Intelligens Számítási Módszerek Fuzzy rendszerek, alkalmazáspéldák
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1 Intelligens Számítási Módszerek Fuzzy rendszerek, alkalmazáspéldák 2013/2014. tanév, II. félév Dr. Kovács Szilveszter Informatikai Intézet 106. sz. szoba Tel: (46) / 21-06
2 Areas in which Fuzzy Logic was succesfully applied: Modelling and control Classification and pattern recognition Databases Expert Systems (Fuzzy) hardware Signal processing Etc. Dr. Kovács Szilveszter Int.Comp. VI. / 2.
3 Fuzzy Logic Control Fuzzification: converts the numerical value to a fuzzy one; determines the degree of matching The knowledge base contains the rule base (fuzzy rules) data base (defines membership functions) The inference engine describes the methodology to compute the output from the input Defuzzification converts the fuzzy term to a classical numerical value Dr. Kovács Szilveszter Int.Comp. VI. / 3.
4 Fuzzy Inference E.g. Zadeh-Mamdani Type max-min composition Dr. Kovács Szilveszter Int.Comp. VI. / 4.
5 Planning of Fuzzy Controllers Determination of fuzzy controllers = determination of the antecedents + consequents and the rules Antecedents: Selection of the input dimensions Determination of the fuzzy partitions for the inputs Determination of the parameters for the fuzzy variables Consequents: Determination of the fuzzy partitions for the outputs Determination of the parameters Rules: Determination of the rules in the form: If antecedent term 1 and and antecedent term n then consequent Dr. Kovács Szilveszter Int.Comp. VI. / 5.
6 Balancing of an inverted pendulum 2 2 ( m + M) sin ( α ) l && α + m l sin( α ) cos( α ) ( & α ) ( m + M) g sin( α ) = F cos( α ) where g is the gravitational constant, l is the length of the pole, m is the mass at the head of the pendulum, M is the mass at the foot point of the pendulum, α is the angle of the pendulum, α& is the angular velocity, and F is the force to control the pendulum stay upright Dr. Kovács Szilveszter Int.Comp. VI. / 6.
7 Balancing of an inverted pendulum Fuzzy model If the angle α is A 1 and the angular velocityα& is A 2 than let the force F be B E.g: If the angle α is zero and the angular velocityα& is zero than let the force F be zero Dr. Kovács Szilveszter Int.Comp. VI. / 7.
8 Balancing of an inverted pendulum Linguistic terms The linguistic terms of the angle α (X 1 ): The linguistic terms of the angular velocity α& (X 2 ): Linguistic terms of the force F(Y). Dr. Kovács Szilveszter Int.Comp. VI. / 8.
9 Balancing of an inverted pendulum Rule base R : α = NL : NM : NS : Z : PS : PM : PL : α = NL : PS PL NM : PM NS : NM NS PS Z : NL NM NS Z PS PM PL PS : NS PS PM PM : NM PL : NL NS Dr. Kovács Szilveszter Int.Comp. VI. / 9.
10 Balancing of an inverted pendulum Rule base R : α = NL : NM : NS : Z : PS : PM : PL : α = NL : NS Z PS PL PL PL PL NM : NM NS Z PM PM PL PL NS : NM NS NS PS PS PM PL Z : NL NM NS Z PS PM PL PS : PL NM NS NS PS PS PM PM : NL NL NM NM Z PS PM PL : NL NL NL NL NS Z PS Dr. Kovács Szilveszter Int.Comp. VI. / 10.
11 Balancing of an inverted pendulum Example of inference Observation α = 36, α& = /s. Fired rules: R 1 : If α= PS and α& = Z then F = PS R 2 : If = PM and = Z then F = PM α α& Dr. Kovács Szilveszter Int.Comp. VI. / 11.
12 Path tracking of an automated guided vehicle AGV with fixed directional wheel configuration, with differential steering Dr. Kovács Szilveszter Int.Comp. VI. / 12.
13 Path tracking of an automated guided vehicle AGV with fixed directional wheel configuration, with differential steering Trajectory of the driving centre of a differential steered AGV using the guide point based tracking strategy. Dr. Kovács Szilveszter Int.Comp. VI. / 13.
14 Path tracking of an automated guided vehicle For finding better trajectory concept of guide zone will be used Differential steered AGV with guide zone: Dr. Kovács Szilveszter Int.Comp. VI. / 14.
15 Path tracking of an automated guided vehicle Analytic model of the AGV motion: P v K P v w Ro VL d K VR Ro d ϕ s L = V dt s = V dt L R R Dr. Kovács Szilveszter Int.Comp. VI. / 15.
16 Path tracking of an automated guided vehicle Analytic model of the AGV motion: Calculation of the estimated momentary path tracking error Dr. Kovács Szilveszter Int.Comp. VI. / 16.
17 Path tracking of an automated guided vehicle Analytic model of the AGV motion: dϕ = s L s d R R o ( 1 cos( ϕ )) ( ) dk = R d ox o dk = R sin dϕ α = oy 2 dk = dk + dk o ox 2 oy sl + s = d 2 R ( s s ) L R arctan dk dk oy ox ( ) ( ) sin( ϕ ) cos( ϕ ) cos( ϕ ) sin( ϕ ) dkx = dk cos α + dϕ dk = dk y sin α + d ϕ evox = dk x + w d + evo d evoy = dky + w d evo d v vox δ m e v - w e e = ξ = arctan e v w evoy w δ = δ cos ξ m ( ) where: e v the distance between the guide path and the guide point (measured on the guide zone), e vo the previous value of e v, s R move of the AGV measured on the right wheel, s L on the left wheel, w distance of the guide point and the driving centre, d δ e e vox voy distance of the two wheels, the estimated momentary path tracking error, we are looking for Dr. Kovács Szilveszter Int.Comp. VI. / 17.
18 Path tracking of an automated guided vehicle Observations of the controller: ev the distance between the guide path and the guide point (measured on the guide zone), δ the estimated momentary path tracking error Conclusions of the controller: Momentary manoeuvres: : speed (Va), steering (Vd). V V V L + a = 2 R Vd = VL VR Dr. Kovács Szilveszter Int.Comp. VI. / 18.
19 Path tracking of an automated guided vehicle Rule base e.g. If the distance between the guide path and the guide point (e v ) is Zero and estimated path tracking error (δ) is Zero then the steering (V d ) is Zero and the speed (V a ) is Large If e v = Z And δ = Z Then V d = Z And V a = L Dr. Kovács Szilveszter Int.Comp. VI. / 19.
20 Path tracking of an automated guided vehicle Rule base e.g. If the distance between the guide path and the guide point (e v ) is Positive Middle and estimated path tracking error (δ) is Negative Middle then the steering (V d ) is Zero and the speed (V a ) is Middle If e v = PM And δ = NM Then V d = Z And V a = M Dr. Kovács Szilveszter Int.Comp. VI. / 20.
21 Path tracking of an automated guided vehicle Rule base e.g. If the distance between the guide path and the guide point (e v ) is Negative Large and estimated path tracking error (δ) is Negative Middle then the steering (V d ) is Positive Large and the speed (V a ) is Small If e v = NL And δ = NM Then V d = PL And V a = S Dr. Kovács Szilveszter Int.Comp. VI. / 21.
22 Path tracking of an automated guided vehicle Antecedent Fuzzy partitions The fuzzy partition of the distance between the guide path and the guide point (e v ) primary fuzzy sets (linguistic terms): The fuzzy partition of the estimated path tracking error (δ) primary fuzzy sets: Dr. Kovács Szilveszter Int.Comp. VI. / 22.
23 Path tracking of an automated guided vehicle Consequent Fuzzy partitions The fuzzy partition of the steering (V d ) primary fuzzy sets: The fuzzy partition of the speed (V a ) primary fuzzy sets: Dr. Kovács Szilveszter Int.Comp. VI. / 23.
24 Path tracking of an automated guided vehicle Rule base For the steering (R Vd ): R Vd : e v = NL : NM : NS : Z : PS : PM : PL : δ = NL : PM PS Z Z NL NL NL NM : PL PS PS PS PS Z NL NS : PL PM PS PS Z Z NL Z : PL PM PS Z NS NM NL PS : PL Z Z NS NS NM NL For the speed (R Va ): PM : PL Z NS NS NS NS NL PL : PL PL PL Z Z NS NM R Va : e v = NL : NM : NS : Z : PS : PM : PL : δ = NL : M S S S S Z Z NM : S M M M M M S NS : Z S L L L M S Z : S M L L L M S PS : S M L L L S Z PM : S M M M M M S PL : Z Z S S S S M Dr. Kovács Szilveszter Int.Comp. VI. / 24.
25 Path tracking of an automated guided vehicle Control surfaces (Zadeh-Mamdani + COG FLC) For the steering V d : For the speed V a : Dr. Kovács Szilveszter Int.Comp. VI. / 25.
26 Path tracking of an automated guided vehicle Structure of the guidance system of a differential steered AGV using the guide zone based path tracking strategy Dr. Kovács Szilveszter Int.Comp. VI. / 26.
27 Path tracking of an automated guided vehicle Performance of the fuzzy logic controlled path tracking guidance Dr. Kovács Szilveszter Int.Comp. VI. / 27.
28 Path tracking of an automated guided vehicle Performance of the fuzzy logic controlled path tracking guidance with respect to the minimal docking distance (ds) Dr. Kovács Szilveszter Int.Comp. VI. / 28.
29 Fuzzy-controlled Washing Machine (Aptronix Examples) Objective Design a washing machine controller, which gives the correct wash time even though a precise model of the input/output relationship is not available Inputs: Dirtyness, type of dirt Output: Wash time Dr. Kovács Szilveszter Int.Comp. VI. / 29.
30 Fuzzy-controlled Washing Machine Rules for our washing machine controller are derived from common sense data taken from typical home use, and experimentation in a controlled environment. A typical intuitive rule is as follows: If saturation time is long and transparency is bad, then wash time should be long. (átitatódási idő, átlátszóság) Dr. Kovács Szilveszter Int.Comp. VI. / 30.
31 Automatic Focusing System Cameras with automatic focusing systems usually measure the distance to the center of a finder's view. This method, however, is inaccurate when the object of interest is not at the center of the view (see fig.). Approach: Measuring more than one distance + fuzzy inference Objective Determine the object distance using three distance measures for an automatic camera focusing system. Inputs - the three distance measures at left, center and right points in the finder s view. Outputs - the plausibility values associated with these three points. The point with the highest plausibility is deemed to be the object of interest. Its distance is then forwarded to the automatic focusing system. Dr. Kovács Szilveszter Int.Comp. VI. / 31.
32 Automatic Focusing System Each input variable, representing distance, has three labels: Near, Medium, and Far. Each output variable, representing plausibility, has four labels: Low, Medium, High, and VeryHigh The guiding principle for establishing rules of this automatic focusing system is that the likelihood of an object being at medium distance (typically 10 meters) is high, and becomes very low as distance increases (say, more than 40 meters). Dr. Kovács Szilveszter Int.Comp. VI. / 32.
33 Automatic Focusing System RULES if Left is Near then Plau_of_Left is Medium; if Center is Near then Plau_of_Center is Medium; if Right is Near then Plau_of_Right is Medium; if Left is Near and Center is Near and Right is Near then Plau_of_Center is High; if Left is Near and Center is Near then Plau_of_Left is Low; if Right is Near and Center is Near then Plau_of_Right is Low; if Left is Medium then Plau_of_Left is High; if Center is Medium then Plau_of_Center is High; if Right is Medium then Plau_of_Right is High; if Left is Medium and Center is Medium and Right is Medium then Plau_of_Center is VeryHigh; if Left is Medium and Center is Medium then Plau_of_Left is Low; if Right is Medium and Center is Medium then Plau_of_Right is Low; if Left is Far then Plau_of_Left is Low; if Center is Far then Plau_of_Center is Low; if Right is Far then Plau_of_Right is Low; if Left is Far and Center is Far and Right is Far then Plau_of_Center is High; if Left is Medium and Center is Far then Plau_of_Center is Low; if Right is Medium and Center is Far then Plau_of_Center is Low Dr. Kovács Szilveszter Int.Comp. VI. / 33.
34 Air Conditioning Temperature Control Temperature control has several unfavorable features: non-linearity, interference, dead time, and external disturbances, etc. Conventional approaches usually do not result in satisfactory temperature control. There is a sensor in the room to monitor temperature for feedback control, and there are two control elements, cooling valve and heating valve, to adjust the air supply temperature to the room. Rules for this controller may be formulated using statements similar to: If temperature is low then open heating valve greatly Dr. Kovács Szilveszter Int.Comp. VI. / 34.
35 Air Conditioning Temperature Control Modified Model There are two sensors in the modified system: one to monitor temperature and one to monitor humidity. There are three control elements: cooling valve, heating valve, and humidifying valve, to adjust temperature and humidity of the air supply. Rules for this controller can be formulated by adding rules for humidity control to the basic model. If temperature is low then open humidifying valve slightly. This rule acts as a predictor of humidity (it leads the humidity value) and is also designed to prevent overshoot in the output humidity curve. Dr. Kovács Szilveszter Int.Comp. VI. / 35.
36 Advanced Model for Automobile Passenger Environment Controller outperforms conventional control systems substantially. It prevents rapid change of temperature in the car when doors or windows are opened and then closed. It even reacts to weather changes - interior humidity changes caused by the weather detected by sensors Temperature control in an automobile passenger environment is more complex than that of a static room. Temperature and humidity should be controlled to provide an enjoyable ride. Critical to keep windows from being fogged cause = a temperature differential between inside and outside air in combination with the interior humidity. To obtain satisfactory control results, the strength of sunshine radiation and the automobile speed must also be factored in. Dr. Kovács Szilveszter Int.Comp. VI. / 36.
37 Other Automotive Applications of Fuzzy Control Antilock brakes Servo Motor Force Control Transmission Control Suspension Smart car / Smart highway concepts Dr. Kovács Szilveszter Int.Comp. VI. / 37.
38 Automatic Transmission Fuzzy logic is employed to infer the best gear selection. The four fuzzy inference unit inputs are sensor based signals from the car itself. Objective: Using throttle, vehicle speed, engine speed, engine load, the fuzzy inference unit determines a shift, i.e., gear number, for the car. Dr. Kovács Szilveszter Int.Comp. VI. / 38.
39 Automatic Transmission Dr. Kovács Szilveszter Int.Comp. VI. / 39.
40 Automatic Transmission Modified Model Performance of the above model is not very good. Driving environment not taken into account. Humans, drive in different "modes" depending on road conditions. For example, we sometimes drive at a constant low gear when negotiating a windy mountainous road. This avoids unnecessary gear shifting, which can add to engine wear and make for a less than smooth ride for passengers. Adding an extra input, mode, to the fuzzy inference unit - influences gear shift behavior. Dr. Kovács Szilveszter Int.Comp. VI. / 40.
41 Automatic Transmission Modified Model If Vehicle_Speed is Low and Variation_of_Vehicle_Speed is Small and Slope_Resistance is Positive_Large and Accelerator is Medium Then Mode is Steep_Uphill_Mode If Vehicle_Speed is Medium and Variation_of_Vehicle_Speed is Small and Slope_Resistance is Negative_Large and Accelerator is Small Then Mode is Gentle_Downhill_Mode The driving mode output of FIU B can then be further used to affect the gear shifting procedure. For example, if mode is Steep_Uphill_Mode, a downshift is necessary in order to obtain greater engine power. If mode is Gentle_Downhill_Mode, we also need a lower gear than would be the case for a flat smooth road. The lower gear provides engine braking power. Typical gear selection rules could look as follows: If Mode is Steep_Uphill_Mode then Shift is No_2 If Mode is Gentle_Downhill_Mode then Shift is No_3 Dr. Kovács Szilveszter Int.Comp. VI. / 41.
42 Platoons of Smart Cars Platoons = high speed groups of smart cars in single lanes. The lead car plans the course of the platoon picks the velocity, car spacing, maneuvers to perform Increase the throughput of the highways The fuzzy platoon controller (FPC) = distributed control system for future freeways that drive a car in or out of a platoon. The FPC includes an integrated maneuver controller (IMC) for course selection and an individual vehicle controller (IVC) for throttle, brake and steering control. Course selection in IMC involves merge, split, velocity change and lane change. Fuzzy throttle controller for velocity and gap control. The controller gets information from its own sensors, the car ahead, and from the platoon goals. Dr. Kovács Szilveszter Int.Comp. VI. / 42.
43 Fuzzy Control of Platoons of Smart Cars Dr. Kovács Szilveszter Int.Comp. VI. / 43.
44 Platoon of Smart Cars 1 - Rules The number of rules depends on the problem. We shall consider only two for the simplicity of the example: Rule 1: If the distance between two cars is short and the speed of your car is high(er than the other one s), then brake hard. Rule 2: If the distance between two cars is moderately long and the speed of your car is high(er than the other one s), then brake moderately hard. Dr. Kovács Szilveszter Int.Comp. VI. / 44.
45 Platoon of Smart Cars 2 Membership Functions Determine the membership functions for the antecedent and consequent blocks Most frequently 3, 5 or 7 fuzzy sets are used (3 for crude control, 5 and 7 for finer control results) Typical shapes (triangular most frequent) Dr. Kovács Szilveszter Int.Comp. VI. / 45.
46 Platton of Smart Cars 3 Simplify Rules using Codes Distance between two cars: X1 speed: X2 Breaking strength: Y Labels- small, medium, large: S, M, L PL - Positive Large PM - Positive Medium PS - Positive Small ZR - Aproximately Zero NS - Negative Small NM - Negative Medium NL - Negative Large In the case of X2 (speed), small, medium, and large mean the amount that this car's speed is higher than the car in front. Rule 1: If X1=S and X2=M, then Y=L Rule 2: If X1=M and X2=L, then Y=M Dr. Kovács Szilveszter Int.Comp. VI. / 46.
47 Platoon of Smart Cars 4 - Inference Determine the degree of matching Adjust the consequent block Total evaluationof the conclusions based on the rules To determine the control amount at a certain point, a defuzzifier is used (e.g. the center of gravity). In this case the center of gravity is located at a position somewhat harder than medium strength, as indicated by the arrow Dr. Kovács Szilveszter Int.Comp. VI. / 47.
48 Modeling Fuel Injection Control Maps Motivation is started to be the need for a development tool for automatic calibration of the engine management systems. In the past look up tables for fuel injection control of engines could be obtained at the engine test bed using a trial and error method. The engine developer constructs a three dimensional map stationary engine operation and subsequently augments these maps with changing operation conditions (acceleration, warm-up, etc.) In practice this worked well with simple gasoline engines. Sequential carburetors, variable manifolds, as well as emission regulations have made this trial and error approach much harder and impractical. A development tool for transferring the developer s expertise into an automated system is needed. Dr. Kovács Szilveszter Int.Comp. VI. / 48.
49 Modeling Fuel Injection Control Maps The initial neural network phase tests the relevance of input parameters to the performance of the system. Initially, all inputs are used in the training of a three layer feedforward neural network. After the first training is complete, a single input value is varied and the results are observed. If the change in the output is negligible, the selected input is deemed to be unimportant and is discarded (sensitivity analysis). This procedure identified that the relevant inputs were engine speed and inlet manifold pressure. Throttle opening angle did not affect the representation. After identification of the relevant inputs a rule generation process reminiscent of neural network training was used. This process identified 65 AND type rules. Dr. Kovács Szilveszter Int.Comp. VI. / 49.
50 Fuzzy Logic Controller for Lateral Vehicle Control Successfully implemented on a full-sized test vehicle(toyota Celica). The FLC design includes a feedback module to infer control action from state errors, a preview module to infer control action with respect to preview information regarding upcoming road curvature, and gain scheduling module to handle the effects of the velocity of the vehicle. All three strategies are implemented on the test vehicle, automatically following a multiple curved track using discrete magnetic markers on the roadway and magnetometers on the vehicle as a lateral error reference sensing system. The use of preview information was determined to be vital for acceptable performance. A comparison is made to similar tests conducted using the frequency shaped linear quadratic controller as well as a PID controller. Dr. Kovács Szilveszter Int.Comp. VI. / 50.
51 Advantages of Fuzzy Controllers Control design process is simpler Design complexity reduced, without need for complex mathematical analysis Code easier to write, allows detailed simulations More robust, as tests with weight changes demonstrate Development period reduced Dr. Kovács Szilveszter Int.Comp. VI. / 51.
52 Ajánlott irodalom The slides of this lecture are partially based on the books: Kóczy T. László és Tikk Domonkos: Fuzzy rendszerek, Typotex Kiadó, 2000, ISBN J.-S. R. Jang, C.-T. Sun, E. Mizutani: Neuro-Fuzzy and Soft Computing, Prentice Hall, 1997, ISBN Michael Negnevitsky: Artificial Intelligence: A Guide to Intelligent Systems, Addison Wesley, Pearson Education Limited, 2002, ISBN Dr. Kovács Szilveszter Int.Comp. VI. / 52.
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