Fuzzy logic 6

1
Fuzzy logic
Fuzzy Control
Aleksandar Rakic rakic_at_etf.rs
2
Contents

• Definitions
• Conventional Feedback Controllers
• Fuzzy Logic Controllers
• Conventional vs. Fuzzy LogicFeedback Controllers
  
• Intuitive Approach to FLC Design
• Approach to FLC Design Fuzzyfying Conventional
  PD

3
Definition of Control

• The term control is generally defined as a
  mechanism used to guide or regulate the operation
  of a machine, apparatus or constellations of
  machines and apparatus.
• Often the notion of control is inextricably
  linked with feedbacka process of returning the
  output (regulated) variable signal to the input
  of a device (optionally compared with some
  reference value) in order to obtain appropriate
  control signal.
• Feedback can be (and usually is) negative,
  whereby feedback opposes and therefore reduces
  the input,or feedback can be positive whereby
  feedback reinforces the input.

4
Conventional Feedback Control

• Feedback control is thus a mechanism for guiding
  or regulating the operation of a system or
  subsystems by returning to the input of the
  (sub)system a fraction of the output.
• The machinery or apparatus etc., to be guided or
  regulated is denoted by P (Plant), the reference
  input by r and the controlled output by y, and
  the feedback controller by K. The input to the
  controller is the so-called error signal e and
  the purpose of the controller is to guarantee a
  desired response of the output y.

5
Fuzzy Logic Controllers (FLC)

• By a fuzzy logic controller (FLC) we mean a
  control law that is described by a
  knowledge-based system consisting of IF...THEN
  rules with vague predicates and a fuzzy logic
  inference mechanism.
• The rule base is the main part of the FLC. It is
  formed by a family of logical rules that
  describes the relationship between the input e
  and the output u of the controller.
• The main difference between a conventional
  control system and a fuzzy logic controlled
  system is not only in the type of logic (Boolean
  or fuzzy) but in the inspiration.
• The former attempts to increase the efficiency of
  control algorithms
• the latter is based on the implementation of
  human understanding and human thinking in control
  algorithms.

6
Fuzzy Logic Controllers (FLC)

• Logical rules with vague predicates can be used
  to derive inference from vaguely formulated data.
• The idea of linguistic control algorithms was a
  generalisation of the human experience of using
  linguistic rules with vague predicates in order
  to formulate control actions.
• The main paradigm of fuzzy control is that the
  control algorithm is a knowledge-based algorithm,
  described by the methods of fuzzy logic.
• The controller can be used with the process in
  two modes
• feedback mode when the fuzzy controller will act
  as a control device
• feedforward mode where the controller can be used
  as a prediction device.
• All inputs to, and outputs from, the controller
  are in the form of linguistic variables. In many
  ways, a fuzzy controller maps the input variables
  into a set of output linguistic variables.

7
Conventional vs. Fuzzy Logic Feedback Controllers
Conventional Control System
e(t)
u(t)
FLC
Internal
ed(t)
Structure
Differentiator
Fuzzy-logic PD based Control System
e(t)
u(t)
D
u(t)
FLC
Integration
Internal
ed(t)
Structure
Differentiator
Fuzzy-logic PD based Incremental Control System
8
Intuitive Approach to FLC Design

• PD based FLC controlling plants with astatism
• Determination of the input and the output
  universes
• u ? Umin, Umax,
• y ? Ymin, Ymax ? e r - y ? Emin, Emax is
  known,
• ed universe can be obtained experimentally by the
  open-loop step response
• Rule base construction
• Example for Tank problem
• PD based FLC for incremental control of plants
  without astatism
• Integrator added in front of the plant, so
  generalized plant has astatism and previous
  experiment to determine ed universe can be
  applied.

9
Systematic Approach to FLC DesignFuzzifying
Conventional PID

• One systematic procedure for fuzzy controller
  design is based on transferring conventionally
  designed PID into the fuzzy domain, according to
  following steps
• Obtain parameters for the conventional PID.
• Substitute PID with equivalent linear fuzzy
  controller.
• Transform to the nonlinear fuzzy controller by
  changing rules and membership functions.
• Fine tuning.

10
Linear Fuzzy PD
e(t)
u(t)
FLC
Internal
ed(t)
Structure
Differentiator

• Choices that make fuzzy inference equivalent to
  plain sum
• Triangular input membership functions with 50
  overlap
• Prod method (algebraic product) for and
  operation.
• Rule base contains and combination of all members
  of input families.
• Output singletons on the positions of sums of
  peak values of input sets.
• Defuzzification - COG method.
• Resulting input-output surface is flat diagonal
  i.e. output signal is the sum of input.
• Program generisanje_lin_fpd.m