynomial is . This means that the transfer function has one
zero ( ). The degree of the denominator polynomial is and we have the four poles
( , , , 2). First the poles (x) and the zeros (o) of the
open loop are drawn on the plane as shown in Figure
1
. According to rule 3 these poles are
just
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Figure 1:
Root locus of . Values of are in red and underlined.
those points of the root locus where and the zeros where . We have
branches that go to infinity and the asymptotes of these three branches are lines which intercept
the real axis according to rule 6.The crossing is at
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and the slopes of the asymptotes are
i.e.
The asymptotes are shown in Figure 1as blue lines. Using Rule 4 it can be checked which
points on the real axis are points on the root locus. The points with and
belong to the root locus, because to the right of them the number of poles and zeros is odd.
According to rule 7 breakaway and break-in points can only occur pair wise on the real axis to
the left of -2. Here we have
or
This equation has the solutions , and . The real
roots and are the positions of the breakaway and the break-in point. The
angle of departure of the root locus from the complex pole at can be
determined from Figure
2
(6.30)
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Figure 2:
Calculating the angle of departure of the complex pole
With this specifications the root locus can be sketched. Using rule 9 the value of can be
determined for some selected points. The value at the intersection with the imaginary axis is