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01. Introduction

System Dynamics and Control 1.01 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

Learning Outcome

After completing this chapter, the student will be able to

• Define a control system and describe some applications

• Describe historical developments leading to modern day

control theory

• Describe the basic features and configurations of control

systems

• Describe control systems analysis and design objectives

• Describe a control system’s design process

• Describe the benefit from studying control systems

System Dynamics and Control 1.02 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§1.Introduction

- Control System Definition

A control system consists of subsystems and processes (or

plants) assembled for the purpose of obtaining a desired output

with desired performance, given a specified input

- Ex.: elevator control system

System Dynamics and Control 1.03 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§1.Introduction

Early elevators were

controlled by hand ropes

or an elevator operator

Today, elevators are fully automatic,

using control systems to regulate

position and velocity

System Dynamics and Control 1.04 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§2.A History of Control Systems

B.C.200 Greece

Float regulator mechanism

B.C.50 Middle East

Water clock

1600 Cornelis Drebbel, Holland

First feedback system

Temperature regulator

1462-1727 Sir Isaac Newton

Mathematical modeling

1685-1731 Brook Taylor

Taylor series

1700 Dennis Papin

Pressure regulator for steam boiler

System Dynamics and Control 1.05 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§2.A History of Control Systems

1749-1827 Pierse Simon Laplace

Laplace Transform

1769 James Watt

First automatic controller

Flyball governer

1765 I. Polzunov, Soviet Union

First level regulator system

1831-1907 Edward John Routh

Routh criterion

1859-1925 Oliver Heaviside

Mathematical analysis

1868 J.C. Maxwell

Mathematical theory for control system

System Dynamics and Control 1.06 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

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§2.A History of Control Systems

1890’ Lyapunov, Soviet Union

Stability theory

1930’ Nyquist, Bode, Black; Bell Telephone Lab

Electronic feedback amplifier

1889-1976 Harry Nyquist

Nyquist criterion

1898-1981 Harold Black

Negative feedback amp

1905-1982 Hendrik Bode

Bode diagram

WWII period Automatic airplane pilot; Gun-positioning system,

radar; Antenna control system; Military systems

System Dynamics and Control 1.07 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§2.A History of Control Systems

Post War Frequency domain analysis

Laplace transform method

1903-1957 John Von Neumann

Basic operation of digital computer

1950’ Root locus method

Computer age open (digital control)

Space age (Sputnik, Soviet Union)

Maximum principle (Pontryagin)

Optimal control

Adaptive control system (Draper)

1960’ Dynamic programming (Bellman)

State space method

System Dynamics and Control 1.08 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

Sputnik, 1957

§2.A History of Control Systems

1970’ Microprocessor based control system

Digital control system

1980 Neural network

Artificial Intelligent

Fuzzy control

Predictive control

Doyle & Stein: LQG / LTR

Remote diagnostic control system

System Dynamics and Control 1.09 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§3.System Configurations

- Open-Loop Systems

- Closed-Loop Systems

- Computer-Controlled Systems

System Dynamics and Control 1.10 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§4.Analysis and Design Objectives

- Analysis: determine a system’s performance

- Design: create or change a system’s performance

- A control system is dynamic → It responds to an input by

undergoing a transient response before reaching a steady-state

response that generally resembles the input

- Three major objectives of systems analysis and design

• Producing the desired transient response

• Reducing steady-state error

• Achieving stability

Other design concerns

• Cost

• The sensitivity of system performance to changes in

parameters

System Dynamics and Control 1.11 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

𝑥 𝑡 =𝑏

𝑎+ 𝑥 0 −

𝑏

𝑎𝑒−𝑎𝑡 = 𝑥 0 𝑒−𝑎𝑡 +

𝑏

𝑎1 − 𝑒−𝑎𝑡

§4.Analysis and Design Objectives

- Response

The solution of 𝑥 + 𝑎𝑥 = 𝑏

𝑥 𝑡 =𝑏

𝑎+ 𝑥 0 −

𝑏

𝑎𝑒−𝑎𝑡

𝑥 𝑡 = 𝑥 0 𝑒−𝑎𝑡 +𝑏

𝑎1 − 𝑒−𝑎𝑡

Response

• Steady-state: the part of the response that remains with time

• Transient: the part of the response that disappears with time

• Free: the part of the response that depends on the initial conditions

• Forced: the part of the response due to the forcing function

System Dynamics and Control 1.12 Introduction

or

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

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𝑥 𝑡 =𝑏

𝑎+ 𝑥 0 −

𝑏

𝑎𝑒−𝑎𝑡 = 𝑥 0 𝑒−𝑎𝑡 +

𝑏

𝑎1 − 𝑒−𝑎𝑡

§4.Analysis and Design Objectives

- Stability

The solution of 𝑥 + 𝑎𝑥 = 𝑏

𝑥 𝑡 = 𝑥 0 𝑒−𝑎𝑡 +𝑏

𝑎1 − 𝑒−𝑎𝑡

• Unstable: the free response approaches ∞ as 𝑡 → ∞

• Stable: the free response approaches 0

• Neutral stability: the borderline between stable and unstable.

The free response does not approach both ∞ and 0

- Other considerations

• Finances

• Robustness

System Dynamics and Control 1.13 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§4.Analysis and Design Objectives

- Case study: An Introduction to Position Control Systems

Scheme

System concept Design layout

Functional block diagram

System Dynamics and Control 1.14 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§4.Analysis and Design Objectives

- Response of a position control system, showing effect of high

and low controller gain on the output response

System Dynamics and Control 1.15 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§5.The Design Process

- The control system design process

- The antenna azimuth position control system are

using as an example through the control system

design process

System Dynamics and Control 1.16 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§5.The Design Process

Step 1: Transform Requirements Into a Physical System

Requirements

• Desire to position the antenna

• System features such as weight and physical dimensions

Using the requirements, design specifications are determined

• Desired transient response

• Steady-state accuracy

System Dynamics and Control 1.17 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§5.The Design Process

Step 2: Draw a Functional Block Diagram

Translates a qualitative description of the system into a

functional block diagram that describes the component parts of

the system (that is, function and/or hardware) and shows their

interconnection

System Dynamics and Control 1.18 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

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§5.The Design Process

Step 3: Create a Schematic

After producing the description of a physical system, the control

systems engineer transforms the physical system into a

schematic diagram. The control system designer can begin with

the physical description to derive a schematic

System Dynamics and Control 1.19 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§5.The Design Process

Step 4: Develop a Mathematical Model (Block Diagram)

Using the physical laws, along with simplifying assumptions, to

model the system mathematically

• Kirchhoff’svoltage law The sum of voltages around a closed path

equals zero

• Kirchhoff’scurrent law The sum of electric currents flowing from

a node equals zero

• Newton’s laws The sum of forces on a body equals zero,

The sum of moments on a body equals zero

The model describes the relationship between the input and output

𝑑𝑛𝑐(𝑡)

𝑑𝑡𝑛+ 𝑑𝑛−1

𝑑𝑛−1𝑐(𝑡)

𝑑𝑡𝑛−1+⋯+ 𝑑0𝑐 𝑡 =

𝑏𝑚𝑑𝑚𝑢(𝑡)

𝑑𝑡𝑚+ 𝑏𝑚−1

𝑑𝑚−1𝑢(𝑡)

𝑑𝑡𝑚−1+⋯+ 𝑏0𝑟 𝑡

System Dynamics and Control 1.20 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§5.The Design Process

Step 5: Reduce the Block Diagram

In order to evaluate system response in this example, we need

to reduce this large system’s block diagram to a single block with

a mathematical description that represents the system from its

input to its output

Equivalent block diagram for the antenna azimuth position control system

System Dynamics and Control 1.21 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§5.The Design Process

Step 6: Analyze and Design

Analyze and design the system to meet specified requirements

and specifications that include stability, transient response, and

steady-state performance

The standard test input signals

• Impulse

Use to place initial energy into a system so that the response

due to that initial energy is only the transient response of a

system

From this response the designer can derive a mathematical

model of the system

System Dynamics and Control 1.22 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§5.The Design Process

• Step

A step input represents a constant command

Use to evaluate both transient and steady-state response

• Ramp

The ramp input represents a linearly increasing command

Use to get additional information about the steady-state error

System Dynamics and Control 1.23 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§5.The Design Process

• Parabola

Use to get additional information about the steady-state error

• Sinusoid

Use to test a physical system to arrive at a mathematical model

System Dynamics and Control 1.24 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

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§6.Computer-Aided Design

- MATLAB

- LabVIEW

System Dynamics and Control 1.25 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

- P.1.1 The resistance of a variable resistor (potentiometer) is

varied by moving a wiper arm along a fixed

resistance. The resistance from 𝐴 to 𝐶 is fixed,

but the resistance from 𝐵 to 𝐶 varies with the

position of the wiper arm. If it takes 10 turns to

move the wiper arm from 𝐴 to 𝐶, draw a block

diagram of the potentiometer

Solution

System Dynamics and Control 1.26 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

- P.1.2 A temperature control system operates by

• sensing the difference between the thermostat setting and the

actual temperature

• opening a fuel valve an amount proportional to this difference

Draw a functional closed-loop block diagram identifying the

input and output transducers, the controller, and the plant.

Further, identify the input and output signals of all subsystems

previously described

Solution

System Dynamics and Control 1.28 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

- P.1.3

Draw a functional block diagram for a closed-loop system that

stabilizes the roll as follows

• The system measures the actual roll angle with a gyro and

compares the actual roll angle with the desired roll angle

• The ailerons respond to the roll angle error by undergoing an

angular deflection

• The aircraft responds to this angular deflection, producing a

roll angle rate

Identify the input and output transducers, the controller, and the

plant. Further, identify the nature of each signal

System Dynamics and Control 1.28 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

Solution

System Dynamics and Control 1.29 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

- P.1.4

A winder controls the material traveling at a constant velocity.

The force transducer measures tension; the winder pulls against

the nip rolls, which provide an opposing force; and the bridle

provides slip. In order to compensate for changes in speed, the

material is looped around a dancer. The loop prevents rapid

changes from causing excessive slack or damaging the material.

If the dancer position is sensed by a potentiometer or other

device, speed variations due to buildup on the take-up reel or

other causes can be controlled by comparing the potentiometer

voltage to the commanded speed. The system then corrects the

speed and resets the dancer to the desired position. Draw a

functional block diagram for the speed control system, showing

each component and signal

System Dynamics and Control 1.30 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

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§7.Problems

Solution

System Dynamics and Control 1.31 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

- P.1.5

In a nuclear power generating plant, heat from a reactor is used

to generate steam for turbines. The rate of the fission reaction

determines the amount of heat generated, and this rate is

controlled by rods inserted into the radioactive core. The rods

regulate the flow of neutrons. If the rods are lowered into the

core, the rate of fission will diminish; if the rods are raised, the

fission rate will increase. By automatically controlling the

position of the rods, the amount of heat generated by the

reactor can be regulated. Draw a functional block diagram for

the nuclear reactor control system

System Dynamics and Control 1.32 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

Solution

System Dynamics and Control 1.33 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

- P.1.6 A university wants to establish a control system model

that represents the student population as an output, with the

desired student population as an input. The administration

determines the rate of admissions by comparing the current

and desired student populations. The admissions office then

uses this rate to admit students. Draw a functional block

diagram showing the administration and the admissions office

as blocks of the system. Also show the following signals: the

desired student population, the actual student population, the

desired student rate as determined by the administration, the

actual student rate as generated by the admissions office, the

dropout rate, and the net rate of influx

System Dynamics and Control 1.34 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

Solution

System Dynamics and Control 1.35 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

- P.1.7 We can build a control system that will automatically

adjust a motorcycle’s radio volume as the noise generated by

the motorcycle changes. The noise generated by the

motorcycle increases with speed. As the noise increases, the

system increases the volume of the radio. Assume that the

amount of noise can be represented by a voltage generated by

the speedometer cable, and the volume of the radio is

controlled by a dc voltage. If the dc voltage represents the

desired volume disturbed by the motorcycle noise, draw the

functional block diagram of the automatic volume control

system, showing the input transducer, the volume control

circuit, and the speed transducer as blocks. Also show the

following signals: the desired volume as an input, the actual

volume as an output, and voltages representing speed, desired

volume, and actual volume

System Dynamics and Control 1.36 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

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§7.Problems

Solution

System Dynamics and Control 1.37 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

- P.1.8 Your bathtub at home is a control system that keeps the

water level constant. A constant flow from the tap yields a

constant water level, because the flow rate through the drain

increases as the water level increases, and decreases as the

water level decreases. After equilibrium has been reached, the

level can be controlled by controlling the input flow rate. A low

input flow rate yields a lower level, while a higher input flow rate

yields a higher level

a.Sketch a control system that uses this principle to precisely

control the fluid level in a tank. Show the intake and drain

valves, the tank, any sensors and transducers, and the

interconnection of all components

b.Draw a functional block diagram of the system, identifying the

input and output signals of each block

System Dynamics and Control 1.38 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

Solution

a.

System Dynamics and Control 1.39 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

b.

System Dynamics and Control 1.40 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

- P.1.11

The vertical position, 𝑥(𝑡), of the grinding wheel is controlled by

a closed-loop system. The input to the system is the desired

depth of grind, and the output is the actual depth of grind. The

difference between the desired depth and the actual depth

drives the motor, resulting in a force applied to the work. This

force results in a feed velocity for the grinding wheel. Draw a

closed-loop functional block diagram for the grinding process,

showing the input, output, force, and grinder feed rate

System Dynamics and Control 1.41 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

Solution

System Dynamics and Control 1.42 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

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§7.Problems

- P.1.11

Consider the high-speed proportional solenoid valve. A voltage

proportional to the desired position of the spool is applied to the

coil. The resulting magnetic field produced by the current in the

coil causes the armature to move. A push pin connected to the

armature moves the spool. A linear voltage differential

transformer (LVDT) that outputs a voltage proportional to

displacement senses the spool’s position. This voltage can be

used in a feedback path to implement closed-loop operation.

Draw a functional block diagram of the valve, showing input

and output positions, coil voltage, coil current, and spool force

System Dynamics and Control 1.43 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien

§7.Problems

Solution

System Dynamics and Control 1.44 Introduction

HCM City Univ. of Technology, Faculty of Mechanical Engineering Nguyen Tan Tien