AUTOMATIC CONTROL SYSTEMeng.sut.ac.th/me/2014/document/AutomaticControl/Control...AUTOMATIC CONTROL...

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PID Controller

System & Control Engineering Lab.

School of Mechanical Engineering

PID Controller

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PID Controller via ZN step response

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PID Controller via Ziegler-Nichol(ZN) step response

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PID Controller via ZN frequency response

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PID Controller design

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PID Controller designOpen-loop TF-Bode diagram

7

-150

-100

-50

0

50

Magnitu

de (

dB

)

System: sys

Gain Margin (dB): 26

At frequency (rad/sec): 2

Closed Loop Stable? Yes

10-2

10-1

100

101

102

-270

-225

-180

-135

-90

System: sys

Frequency (rad/sec): 2

Phase (deg): -180

Phase (

deg)

Bode Diagram

Frequency (rad/sec)

26

200 020log 26 dB 10 19.95K K= → = =

0 0

2 at 2 rad/secT T

= = → =

PID Controller design

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0

0

0

0.6 9.976

0.5 =1.57

0.125 0.3927

p

i

d

K K

T T

T T

= =

=

= =

9.976

6.354

9.976(0.3927) 3.917

P

P

i

P d

P K

KI

T

D K T

= =

= =

= = =

PID parameters for Simulink/MATLAB

PID Controller design

90 2 4 6 8 10 12 14 16 18 20

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Time,(sec)

c(t

), O

utp

ut

response

P Controller

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PI Controller

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PD Controller

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13

DC motorSpeed control

Armature Controlled DC motor

Field Controlled DC motor

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DC motorPosition control

Armature Controlled DC motor

Field Controlled DC motor

Speed control for Armature controlled DC motor

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Speed control for Armature controlled DC motor

16 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

Time, (sec)

Speed r

esponse,

RP

M

Unit-Step Response

System type = 0

PI-Speed control for Armature controlled DC motor

17

PI parameters for Simulink/MATLAB

0.05

0.055

0.01

P

P

i

P K

KI

T

= =

= = =

Speed control for Armature controlled DC motor

18

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

X: 0.05072

Y: 1.06

Time, (sec)

Speed r

esponse,

RP

M

Unit-Step Response

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.005

0.01

0.015

Time, (sec)

Err

or

sig

nal

%Overshoot = 6%, Steady state error for unit-ramp input = 0.012

Settling time = 0.08 sec

Position control for Armature controlled DC motor

19Td =0

System type = 1

Position control for Armature controlled DC motor

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Position control for Armature controlled DC motor

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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.2

0.4

0.6

0.8

1

Time, (sec)

Positio

n r

esponse,

(degre

e)

Unit-Step Response

1; 0; 0PP P d

i

KP K I D K T

T= = = = = =

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.01

0.02

0.03

0.04

0.05

0.06

Time, (sec)

Err

or

sig

nal

Steady state error for unit-ramp input = 0.06