ANSWERS TO REVIEW QUESTIONS

O N E

Introduction

ANSWERS TO REVIEW QUESTIONS

• Guided missiles, automatic gain control in radio receivers, satellite tracking antenna
• Yes - power gain, remote control, parameter conversion; No - Expense, complexity
• Motor, low pass filter, inertia supported between two bearings
• 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.

• Under the condition that the feedback element is other than unity
• Actuating signal
• Multiple subsystems can time share the controller. Any adjustments to the controller can be

implemented with simply software changes.

• Stability, transient response, and steady-state error
• Steady-state, transient
• 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.

• Transient response
• True
• Transfer function, state-space, differential equations
• 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

• Five turns yields 50 v. Therefore K =

50 volts

• x 2πrad

= 1.59

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2 Chapter 1: Introduction

2.

Thermostat Amplifier and valves Heater Temperature difference Voltage difference Fuel flow Actual temperature Desired temperature + -

3.

Desired roll angle Input voltage + - Pilot controls Aileron position control Error voltage Aileron position Aircraft dynamics Roll rate Integrate Roll angle Gyro Gyro voltage

4.

Speed Error voltage Desired speed Input voltage + - transducerAmplifier Motor and drive system Actual speed Voltage proportional to actual speed Dancer position sensor Dancer dynamics

5.Desired power

Power Error voltage Input voltage + - TransducerAmplifier Motor and drive system Voltage proportional to actual power Rod position Reactor Actual power Sensor & transducer

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Solutions to Problems 3

6.Desired student population + - Administration Population error Desired student rate Admissions Actual student rate+ - Graduating and drop-out rate Net rate of influx Integrate Actual student population

7.Desired volume+ - Transducer Volume control circuit Voltage proportional to desired volume Volume error Radio Voltage representing actual volume Actual volume - + Transducer - Speed Voltage proportional to speed Effective volume

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4 Chapter 1: Introduction

8.a.R +V -V Differential amplifier Desired level +- Power amplifier Actuator Valve Float Fluid input Drain Tank R +V -V

b.Desired level Amplifiers Actuator and valve Flow rate in Integrate Actual level Flow rate out Potentiometer + - + Drain FloatPotentiometer - voltage in voltage out Displacement

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