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

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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

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INTRODUCTION Mapping of concept temperature to the interval [0 1] with membership functions very cold 4560 1 0 cold warm hot 70758595105115 very hot (°C)

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Mapping of Inputs to the Interval [0 1] 1 very cold 0.5 (°C) 4560 1 0 cold warm hot very hot 70758595105115 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. Mapping of concept temperature to the interval [0 1] (°C) very cold 0.5 4560 1 0 cold warm hot very hot 70758595105115 The shape of the curves will be in the form of increasing or decreasing.

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Mapping of Outputs to the Interval [0 1] 2 (V) There are not any horizontal lines at the output curve hence the controller output will be unique. Mapping of voltage to the interval [0 1] 0.5 -12 1 0 120 PB PM P N NM NB

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Obtaining the Output from the Controller 3 Every input is intersected with the curve assigned to it and obtained values are conciliated by taking the arithmetic average. 1 0 0.5 0 1 b a 2 1 U1U2 (a+b)/2 U Obtained single logical value is intersected with the output curve which will yield the corresponding output value assigned to this logical value. Input 2 Input 1 Output Output The procedure is same in case of there are more than two inputs.

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The Rules Consisted Inherently in the Structure 4 Change in Error 1 NB PB Z 0 0.5 Error N P Z 0 1 Output Output 1 1 0 0 -60 -4009001 01-20020 60 PM NM -9040 0.5 PM P NM N 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]

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Weighting Filter 5 IF the change in error is POSITIVE THEN reduce the importance of the error Change in Error U1 1 NB PB Z 0 0.5 Error N P Z 0 1 Output Output 1 1 0 0 -60 -4009001 01-20020 1 0 0 1 Input 1 Input 2 0.1 WeightingFilter U2U1 0.8 U 0.4 (0.1*0.8+0.4)/(1+0.1) 60 PM NM -9040

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Tuning of the Controller 6 1 0 -10100 1 0 -10100 0 1 0 -10 0 1 0.5 0 10 -10 0.5 1 0 -10100 0.5 0 1 0 10 -10 Tuning of the Inputs Tuning of the Output 1 0 -5 5 0 0.5 1 0 -505 0 0 1 0.5 5 P N Z PZN N P PM NM Z PNZPMNM P PM NM N Z PN PMZ Proposed FLC Conventional FLC

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Application Example 1 - Quadrotor 7 X Z Y θ Total Thrust FxFx FzFz Rotate Right Rotate Left Move Right Going Up 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. 1 2 3 4 y x z Force to moment scaling factor : Propeller Forces

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Application Example 1 - Quadrotor 8

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Z Controller Structure 9 INPUTSOUTPUT Error Change in Error CONTROL SURFACE

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X and Y Controller Structure 10 INPUTSOUTPUT Error Change in Error CONTROL SURFACE

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θ and ψ Controller Structure 11 INPUTSOUTPUT Error Change in Error CONTROL SURFACE

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Φ Controller Structure 12 INPUTSOUTPUT Error Change in Error CONTROL SURFACE

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

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Quadrotor Simulation 1 14 x y z

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Quadrotor Simulation 2 15 x y z

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

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

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Inverted Pendulum Simulation 1 18 θ 0 =0.9rad, X d =-9m, F max =10N

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Inverted Pendulum Simulation 2 19 θ 0 =3rad, X d =-9m, F max =10N

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Inverted Pendulum Simulation 3 20 X d =Sinusoidal Amp=9m, F max =10N, Disturbance(±1N), Noise(±0.1rad)

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

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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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