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Fuzzy Logic. Fuzzy Control. LI. FV. Single Tank System. Desired liquid level: 5 cm ( 0.05 m ). Required inflow rate: ? 0.0119 m 3 /s ( 11.9 l /s ). A : cross-sectional area of the tank a : cross-sectional area of the pipe. Fuzzy Logic. Fuzzy Control. high. low. okay.

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Single tank system

Fuzzy Logic

Fuzzy Control

LI

FV

Single Tank System

Desired liquid level:

5 cm (0.05 m)

Required inflow rate: ?

0.0119 m3/s (11.9 l/s)

A : cross-sectional area of the tank

a : cross-sectional area of the pipe


Single tank system 3 rules

Fuzzy Logic

Fuzzy Control

high

low

okay

close fast

no change

open fast

1

1

015 9 14

–30 –10 0 10 30

Single Tank System: 3 Rules

Desired liquid level

Liquid level [cm]

Valve control signal [%/s]

FC with 3 Rules

  • Rule 1:IF level is okay, THEN valve is no change.

  • Rule 2: IF level is low, THEN valve is open fast.

  • Rule 3: IF level is high, THEN valve is close fast.


Single tank system 3 rules1

Fuzzy Logic

Fuzzy Control

Single Tank System: 3 Rules

Simulation in Simulink

Liquid

level

Valve

control

signal

Valve

opening


Single tank system 3 rules2

Fuzzy Logic

Fuzzy Control

Single Tank System: 3 Rules

Subsystem Valve

Subsystem Single-Tank

  • Double-click a subsystem block to see the elements inside


Fuzzy logic controller in simulink

Fuzzy Logic

Fuzzy Control

Fuzzy Logic Controller in Simulink

  • In Matlab workspace, design the fuzzy controller using fuzzy inference system (FIS) editor.

  • Export the fuzzy logic controller to workspace, give name.

  • File > Export > To Workspace, (i.e. : STFC_3)

  • In Simulink, create a new model.

  • Open the Fuzzy Logic Toolbox and drag “Fuzzy Logic Controller” to the new model.

  • Double-click the “FLC” and insert the name given to the controller above.


Single tank system 3 rules3

Fuzzy Logic

Fuzzy Control

Single Tank System: 3 Rules

Evaluation

“overshoot” too large

slow response


Single tank system 5 rules

Fuzzy Logic

Fuzzy Control

no change

close slow

open slow

close fast

high

low

okay

open fast

1

1

015 9 14

–30 –20 –10 0 10 20 30

negative

zero

positive

1

–4 –0.5 0 0.5 4

Single Tank System: 5 Rules

Valve control signal [%/s]

Liquid level [cm]

Rate of liquid level [cm/s]


Single tank system 5 rules1

Fuzzy Logic

Fuzzy Control

Single Tank System: 5 Rules

no change

close slow

open slow

close fast

open fast

negative

high

zero

positive

low

okay

1

1

1

–4 –0.5 0 0.5 4

015 9 14

–30–20 –10 0 10 20 30

Rate of liquid level [cm/s]

Valve control signal [%/s]

Liquid level [cm]

FC with 5 Rules

  • Rule 1:IF level is okay, THEN valve is no change.

  • Rule 2: IF level is low, THEN valve is open fast.

  • Rule 3: IF level is high, THEN valve is close fast.

  • Rule 4: IF level is okay AND rate is negative, THEN valve is open slow.

  • Rule 5: IF level is okay AND rate is positive, THEN valve is close slow.


S ingle tank system 5 rules

Fuzzy Logic

Fuzzy Control

Single Tank System: 5 Rules

FIS Editor

Simulink


Single tank system 5 rules2

Fuzzy Logic

Fuzzy Control

Single Tank System: 5 Rules

  • With all other factors stay the same, a better fuzzy control behavior and performance can be achieved by the combination of:

    • Redefining existing membership functions.

    • Refining existing rule.

    • Adding new membership functions and new rules.

acceptable “overshoot”

Liquid

level

faster response

Valve

control

signal

Valve

opening


Single tank system feedback control

Fuzzy Logic

Fuzzy Control

+

LI

FV

Single Tank System: Feedback Control

  • How if the desired liquid level should be changed to 10 cm? 7cm? 12cm?

Error

e

Set point

r

Measured variable

y

  • Practical solution: Error signal as the input to the fuzzy controller.


Single tank system feedback control1

Fuzzy Logic

Fuzzy Control

no change

close slow

open slow

close fast

open fast

positive

negative

zero

1

1

–10 –2 0 210

–30 –20 –10 0 10 20 30

negative

zero

positive

1

–4 –0.5 0 0.5 4

Single Tank System: Feedback Control

.

.

e < 0

e < 0

e > 0

e > 0

Error of liquid level [cm]

Rate of error [cm/s]

Valve control signal [%/s]


H omework 10

Fuzzy Logic

Fuzzy Control

r [cm]

6

5

4

t [s]

0 40 80 120

Homework 10

  • Implement the fuzzy logic controller as a feedback control for the single tank system in Matlab-Simulink.

  • Apply the 5 rule version with the corresponding membership functions.

  • Test the control loop to follow the reference trajectory as shown below.

Reference trajectory

Method Settings


H omework 10a

Fuzzy Logic

Fuzzy Control

Homework 10A

  • A DC motor is a common actuator in control system. The input to this device is a voltage given in Volt and the output is the rotation speed given in rad/s.

  • The electric circuit of a DC motor and its rotor is shown on the lower left figure.

  • A model of the DC motor in Matlab Simulink is also provided, as shown through the lower right figure.


H omework 10a1

Fuzzy Logic

Fuzzy Control

Homework 10A

  • In case there is no load change, the DC motor will rotate with a constant speed.

  • If the load is changed, the supplied voltage must be adjusted so that adequate current may flow and the desired rotation speed can be achieved.

  • Design a fuzzy logic control that will maintain the motor to rotate with the velocity of Student-ID/10 rad/s.

  • Embed the controller in the Matlab-Simulink file.

  • Submit the softcopy (*.fis, *.mdl) and the hardcopy (screenshots of *.fis, *.mdl and scope)


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