, O N E z ! z !
Introduction
ANSWERS TO REVIEW QUESTIONS z! z! z!
1. Guided missiles, automatic gain control in radio receivers, satellite tracking antenna
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2. Yes - power gain, remote control, parameter conversion; No - Expense, complexity
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3. Motor, low pass filter, inertia supported between two bearings
z! z! z! z! z! z! z! z!
4. Closed-
loop systems compensate for disturbances by measuring the response, comparing it to the inpu
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t response (the desired output), and then correcting the output response.
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5. Under the condition that the feedback element is other than unity
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6. Actuating signal z!
7. Multiple subsystems can time share the controller. Any adjustments to the controller can b
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e implemented with simply software changes.
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8. Stability, transient response, and steady-state error
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9. Steady-state, transient z!
10. It follows a growing transient response until the steady-
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state response is no longer visible. The system will either destroy itself, reach an equilibrium sta
z! z! z! z! z! z! z! z! z! z! z! z! z! z! z!
te because of saturation in driving amplifiers, or hit limit stops.
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11. Transient response z!
12. True
13. Transfer function, state-space, differential equations
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14. Transfer function - the Laplace transform of the differential equation
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State-space - representation of an nth order differential equation as n simultaneous first-
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order differential equations
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Differential equation - Modeling a system with its differential equation
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SOLUTIONS TO PROBLEMS z! z!
50 volts z! z!
1. Five turns yields 50 v. Therefore K = 1.59
5 x 2 rad
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= z! z! z!
,
, 2
z ! Chapter 1: z! z ! Introductio
n
2.
Desiredz!t Temperature Voltagez! Actualz!temperatur
Fuelz!flo
emperature z!difference
difference e
w
z!
+ Amplifierz!and
Thermostat Heater
z! valves
-
3.
Desired Inputz! Errorz! Aileronz Roll Rollz!
z!rollz!a voltage voltage positio
! z!rat angle
ngle n e
+
controls
-
4.
Inputz!
Speed
Desired voltage Actual
Errorz!
z! Motorz!a
z!speed z!spee
+ voltage ndz!drive
transducer Amplifier system d
-
Dancer
Dancerz!
positionz!sen
Voltagez!pr dynamics
sor
oportional
toz!actualz!speed
5.
Inputz! Power Rodz!
voltage Errorz!
z!
position
Desired voltage Motorz! Actual
power andz!dri z!powe
Transducer
+ Amplifier vez!syst Reactor r
em
-
Sensorz!&z!
transducer
Voltagez!pro
portional
toz!actualz!power
Introduction
ANSWERS TO REVIEW QUESTIONS z! z! z!
1. Guided missiles, automatic gain control in radio receivers, satellite tracking antenna
z! z! z! z! z! z! z! z! z! z!
2. Yes - power gain, remote control, parameter conversion; No - Expense, complexity
z! z! z! z! z! z! z! z! z! z! z!
3. Motor, low pass filter, inertia supported between two bearings
z! z! z! z! z! z! z! z!
4. Closed-
loop systems compensate for disturbances by measuring the response, comparing it to the inpu
z! z! z! z! z! z! z! z! z! z! z! z! z!
t response (the desired output), and then correcting the output response.
z! z! z! z! z! z! z! z! z! z!
5. Under the condition that the feedback element is other than unity
z! z! z! z! z! z! z! z! z! z!
6. Actuating signal z!
7. Multiple subsystems can time share the controller. Any adjustments to the controller can b
z! z! z! z! z! z! z! z! z! z! z! z! z!
e implemented with simply software changes.
z! z! z! z! z!
8. Stability, transient response, and steady-state error
z! z! z! z! z!
9. Steady-state, transient z!
10. It follows a growing transient response until the steady-
z! z! z! z! z! z! z! z!
state response is no longer visible. The system will either destroy itself, reach an equilibrium sta
z! z! z! z! z! z! z! z! z! z! z! z! z! z! z!
te because of saturation in driving amplifiers, or hit limit stops.
z! z! z! z! z! z! z! z! z! z!
11. Transient response z!
12. True
13. Transfer function, state-space, differential equations
z! z! z! z!
14. Transfer function - the Laplace transform of the differential equation
z! z! z! z! z! z! z! z! z!
State-space - representation of an nth order differential equation as n simultaneous first-
z! z! z! z! z! z! z! z! z! z! z! z!
order differential equations
z! z!
Differential equation - Modeling a system with its differential equation
z! z! z! z! z! z! z! z! z!
SOLUTIONS TO PROBLEMS z! z!
50 volts z! z!
1. Five turns yields 50 v. Therefore K = 1.59
5 x 2 rad
z! z! z! z! z! z! z! z!
= z! z! z!
,
, 2
z ! Chapter 1: z! z ! Introductio
n
2.
Desiredz!t Temperature Voltagez! Actualz!temperatur
Fuelz!flo
emperature z!difference
difference e
w
z!
+ Amplifierz!and
Thermostat Heater
z! valves
-
3.
Desired Inputz! Errorz! Aileronz Roll Rollz!
z!rollz!a voltage voltage positio
! z!rat angle
ngle n e
+
controls
-
4.
Inputz!
Speed
Desired voltage Actual
Errorz!
z! Motorz!a
z!speed z!spee
+ voltage ndz!drive
transducer Amplifier system d
-
Dancer
Dancerz!
positionz!sen
Voltagez!pr dynamics
sor
oportional
toz!actualz!speed
5.
Inputz! Power Rodz!
voltage Errorz!
z!
position
Desired voltage Motorz! Actual
power andz!dri z!powe
Transducer
+ Amplifier vez!syst Reactor r
em
-
Sensorz!&z!
transducer
Voltagez!pro
portional
toz!actualz!power
