Self-Ruled%20Fuzzy%20Logic%20Based%20Controller

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Self-Ruled Fuzzy LogicBased Controller
K. Oytun Yapici Istanbul Technical
University Mechanical Engineering System Dynamics
and Control Laboratory
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Presentation Outline
CONTROLLER STRUCTURE 1 Mapping of Inputs to
the Interval 0 1 2 Mapping of Outputs to the
Interval 0 1 3 Obtaining the Output from the
Controller 4 The Rules Consisted Inherently in
the Structure 5 Weighting Filter 6 Tuning
of the Controller APPLICATION EXAMPLE 1
QUADROTOR APPLICATION EXAMPLE 2 INVERTED
PENDULUM APPLICATION EXAMPLE 3 BIPEDAL WALKING
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INTRODUCTION
Mapping of concept temperature to the interval 0
1 with membership functions
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Mapping of Inputs to the Interval 0 1
Mapping of concept temperature to the interval 0
1
very hot
very cold
1
1
cold
hot
warm
warm
0.5
0.5
cold
hot
very cold
very hot
0
0
(C)
45
60
70
75
85
95
105
115
(C)
45
60
70
75
85
95
105
115

• Concepts are modelled as a whole with one curve.

• Logical 0 and logical 1 are assigned to the
  poles of the concepts, hence there can be two
  possible mappings.

• The shape of the curves will be in the form of
  increasing or decreasing.

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Mapping of Outputs to the Interval 0 1
Mapping of voltage to the interval 0 1
(V)

• There are not any horizontal lines at the output
  curve hence the controller output will be unique.

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Obtaining the Output from the Controller
1
a
0.5
0
2
Output
Input 2
1
0.5
(ab)/2
b
0
U1
U2
U
1
Output
Input 1

• Every input is intersected with the curve
  assigned to it and obtained values are
  conciliated by taking the arithmetic average.

• Obtained single logical value is intersected
  with the output curve which will yield the
  corresponding output value assigned to this
  logical value.

• The procedure is same in case of there are more
  than two inputs.

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The Rules Consisted Inherently in the Structure
PB
P
1
1
PM
Z
NM
NM
0.5
0.5
PM
NB
0
0
N
-60
-40
0
90
0
1
-1
60
-90
40
Error
Output
N
1
1
Z
0.5
0.5
P
0
0
-1
0
1
-20
0
20
Change in Error
Output

• If the error is PB 1 and the change in error
  is N 1 then the output will be P 1
• If the error is NB 0 and the change in error
  is N 1 then the output will be Z 0.5
• If the error is Z 0.5 and the change in error
  is Z 0.5 then the output will be Z 0.5
• If the error is Z 0.5 and the change in error
  is N 1 then the output will be PM 0.75

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8
Weighting Filter
PB
1
1
PM
Z
0.8
NM
0.5
0.5
NB
0
0
U1
-60
-40
0
90
0
1
-1
60
-90
40
Error
Output
Input 1
N
0
1
0.1
1
1
1
Z
(0.10.80.4)/(10.1)
0.5
0.4
P
0
0
0
U2
U1
U
-1
0
1
-20
0
20
Weighting Filter
Change in Error
Output
Input 2
IF the change in error is POSITIVE THEN reduce
the importance of the error
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Tuning of the Controller
Tuning of the Inputs
Tuning of the Output
Proposed FLC
Conventional FLC
P
P
Z
N
1
1
1
Z
0.5
0.5
N
0
0
0
10
-5
0
5
-10
10
0
0
-10
P
P
N
Z
PM
NM
1
1
1
Z
PM
0.5
0.5
0.5
NM
N
0
0
0
10
-5
0
5
-10
10
0
0
-10
P
P
N
NM
PM
Z
1
1
1
PM
Z
0.5
0.5
NM
0.5
N
0
0
0
10
-5
0
5
-10
10
0
0
-10
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Application Example 1 - Quadrotor

• Angular motions will be controlled with 3
  SRFLCs, X and Y motion will be controlled through
  the angles ? and ? with 2 SRFLCs, Z motion will
  be controlled with 1 SRFLC.

Force to moment scaling factor
Propeller Forces
x
y
z
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Rotate Right
Move Right
Going Up
Rotate Left
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Application Example 1 - Quadrotor
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Z Controller Structure
INPUTS
OUTPUT
Error
CONTROL SURFACE
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Change in Error
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X and Y Controller Structure
INPUTS
OUTPUT
Error
CONTROL SURFACE
10
Change in Error
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? and ? Controller Structure
INPUTS
OUTPUT
Error
CONTROL SURFACE
11
Change in Error
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F Controller Structure
INPUTS
OUTPUT
Error
CONTROL SURFACE
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Change in Error
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Rule Bases
White Strictly PB output Black Strictly NB
output Gray Strictly Z output
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Quadrotor Simulation 1
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Quadrotor Simulation 2
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Application Example 2 Inverted Pendulum

• There is a logical switch point at angle pi
  which must be considered.

• Logical 1 and Logical 0 are assigned to the same
  angle of the pendulum. Hence the controller will
  lock up at the angle pi.

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Application Example 2 Inverted Pendulum
INPUTS
OUTPUT
WEIGHTING FILTERS
Distance error
Velocity error
IF the pendulum angle or angular velocity is
PB-NB THEN reduce the importance of the distance
error and velocity error
Pendulum angle error
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Pendulum angular velocity error
distance weight
velocity weight
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Inverted Pendulum Simulation 1
?00.9rad , Xd-9m , Fmax10N
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Inverted Pendulum Simulation 2
?03rad , Xd-9m , Fmax10N
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Inverted Pendulum Simulation 3
XdSinusoidal Amp9m , Fmax10N ,
Disturbance(1N) , Noise(0.1rad)
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Application Example 3 Bipedal Walking
du
Angle error

SRFLC
Torque
u
Angular velocity error
1/s

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CONCLUSION

• Obtaining the output from the controller is
  computationally efficient.
• The controller has guaranteed continuity at the
  output.
• Due to the simple and systematic nature of the
  structure applications with multi-input
  controllers will be easier.
• The structure may not be as flexible as
  conventional FLCs.
• The controller can be tuned with a trial and
  error method however there is a need to make the
  controller adaptive.

THANKS FOR YOUR ATTENTION