O N E
Introduction
ANSWERS TO REVIEW QUESTIONS
1. Guided missiles, automatic gain control in radio receivers, satellite tracking antenna
2. Yes - power gain, remote control, parameter conversion; No - Expense, complexity
3. Motor, low pass filter, inertia supported between two bearings
4. Closed-loop systems compensate for disturbances by measuring the response, comparing it to
the input response (the desired output), and then correcting the output response.
5. Under the condition that the feedback element is other than unity
6. Actuating signal
7. Multiple subsystems can time share the controller. Any adjustments to the controller can be
implemented with simply software changes.
8. Stability, transient response, and steady-state error
9. Steady-state, transient
10. It follows a growing transient response until the steady-state response is no longer visible. The
system will either destroy itself, reach an equilibrium state because of saturation in driving
amplifiers, or hit limit stops.
11. Transient response
12. True
13. Transfer function, state-space, differential equations
14. Transfer function - the Laplace transform of the differential equation
State-space - representation of an nth order differential equation as n simultaneous first-order
differential equations
Differential equation - Modeling a system with its differential equation
SOLUTIONS TO PROBLEMS
50 volts
1. Five turns yields 50 v. Therefore K = = 1.59
5 x 2π rad
,2 Chapter 1: Introduction
2.
Desired Temperature Voltage Actual
Fuel
temperature difference difference temperature
flow
+ Amplifier and
Thermostat Heater
valves
-
3.
Desired Input Error Aileron Roll Roll
roll voltage voltage position rate angle
angle
+ Aileron Aircraft
Pilot Integrate
position dynamics
controls
control
-
Gyro
Gyro voltage
4.
Input
Speed
Desired voltage Actual
Error Motor
speed speed
transducer
+ voltage and
Amplifier drive
system
-
Dancer
Dancer
position
Voltage dynamics
sensor
proportional
to actual speed
5.
Input Power Rod
voltage Error position
Desired voltage Motor Actual
power and power
Transducer
+ Amplifier drive Reactor
system
-
Sensor &
Voltage transducer
proportional
to actual power
, Solutions to Problems 3
6.
Graduating
and
drop-out
rate
Desired Actual
Desired Population student Actual
Net rate student
student error rate student - of influx population
population + rate +
Administration Admissions Integrate
-
7.
Voltage Voltage
proportional representing
to desired Volume actual volume Actual
Desired volume error volume
volume + Volume
Transducer Radio
control circuit
-
Effective
volume
+
Voltage
- proportional
to speed
Transducer
-
Speed
, 4 Chapter 1: Introduction
8.
a.
Fluid input
Valve
Actuator
Power
amplifier
+V
Differential Desired
amplifier R level
- + -V
+V
R
Float -V
Tank
Drain
b.
Flow Actual
Desired voltage level
in rate in
level + +
Potentiometer Amplifiers Actuator Integrate
and valve
- -
Drain
Flow
rate out
Displacement
voltage
out
Potentiometer Float
Introduction
ANSWERS TO REVIEW QUESTIONS
1. Guided missiles, automatic gain control in radio receivers, satellite tracking antenna
2. Yes - power gain, remote control, parameter conversion; No - Expense, complexity
3. Motor, low pass filter, inertia supported between two bearings
4. Closed-loop systems compensate for disturbances by measuring the response, comparing it to
the input response (the desired output), and then correcting the output response.
5. Under the condition that the feedback element is other than unity
6. Actuating signal
7. Multiple subsystems can time share the controller. Any adjustments to the controller can be
implemented with simply software changes.
8. Stability, transient response, and steady-state error
9. Steady-state, transient
10. It follows a growing transient response until the steady-state response is no longer visible. The
system will either destroy itself, reach an equilibrium state because of saturation in driving
amplifiers, or hit limit stops.
11. Transient response
12. True
13. Transfer function, state-space, differential equations
14. Transfer function - the Laplace transform of the differential equation
State-space - representation of an nth order differential equation as n simultaneous first-order
differential equations
Differential equation - Modeling a system with its differential equation
SOLUTIONS TO PROBLEMS
50 volts
1. Five turns yields 50 v. Therefore K = = 1.59
5 x 2π rad
,2 Chapter 1: Introduction
2.
Desired Temperature Voltage Actual
Fuel
temperature difference difference temperature
flow
+ Amplifier and
Thermostat Heater
valves
-
3.
Desired Input Error Aileron Roll Roll
roll voltage voltage position rate angle
angle
+ Aileron Aircraft
Pilot Integrate
position dynamics
controls
control
-
Gyro
Gyro voltage
4.
Input
Speed
Desired voltage Actual
Error Motor
speed speed
transducer
+ voltage and
Amplifier drive
system
-
Dancer
Dancer
position
Voltage dynamics
sensor
proportional
to actual speed
5.
Input Power Rod
voltage Error position
Desired voltage Motor Actual
power and power
Transducer
+ Amplifier drive Reactor
system
-
Sensor &
Voltage transducer
proportional
to actual power
, Solutions to Problems 3
6.
Graduating
and
drop-out
rate
Desired Actual
Desired Population student Actual
Net rate student
student error rate student - of influx population
population + rate +
Administration Admissions Integrate
-
7.
Voltage Voltage
proportional representing
to desired Volume actual volume Actual
Desired volume error volume
volume + Volume
Transducer Radio
control circuit
-
Effective
volume
+
Voltage
- proportional
to speed
Transducer
-
Speed
, 4 Chapter 1: Introduction
8.
a.
Fluid input
Valve
Actuator
Power
amplifier
+V
Differential Desired
amplifier R level
- + -V
+V
R
Float -V
Tank
Drain
b.
Flow Actual
Desired voltage level
in rate in
level + +
Potentiometer Amplifiers Actuator Integrate
and valve
- -
Drain
Flow
rate out
Displacement
voltage
out
Potentiometer Float
