Improving%20A%20PID%20Controller%20Using%20Fuzzy%20Logic

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Improving A PID Controller Using Fuzzy Logic

• Andrew Thompson
• Ni Li
• Ara Tchobanian
• Professor Riadh Habash
• TA Hanliu Chen

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Problem

• Although PID controllers are able to provide
  adequate control for simple systems, they are
  unable to compensate for disturbances.
• We will use Fuzzy Logic controllers to improve
  the PID controllers ability to handle
  disturbances.

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Hypothesis

• We feel like all the designs for the fuzzy
  compensator will be an improvement upon the PID
  controller and will have greater ability to deal
  with disturbances.

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IEEE Papers
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Group Contribution

• Andrew Thompson
• Research and development of Fuzzy precompensator
  design and rules
• Research and development of PID Controller
• Ni Li
• Research and development of various Fuzzy logic
  compensator (PD, PI) designs and rules
• Ara Tchobanian
• Research and modeling of DC motor
• Research and development of PID Controller

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Procedure

• We first needed to decide upon a system which we
  could control using a PID controller as well as
  be able to introduce a disturbance.
• We chose to model a basic DC motor.

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DC Motor

• We used the following values for the model of the
  DC Motor
• moment of inertia of the rotor
• J 0.01 kg.m2/s2
• damping ratio of the mechanical system b 0.1
  Nms
• electromotive force constant K 0.01 Nm/Amp
• electric resistance R 1 ohm
• electric inductance L 0.5 H
• input V Source Voltage
• output T Speed of motor

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DC Motor Model
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Step 2

• We next had to design a PID controller to control
  the speed of the motor.

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PID Controller

• We wanted the PID controller to satisfy the
  following criteria
• Settling time less than 2 seconds
• Overshoot less than 5
• Steady-state error less than 1
• By using trial and error, and examining the step
  response we obtained the following gains
• Kp 100, Ki 200, Kd 10

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PID Model
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Step 3

• The final step in the development of our
  controllers was to design various forms Fuzzy
  logic compensators in order to improve the
  performance of the PID controller and to allow it
  to account for the disturbance.
• We designed three types of Fuzzy logic
  Compensators
• Fuzzy PI
• Fuzzy PD
• Fuzzy Precompensated

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Fuzzy logic Introduction

• Fuzzy logic is a problem-solving control system
  methodology that lends itself to implementation
  in systems ranging from simple, small, embedded
  micro-controllers to large, networked,
  multi-channel PC or workstation-based data
  acquisition and control systems. It can be
  implemented in hardware, software, or a
  combination of both.

Inputs
Rules
Output
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Fuzzy Precompensated PID
Membership Functions, and Fuzzy Rule Sets
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Surface and Rule Sets
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Fuzzy Precompensated PID Model
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Fuzzy logic Equation for the fuzzy PI

• KpX KiY Z

The output for the fuzzy
Y example input for Ki
The gain for Ki
X example input for Kp
The gain for Kp
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Membership functions for the PI component.
Optical
A)
High
Low
L
B)

• (a) Input membership functions.
• (b) Output membership functions.

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Fuzzy Logic Rules for the PI

• The P is Low and I is Low then output is R
• The P is Low and I is Optimal then output is
  (RS)/2
• The P is Low and I is High then output is -S
• The P is Optimal and I is Low then output is
  (RS)/2
• The P is Optimal and I is Optimal then output is
  0
• The P is Optimal and I is High then output is
  (R-S)/2
• The P is High and I is Low then output is S
• The P is High and I is optimal then output is
  (RS)/2
• The P is High and I is High then output is R

Where RL1KiL2Kp SL2KpL1Ki
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Linear Fuzzy PI Control Table
Output Low ( D) Optimal ( D ) High ( D )
Low ( P ) -R -(RS)/2 -S
Optimal ( P ) -(R-S)/2 0 (R-S)/2
High ( P ) S (RS)/2 R
Surface Viewer
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Fuzzy PI Model
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Fuzzy PD
Membership Functions
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Fuzzy PD Model
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Simulation Results
Step Response
Fuzzy Precompensated
PID
FuzzyPI
Fuzzy PD
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Simulation Results
Step Response with sine disturbance
Fuzzy Precompensated
PID
FuzzyPI
Fuzzy PD
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Simulation Results
Step Response with Gaussian Noise disturbance
Fuzzy Precompensated
PID
FuzzyPI
Fuzzy PD
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Simulation Results
Sine Input
Fuzzy Precompensated
PID
FuzzyPI
Fuzzy PD
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Simulation Results
Sine Input with sine disturbance
Fuzzy Precompensated
PID
FuzzyPI
Fuzzy PD
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Simulation Results
Sine Response with Gaussian Noise disturbance
Fuzzy Precompensated
PID
FuzzyPI
Fuzzy PD