Automatic Control Systems, 9th Edition - CEMS Homegmirchan/classes/EE295/ch03.pdf · Automatic...
Transcript of Automatic Control Systems, 9th Edition - CEMS Homegmirchan/classes/EE295/ch03.pdf · Automatic...
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Text Illustrations in PPTChapter 3: THEORETICAL FOUNDATION AND BACKGROUND MATERIAL: COMPLEX VARIABLES,
DIFFERENTIAL EQUATIONS, LAPLACE TRANSFORM
Automatic Control Systems, 9th Edition
Farid Golnaraghi, Simon Fraser UniversityBenjamin C. Kuo, University of Illinois
ISBN: 978-0-470-04896-2
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fig_03_01
Heating system block diagram (simplified).Actual temp. (output)measured by sensor in the thermostat. Simple electronic circuit (comparator) compares temps. Generates error voltage that acts as as switch to open the gas valve to turn out the furnace. Opening windows and doors etc. in room causes heat loss (disturbance). Process of sensing output and comparing with input to generate error signal called Feedback.
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fig_03_02
(a) Open loop, dc-motor, speed control system (b) Block diagram; input voltage to the motor, output of (non linear) power amp. Representation issue for NL blocks.
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fig_03_03
Common elements in block diagram of most control systems (Compare to Figs.3-1, 3-2
. Comparators (electronic circuit measures error)
. BLOCKS representing transfer functions . Reference sensor . Output sensor . Actuator . Controller . Plant . INPUT or reference signals. OUTPUT signals. Disturbance signal. Feedback loops
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fig_03_04
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fig_03_05
X(s) = G(s) U(s)
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fig_03_06
X(s) = G_1(s) G_2(s) U(s)
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fig_03_07
G(s) = G_1(s) + G_2(s)
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fig_03_08
M(s) = Y(s) = G(s) R(s) 1 + G(s) H(s)
M(s) = Y(s) = G(s) R(s) 1 - G(s) H(s)
negative feedback
positive feedback
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x(t) + 2ζωnx(t) + ω2n(t)x(t) = ω2
nu(t)
fig_03_09
2ζω2nsX(s)
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fig_03_10
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fig_03_11
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fig_03_12
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fig_03_13
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fig_03_14
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ω2n
fig_03_15
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fig_03_16
Moving a branch point
H_1(s) G_2(s)
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fig_03_17
Moving a comparator from RHS of G_2(s) to its LHS
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fig_03_18a
Block diagram reduction
first move branch pt. at Y_1 to left of G_2
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fig_03_18b
1 + G_1G_2H_1
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Y (s)R(s)
=G1(s)G2(s)
1 + G1(s)G2(s)H1(s)
Y (s)R(s)
=−G2(s)
1 + G1(s)G2(s)H1(s)
Ytotal = YR|D=0 + YD|R=0
fig_03_19
Block diagram of system undergoing disturbance
We need to determine effects of D(s) on the system
So disturbance interferes with controller signal and adversely affectssystem performance.
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fig_03_20
Block diagram for D(s) = 0
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fig_03_21
Block diagram for R(s)=0
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fig_03_22
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Y (s) = [I + G(s)H(s)]−1G(s)R(s)
fig_03_23
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fig_03_24
Signal Flow Graphs
Basic properties of SFG. Only for linear systems. Equations for SFG algebraic equations. Nodes are used to represent variables. Signals travel along branches only in direction of arrows. Branch from node y_1 to y_2 shows dependence of node y_2 on node y_1
Other SFG termsInput node (source) - A node that only has outgoing branchesOutput node (sink) - A node that only has incoming branches
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fig_03_25
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fig_03_26
Can make y_2 an output node.
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fig_03_27
Erroneous operation for SFG of Fig. 3-26(a)
Cannot make y_2 an input node; equation for y_2 different from original SFG.
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fig_03_28
4 loops in the SFG of Fig.3-25(d)
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fig_03_29
Node y_1 a summing point; also a transmitting point.
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fig_03_30
Simplification of SFG
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fig_03_31
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fig_03_32
SFG for feedback system of Fig.3-8
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SFG Terms
Forward Path: a path that starts at an input node and ends at an output node and along which no no node is traversed more than once.
Path Gain: The product of the branch gains encountered in traversing a path.
Loop: A path that starts and terminates at the same node and along which no other node is encountered more than once.
Forward-Path Gain: Path gain of a forward path.
Loop Gain: Path gain of a loop.
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fig_03_33
What is the gain y7/y1 ?
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fig_03_35
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fig_03_36
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figun_03_01
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figun_03_02
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figun_03_03
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figun_03_04
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figun_03_05a
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figun_03_05b
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figun_03_06
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figun_03_07
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figun_03_08
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figun_03_09
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figun_03_10
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figun_03_11
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figun_03_12
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figun_03_13
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figun_03_14
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figun_03_15
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figun_03_16
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figun_03_17
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figun_03_18
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figun_03_19a
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figun_03_19b
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figun_03_20
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figun_03_21
![Page 62: Automatic Control Systems, 9th Edition - CEMS Homegmirchan/classes/EE295/ch03.pdf · Automatic Control Systems, 9th Edition Farid Golnaraghi, Simon Fraser University Benjamin C. Kuo,](https://reader034.fdocuments.us/reader034/viewer/2022042504/5a78656f7f8b9aa2448b4c06/html5/thumbnails/62.jpg)
figun_03_22
![Page 63: Automatic Control Systems, 9th Edition - CEMS Homegmirchan/classes/EE295/ch03.pdf · Automatic Control Systems, 9th Edition Farid Golnaraghi, Simon Fraser University Benjamin C. Kuo,](https://reader034.fdocuments.us/reader034/viewer/2022042504/5a78656f7f8b9aa2448b4c06/html5/thumbnails/63.jpg)
figun_03_23
![Page 64: Automatic Control Systems, 9th Edition - CEMS Homegmirchan/classes/EE295/ch03.pdf · Automatic Control Systems, 9th Edition Farid Golnaraghi, Simon Fraser University Benjamin C. Kuo,](https://reader034.fdocuments.us/reader034/viewer/2022042504/5a78656f7f8b9aa2448b4c06/html5/thumbnails/64.jpg)
table_03_01