2. Fuzzy Logic
Fuzzy Control
Solution: Homework 7

3. Solution: Homework 7 (Cont.)
Fuzzy Logic
Fuzzy Control
Solution: Homework 7 (Cont.)

4. Single Tank System FV Desired liquid level: 5 cm (0.05 m)
Fuzzy Logic
Fuzzy Control
Single Tank System FV
Desired liquid level:
5 cm (0.05 m)
Required inflow rate: ?
m3/s (11.9 l/s) LI
A : cross-sectional area of the tank
a : cross-sectional area of the pipe

5. Single Tank System: 3 Rules
Fuzzy Logic
Fuzzy Control
Single Tank System: 3 Rules
Desired liquid level
okay
high
low 1
no change
open fast
close fast
–30 – 1
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.

6. Single Tank System: 3 Rules
Fuzzy Logic
Fuzzy Control
Single Tank System: 3 Rules
Simulation in Simulink
Liquid
level
Valve
control
signal
Valve
opening

7. Single Tank System: 3 Rules
Fuzzy Logic
Fuzzy Control
Single Tank System: 3 Rules
Subsystem Valve
Subsystem Single-Tank
Double-click a subsystem block to see the elements inside

8. Fuzzy Logic Controller in Simulink
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.

9. Single Tank System: 3 Rules
Fuzzy Logic
Fuzzy Control
Single Tank System: 3 Rules
Evaluation
“overshoot” too large
slow response

10. Single Tank System: 5 Rules
Fuzzy Logic
Fuzzy Control
Single Tank System: 5 Rules
no change
open fast
close fast
–30 –20 – 1
open slow
close slow
okay
high
low 1
liquid level [cm]
valve control signal [%/s]
zero
positive
negative
– – 1
rate of liquid level [cm/s]

11. Single Tank System: 5 Rules
Fuzzy Logic
Fuzzy Control
Single Tank System: 5 Rules
no change
– –
valve control signal [%/s]
–30–20 –
liquid level [cm]
rate of liquid level [cm/s]
okay
high
low 1
zero
positive
negative
open fast
close fast
open slow
close slow
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.

12. Single Tank System: 5 Rules
Fuzzy Logic
Fuzzy Control
Single Tank System: 5 Rules
FIS Editor
Simulink
Low pass filter,
to smooth the derivation result
Derivation,
to obtain the rate of liquid level

13. Single Tank System: 5 Rules
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

14. Single Tank System: Feedback Control
Fuzzy Logic
Fuzzy Control
Single Tank System: Feedback Control
How if the desired liquid level should be changed to 10 cm? 7 cm? 12 cm?
Set point r
Error e + – FV
Measured variable y LI
Practical solution: Error signal as the input to the fuzzy controller.

15. Single Tank System: Feedback Control
Fuzzy Logic
Fuzzy Control
Single Tank System: Feedback Control
e < 0 .
e > 0 .
e < 0
e > 0
– –
zero
positive
negative 1
zero
positive
negative
– – 1
Error of liquid level [cm]
Rate of error [cm/s]
no change
open fast
close fast
–30 –20 – 1
open slow
close slow
Valve control signal [%/s]

16. Fuzzy Logic
Fuzzy Control
Homework 8
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.
r [cm] 6 5 4
t [s]
Reference trajectory
Method Settings