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Self-Ruled Fuzzy Logic Based Controller

Self-Ruled Fuzzy Logic Based Controller. K. Oytun Yapıcı Istanbul Technical University Mechanical Engineering System Dynamics and Control Laboratory. Presentation Outline. CONTROLLER STRUCTURE 1 – Mapping of Inputs to the Interval [0 1] 2 – Mapping of Outputs to the Interval [0 1]

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Self-Ruled Fuzzy Logic Based Controller

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  1. Self-Ruled Fuzzy LogicBased Controller K. Oytun Yapıcı Istanbul Technical University Mechanical Engineering System Dynamics and Control Laboratory

  2. Presentation Outline CONTROLLER STRUCTURE 1 – Mapping of Inputs to the Interval [0 1] 2 – Mapping of Outputs to the Interval [0 1] 3 – Obtaining the Output from the Controller 4 – The Rules Consisted Inherently in the Structure 5 – Weighting Filter 6 – Tuning of the Controller APPLICATION EXAMPLE 1 – QUADROTOR APPLICATION EXAMPLE 2 – INVERTED PENDULUM APPLICATION EXAMPLE 3 – BIPEDAL WALKING

  3. very cold very hot hot cold warm 1 0 (°C) 45 60 70 75 85 95 105 115 INTRODUCTION Mapping of concept temperature to the interval [0 1] with membership functions

  4. Mapping of Inputs to the Interval [0 1] Mapping of concept temperature to the interval [0 1] very hot very cold 1 1 cold hot warm warm 0.5 0.5 cold hot very cold very hot 0 0 (°C) 45 60 70 75 85 95 105 115 (°C) 45 60 70 75 85 95 105 115 • Concepts are modelled as a whole with one curve. • Logical 0 and logical 1 are assigned to the poles of the concepts, hence there can be two possible mappings. • The shape of the curves will be in the form of increasing or decreasing. 1

  5. PB 1 PM 0.5 P N NM 0 NB -12 0 12 Mapping of Outputs to the Interval [0 1] Mapping of voltage to the interval [0 1] (V) • There are not any horizontal lines at the output curve hence the controller output will be unique. 2

  6. Obtaining the Output from the Controller 1 a 0.5 0 2 Output Input 2 1 0.5 (a+b)/2 b 0 U1 U U2 1 Output Input 1 • Every input is intersected with the curve assigned to it and obtained values are conciliated by taking the arithmetic average. • Obtained single logical value is intersected with the output curve which will yield the corresponding output value assigned to this logical value. • The procedure is same in case of there are more than two inputs. 3

  7. The Rules Consisted Inherently in the Structure PB P 1 1 PM Z NM NM 0.5 0.5 PM NB 0 0 N -90 -60 -40 0 40 60 90 -1 0 1 Output Error N 1 1 Z 0.5 0.5 P 0 0 -20 0 20 -1 0 1 Change in Error Output • If the error is PB [1] and the change in error is N [1] then the output will be P [1] • If the error is NB [0] and the change in error is N [1] then the output will be Z [0.5] • If the error is Z [0.5] and the change in error is Z [0.5] then the output will be Z [0.5] • If the error is Z [0.5] and the change in error is N [1] then the output will be PM [0.75] 4

  8. Weighting Filter PB 1 1 PM Z 0.8 NM 0.5 0.5 NB 0 0 U1 -90 -60 -40 0 40 60 90 -1 0 1 Error Output Input 1 N 0 0.1 1 1 1 1 Z (0.1*0.8+0.4)/(1+0.1) 0.5 0.4 P 0 0 0 U2 U U1 -20 0 20 -1 0 1 Weighting Filter Change in Error Output Input 2 IF the change in error is POSITIVE THEN reduce the importance of the error 5

  9. Tuning of the Controller Tuning of the Inputs Tuning of the Output Proposed FLC Conventional FLC P N Z P 1 1 1 Z 0.5 0.5 N 0 0 0 10 -5 0 5 -10 0 10 0 -10 P N NM Z PM P 1 1 1 Z PM 0.5 0.5 0.5 NM N 0 0 0 10 -5 0 5 -10 0 10 0 -10 P N NM Z PM P 1 1 1 PM Z 0.5 0.5 NM 0.5 N 0 0 0 10 -5 0 5 0 -10 0 10 -10 6

  10. 1 2 4 3 Z Fz Total Thrust θ Fx X Y Application Example 1 - Quadrotor • Angular motions will be controlled with 3 SRFLCs, X and Y motion will be controlled through the angles θ and ψ with 2 SRFLCs, Z motion will be controlled with 1 SRFLC. Force to moment scaling factor : Propeller Forces x y z 7 Rotate Right Move Right Going Up Rotate Left

  11. Application Example 1 - Quadrotor 8

  12. Z Controller Structure INPUTS OUTPUT Error CONTROL SURFACE 9 Change in Error

  13. X and Y Controller Structure INPUTS OUTPUT Error CONTROL SURFACE 10 Change in Error

  14. θ and ψ Controller Structure INPUTS OUTPUT Error CONTROL SURFACE 11 Change in Error

  15. ΦController Structure INPUTS OUTPUT Error CONTROL SURFACE 12 Change in Error

  16. Rule Bases White – Strictly PB output Black – Strictly NB output Gray – Strictly Z output 13

  17. z y x Quadrotor Simulation 1 14

  18. z y x Quadrotor Simulation 2 15

  19. Positive Region Negative Region Positive Region Negative Region 0.5 0 - 1 F Application Example 2 – Inverted Pendulum • There is a logical switch point at angle ±pi which must be considered. • Logical 1 and Logical 0 are assigned to the same angle of the pendulum. Hence the controller will lock up at the angle ±pi. 16

  20. Application Example 2 – Inverted Pendulum INPUTS WEIGHTING FILTERS OUTPUT Distance error Velocity error IF the pendulum angle or angular velocity is PB-NB THEN reduce the importance of the distance error and velocity error Pendulum angle error 17 Pendulum angular velocity error distance weight velocity weight

  21. Inverted Pendulum Simulation 1 θ0=0.9rad , Xd=-9m , Fmax=10N 18

  22. Inverted Pendulum Simulation 2 θ0=3rad , Xd=-9m , Fmax=10N 19

  23. Inverted Pendulum Simulation 3 Xd=Sinusoidal Amp=9m , Fmax=10N , Disturbance(±1N) , Noise(±0.1rad) 20

  24. Application Example 3 – Bipedal Walking du Angle error + SRFLC Torque u 1/s Angular velocity error + 21

  25. CONCLUSION • Obtaining the output from the controller is computationally efficient. • The controller has guaranteed continuity at the output. • Due to the simple and systematic nature of the structure applications with multi-input controllers will be easier. • The structure may not be as flexible as conventional FLCs. • The controller can be tuned with a trial and error method however there is a need to make the controller adaptive. THANKS FOR YOUR ATTENTION

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