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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 inputresponse (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 agrowing 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
1. Five turns yields 50 v. Therefore K =

50 volts = 1.59 5 x 2π rad

2 Chapter 1: Introduction

2.

Desired temperature

Temperature difference

Voltage difference

Fuel flow

Actualtemperature Heater

+
Thermostat

Amplifier and valves

-

3.

Desired roll angle

Input voltage

Error voltage Aileron position control

Aileron position Aircraft dynamics

Roll rate Integrate

Roll angle

Pilot controls

+ -

Gyro voltage

Gyro

4.
Desired speed
transducer

Input voltage

+ -

Speed Error voltage
Amplifier

Motor and drive system
Dancerdynamics

Actual speed

Voltage proportional to actual speed

Dancer position sensor

5.
Input voltage

Desired power
Transducer

Power Error voltage
Amplifier

Rod position

+ -

Motor and drive system

Actual power Reactor

Voltage proportional to actual power

Sensor & transducer

Solutions to Problems 3

6.
Graduating and drop-out rate Actual student rate AdmissionsDesired student population

Population error

Desired student rate Administration

+

Net rate of influx Integrate

Actual student population

+ -

7.
Voltage proportional to desired volume Voltage representing actual volume Volume control circuit Radio

Desired volume Transducer

+

Volume error

Actual volume

Effective volume

+ Voltage proportional to speedTransducer

Speed

4 Chapter 1: Introduction

8. a.
Fluid input

Valve Actuator

Power amplifier +V Differential amplifier + +V -V

R

Desired level

R
Float Tank -V Drain

b.
Desired level Potentiometer voltage in + Amplifiers Flow rate in + Integrate Actual level

Actuator and valve

Drain Flow rate out Displacement Potentiometer Float

voltage out

Solutions toProblems 5

9.

Desired force Transducer

+ Amplifier -

Current Valve

Displacement Actuator and load

Displacement Tire

Actual force

Load cell

10.

Commanded blood pressure + Vaporizer -

Isoflurane concentration Patient

Actual blood pressure

11.

Desired depth + -

Controller & motor

Force Grinder

Feed rate Integrator

Depth

12.

Desired positionCoil voltage + Transducer -

Coil circuit

Coil current

Solenoid coil & actuator

Force

Armature & spool dynamics

Depth

LVDT

13. a. L

di + Ri = u(t) dt

6 Chapter 1: Introduction

b. Assume a steady-state solution iss = B. Substituting this into the differential equation yields RB = 1,

1 R . The characteristic equation is LM + R = 0, from which M = - . Thus, the...
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