Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh...
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Transcript of Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh...
![Page 1: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/1.jpg)
Improving A PID Controller Using Fuzzy Logic
Andrew ThompsonNi Li
Ara TchobanianProfessor: Riadh Habash
TA: Hanliu Chen
![Page 2: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/2.jpg)
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.
![Page 3: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/3.jpg)
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.
![Page 4: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/4.jpg)
IEEE Papers
![Page 5: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/5.jpg)
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
![Page 6: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/6.jpg)
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.
![Page 7: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/7.jpg)
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 Θ’: Speed of motor
![Page 8: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/8.jpg)
DC Motor Model
![Page 9: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/9.jpg)
Step 2
• We next had to design a PID controller to control the speed of the motor.
![Page 10: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/10.jpg)
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
![Page 13: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/13.jpg)
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
![Page 17: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/17.jpg)
Fuzzy logic Equation for the fuzzy PI
Kp*X + Ki*Y = 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.
• (a) Input membership functions. • (b) Output membership functions.
L
A)
B)
Optical
HighLow
![Page 19: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/19.jpg)
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 –(R+S)/2
• The P is Low and I is High then output is -S
• The P is Optimal and I is Low then output is (–R+S)/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 (R+S)/2
• The P is High and I is High then output is R
Where R=L1*Ki+L2*Kp S=L2*Kp+L1*Ki
![Page 20: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/20.jpg)
Linear Fuzzy PI Control Table
Output Low ( D) Optimal ( D ) High ( D )
Low ( P ) -R -(R+S)/2 -S
Optimal ( P ) -(R-S)/2 0 (R-S)/2
High ( P ) S (R+S)/2 R
Surface Viewer
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Fuzzy PI Model
![Page 22: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/22.jpg)
Fuzzy PD
Membership Functions
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Fuzzy PD Model
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Simulation ResultsStep Response
PIDFuzzy
Precompensated
FuzzyPI
Fuzzy PD
![Page 25: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/25.jpg)
Simulation ResultsStep Response with sine disturbance
PIDFuzzy
Precompensated
FuzzyPI
Fuzzy PD
![Page 26: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/26.jpg)
Simulation ResultsStep Response with Gaussian Noise disturbance
PIDFuzzy
Precompensated
FuzzyPI
Fuzzy PD
![Page 27: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/27.jpg)
Simulation ResultsSine Input
PIDFuzzy
Precompensated
FuzzyPI
Fuzzy PD
![Page 28: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/28.jpg)
Simulation ResultsSine Input with sine disturbance
PIDFuzzy
Precompensated
FuzzyPI
Fuzzy PD
![Page 29: Improving A PID Controller Using Fuzzy Logic Andrew Thompson Ni Li Ara Tchobanian Professor: Riadh Habash TA: Hanliu Chen.](https://reader030.fdocuments.in/reader030/viewer/2022032600/56649dbc5503460f94aaef19/html5/thumbnails/29.jpg)
Simulation ResultsSine Response with Gaussian Noise disturbance
PIDFuzzy
Precompensated
FuzzyPI
Fuzzy PD