page 126
8. FUZZY LOGIC
•Well suited when we can’t get an exact mathematical model (like we did with Laplace transforms)
•Based on a set of rules, and some fuzzy descriptions about the problem.
•We examine each rule, and each set, and then determine how much each rule applies, and then perform an operation as a combination of the rule effects.
•The fuzzy logic controller works like the PID before (except it does more)
page 127
e.g. |
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Suppose we want to control a servo motor [Li and Lau, 1989] |
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vdesired |
verror |
Fuzzy |
Vmotor |
Motor |
Imotor |
vactual |
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Logic |
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Servo |
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Motor |
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Controller |
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Amplifier |
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The rules for the fuzzy logic controller would be as below,
1.If verror is LP and d/dtverror is any then Vmotor is LP.
2.If verror is SP and d/dtverror is SP or ZE then Vmotor is SP.
3.If verror is ZE and d/dtverror is SP then Vmotor is ZE.
4.If verror is ZE and d/dtverror is SN then Vmotor is SN.
5.If verror is SN and d/dtverror is SN then Vmotor is SN.
6.If verror is LN and d/dtverror is any then Vmotor is LN.
The sets for v |
, d/ |
dt |
v |
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, and V |
are given below, |
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error |
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error |
motor |
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v |
error |
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d/ |
v |
error |
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V |
motor |
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dt |
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1 |
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1 |
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1 |
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LN |
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50 |
100 |
rps |
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-3 |
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rps/s |
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6 |
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18 |
V |
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-100 -50 0 |
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1 |
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1 |
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SN |
0 |
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50 |
100 |
rps |
0 |
-3 |
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3 |
rps/s |
0 |
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6 |
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18 |
V |
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1 |
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ZE |
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rps |
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rps/s |
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V |
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-100 -50 0 |
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-6 |
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SP |
0 |
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rps |
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rps/s |
0 |
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V |
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-100 -50 0 |
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LP |
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rps |
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V |
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page 128
After we have the rules, and sets, we must be able to make decisions with the rules Assume the controller has
verror = 30 rps d/dtverror = 1 rps/s
Determine Vmotor
To do this we look at each rule separately
1. If verror is LP and d/dtverror is any then Vmotor is LP.
1 |
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rps |
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rps/s |
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-100 -50 0 |
50 100 |
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-6 -3 0 3 6 |
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0 6 12 |
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ANY VALUE |
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17V |
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30rps |
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(so ignore) |
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This has about 0.6 (out of 1) membership |
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(could also |
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have chosen |
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some value |
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above 17V) |
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2. If v |
error |
is SP and d/ |
v |
is SP or ZE then V |
motor |
is SP. |
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dt |
error |
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the OR means take the highest of the two memberships
the AND means take the lowest of the two memberships
1 |
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1 |
1 |
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1 |
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rps |
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rps/s |
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V |
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rps/s |
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-100 -50 |
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-6 -3 0 3 6 |
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-3 0 3 6 |
0 |
6 |
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30rps |
1rps/s |
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1rps/s |
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14V |
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This has about 0.4 (out of 1) membership
page 129
3. If verror is ZE and d/dtverror is SP then Vmotor is ZE.
1 |
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1 |
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1 |
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0 |
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rps/s |
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rps |
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0 |
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V |
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-100 -50 |
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-6 |
-3 |
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3 |
6 |
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6 |
12 18 |
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30rps |
1rps/s |
the lowest results in 0 set |
membership |
This has about 0.0 (out of 1) membership
4. If verror is ZE and d/dtverror is SN then Vmotor is SN. |
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1 |
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rps |
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rps/s |
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V |
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-100 -50 |
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-6 |
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6 |
12 18 |
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100 |
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24 |
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30rps |
1rps/s |
the lowest results in 0 set |
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membership
This has about 0.0 (out of 1) membership
5. If v |
error |
is SN and d/ |
dt |
v |
is SN then V |
motor |
is SN. |
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error |
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rps |
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rps/s |
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V |
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-100 -50 0 |
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-6 -3 |
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1rps
30rps
This has about 0.0 (out of 1) membership