Presentacin de PowerPoint

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Implementation of a Stable Indirect Fuzzy
Controller
O. Sánchez, A. Ollero Departamento de
Ingeniería Electrónica Sist. Inf. Y
Automática Universidad de Huelva Departamento de
Ingeniería de Sistemas y Automática Universidad
de Sevilla
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Outline

• Introduction
• Fuzzy control of fuzzy system model
• The closed loop system
• Stability indices Subspace analysis
• The uniform distribution of fuzzy sets overlap
  ratio
• The design of the control law
• Simulation results
• Conclusions

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Introduction

• Stability assessment
• Frequency response methods
• Input-output stability
• Circle criterion
• Conicity criterion
• Quadratic Lyapunov functions
• Stability Indices

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Fuzzy control of fuzzy system model

Fuzzy model
-
Real plant
Fuzzy Controller
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The closed loop system
Global coefficients
Affine term
Control laws
Degree of firing of fuzzy controller
Degree of firing of fuzzy model
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Stability indices supervisor

Fuzzy model
-
Phase II
Real plant
Fuzzy Controller
Stability Indices Supervisor
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Stability indices supervisor (II)
I1 (-1)ndet(Lx0)
I2Mn-1
f(0)0
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Stability indices supervisor (III)
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Overlap ratio for Bell MFs
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Relation between centers, width and ORa for Bell
MFs
Plane projection
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Uniform distribution of fuzzy sets
- The parameters are initialized so that the MFs
are uniformly distributed   WHILE (e gt
Max_e) - The non-linear fuzzy function is
estimated - The parameters are adapted using
the gradient descent method - The
parameters are adjusted based on the ORa -
The function is estimated with the adapted
parameters and adjusted - The error is
computed
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Fundamentals of parameters adjusted based on the
ORa
Cost function
0.11
Gradient descendent rule
Centers and width update
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Implementation of the MIMO indirect controller
The controller parameters are updated based on
desired behaviour for Stability Indices
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Implementation of the MIMO indirect controller
(II)

• Obtain the plant model
• Repeat until stability indices fulfilled
• Define a desired behaviour for the indices I3i
• Update the controllers parameters
• Evaluate the stability indices

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Example I
Initial conditions to obtain the model
two saddle points
Nodal sink
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Results of the example I

Closed loop response

• Fuzzy model15 rules
• Fuzzy controller15 rules
• Overlap ratio 0.11
• I10.8516
• I23.1579

Distribution of bell MFs in the fuzzy controller
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Control of the inverted pendulum
Region of interest to design a local regulator
u
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Control of the inverted pendulum

• Fuzzy model23 rules
• Fuzzy controller17 rules
• Overlap ratio 0.11
• I11.3253
• I22.2387

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Conclusions

• Indirect MIMO fuzzy controller based on stability
  indices
• The fuzzy model and fuzzy controller have an
  uniform distribution of bell MFs.
• The heuristic acknowledge can be extracted of
  fuzzy systems