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Fuzzy Control

LI

FV

Single Tank SystemDesired 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

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 RulesDesired 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.

Fuzzy Control

Single Tank System: 3 RulesSimulation in Simulink

Liquid

level

Valve

control

signal

Valve

opening

Fuzzy Control

Single Tank System: 3 RulesSubsystem Valve

Subsystem Single-Tank

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

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.

Fuzzy Control

Single Tank System: 3 RulesEvaluation

“overshoot” too large

slow response

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 RulesValve control signal [%/s]

Liquid level [cm]

Rate of liquid level [cm/s]

Fuzzy Control

Single Tank System: 5 Rulesno 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.

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

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.

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]

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

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.

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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