Lecture Control system design: Frequency response methods - Nguyễn Công Phương

Lecture Control system design: Frequency response methods presents the following content: Frequency response plots, performance specifications in the frequency domain, frequency response methods using control system software.

Nguyễn Công Phương

CONTROL SYSTEM DESIGN

Frequency Response Methods

I Introduction

II Mathematical Models of Systems

III State Variable Models

IV Feedback Control System Characteristics

V The Performance of Feedback Control Systems

VI The Stability of Linear Feedback Systems

VII The Root Locus Method

VIII.Frequency Response Methods

IX Stability in the Frequency Domain

X The Design of Feedback Control Systems

XI The Design of State Variable Feedback Systems

XII Robust Control Systems

XIII.Digital Control Systems

Frequency Response Methods

1 Introduction

2 Frequency Response Plots

3 Performance Specifications in the Frequency

Domain

4 Frequency Response Methods Using Control

System Software

Introduction (1)

• The frequency response of a system: the steady

– state response of the system to a sinusoidal input signal.

• The sinusoid is a unique input signal, and the resulting output signal for a linear system, as well as signals throughout the system, is

sinusoidal in the steady state.

• It differs from the input waveform only in

amplitude and phase angle.

Frequency Response Methods

1 Introduction

2 Frequency Response Plots

3 Performance Specifications in the Frequency

Domain

4 Frequency Response Methods Using Control

System Software

Frequency Response Plots (1)

Frequency Response Plots (2)

Cs

1

1 ( ) ( )

( ) 1

, ( / ) 1

Frequency Response Plots (3)

Semilog plots of the magnitude (in decibels) and phase (in degrees)

of a transfer function versus frequency

Frequency Response Plots (4)

2

1

2 2

1

1 j : simple zero

z

ω +

2 2

1

: quadratic pole 2

Frequency Response Plots (5)

10

20 log ( )

Frequency Response Plots (6)

20 log 1

( )

90

dB

T j

ω ω

Frequency Response Plots (7)

20 log ( )

Frequency Response Plots (8)

10

11

1

1

20log 1 1

( )

dB

j T

p j

Frequency Response Plots (9)

1

1

20log 1 1

( )

dB

j T

p j

Frequency Response Plots (10)

tan

dB

j T

z j

z

z

ω ω

Frequency Response Plots (11)

tan

dB

j T

z j

z

z

ω ω

Frequency Response Plots (12)

22

1 ( )

Frequency Response Plots (13)

1 ( )

2

1 2

2 2

2 20log 1

2 ( ) 1

2 / tan

Frequency Response Plots (15)

102

2

1 2

2 2

2 20log 1

2 ( ) 1

2 / tan

Frequency Response Plots (16)

Frequency Response Plots (17)

1 1

N

j p

2 1

1

2 1

Frequency Response Plots (18)

500 ( )

j

ω ω

Frequency Response Plots (19)

j

ω ω

ω ω

Frequency Response Plots (21)

j

ω ω

Frequency Response Plots (22)

j

ω ω

Frequency Response Plots (23)

j

ω ω

0.1 0.5 1 5 10 20 50 100 200 500

-90 -60 -40 -20 0 20 40 60 90

j

ω ω

0.1 0.5 1 5 10 20 50 100 200 500

-90 -60 -40 -20 0 20 40 60 90

j

ω ω

0.1 0.5 1 5 10 20 50 100 200 500

-90 -60 -40 -20 0 20 40 60 90

j

ω ω

ω ω

Frequency Response Plots (28)

( 5) ( ) 40 100

j

ω ω

( 5) ( ) 40 100

j

ω ω

Frequency Response Plots (30)

-100 -80 -60 -40 -20 0 20 40

( 5) ( ) 40 100

j

ω ω

Frequency Response Plots (31)

-100 -80 -60 -40 -20 0 20 40

( 5) ( ) 40 100

j

ω ω

Frequency Response Plots (32)

-100 -80 -60 -40 -20 0 20 40

( 5) ( ) 40 100

j

ω ω

Frequency Response Plots (33)

Frequency Response

-100 -80 -60 -40 -20 0 20 40

( 5) ( ) 40 100

j

ω ω

-200 -180

-90 -50 0 50 90

Frequency Response Plots (34)

ω φ

( 5) ( ) 40 100

j

ω ω

-300 -270

-200 -180

-90 -50 0 50 90

Frequency Response Plots (35)

ω φ

( 5) ( ) 40 100

j

ω ω

-300 -270

-200 -180

-90 -50 0 50 90

Frequency Response Plots (36)

ω φ

( 5) ( ) 40 100

j

ω ω

-300 -270

-200 -180

-90 -50 0 50 90

Frequency Response Plots (37)

ω φ

2 2

( 5) ( ) 40 100

j

ω ω

Frequency Response Plots (38)

-20 -10 0 10 20 30 40

Frequency Response Plots (39)

-20 -10 0 10 20 30

Ex 4

Frequency Response Plots (40)

-20 -10 0 10 20 30

Frequency Response Plots (41)

-20 -10 0 10 20 30

j

ω ω

Frequency Response Methods

1 Introduction

2 Frequency Response Plots

3 Performance Specifications in the

Frequency Domain

4 Frequency Response Methods Using Control

System Software

Performance Specifications in the

Frequency Domain (1)

22

1 ( )

2 1

Performance Specifications in the

Frequency Response Methods

1 Introduction

2 Frequency Response Plots

3 Performance Specifications in the Frequency

Domain

4 Frequency Response Methods Using

Control System Software

Frequency Response Methods Using Control System Software

500 ( )