Improving A PID Controller Using Fuzzy Logic
Andrew ThompsonNi Li
Ara TchobanianProfessor: Riadh Habash
TA: Hanliu Chen
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.
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.
IEEE Papers
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
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.
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
DC Motor Model
Step 2
• We next had to design a PID controller to control the speed of the motor.
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
PID Model
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
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
Fuzzy Precompensated PID
Membership Functions, and Fuzzy Rule Sets
Surface and Rule Sets
Fuzzy Precompensated PID Model
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
Membership functions for the PI component.
• (a) Input membership functions. • (b) Output membership functions.
L
A)
B)
Optical
HighLow
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
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
Fuzzy PI Model
Fuzzy PD
Membership Functions
Fuzzy PD Model
Simulation ResultsStep Response
PIDFuzzy
Precompensated
FuzzyPI
Fuzzy PD
Simulation ResultsStep Response with sine disturbance
PIDFuzzy
Precompensated
FuzzyPI
Fuzzy PD
Simulation ResultsStep Response with Gaussian Noise disturbance
PIDFuzzy
Precompensated
FuzzyPI
Fuzzy PD
Simulation ResultsSine Input
PIDFuzzy
Precompensated
FuzzyPI
Fuzzy PD
Simulation ResultsSine Input with sine disturbance
PIDFuzzy
Precompensated
FuzzyPI
Fuzzy PD
Simulation ResultsSine Response with Gaussian Noise disturbance
PIDFuzzy
Precompensated
FuzzyPI
Fuzzy PD