CONTROL FUZZY INTRODUCCION

Presentación del tema: "CONTROL FUZZY INTRODUCCION"— Transcripción de la presentación:

1 CONTROL FUZZY INTRODUCCION
Martes 14 de junio de 2005 CONTROL FUZZY INTRODUCCION

2 CONTENIDO Motivacion para el control fuzzy
Controladores PID usando tecnicas fuzzy Controlador proporcional difuso Controlador PD difuso Controlador PI difuso Analisis de controladores PID fuzzy 12-abr-17

3 Motivacion para el control fuzzy
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4 El control convencional
Conventional control theory uses a mathematical model of a process to be controlled and specifications of the desired closed-loop behaviour to design a controller. This approach may fall short if the model of the process is difficult to obtain, (partly) unknown, or highly nonlinear. The design of controllers for seemingly easy everyday tasks such as driving a car or grasping a fragile object continues to be a challenge for robotics, while these tasks are easily performed by human beings. Yet, humans do not use mathematical models nor exact trajectories for controlling such processes. Many processes controlled by human operators in industry cannot be automated using conventional control techniques, since the performance of these controllers is often inferior to that of the operators. One of the reasons is that linear controllers, which are commonly used in conventional control, are not appropriate for nonlinear plants. (Babuska, 2002) The FLC is considered as a good methodology because it yields results superior to those obtained by conventional control algorithms. In particular the FLC is useful in two cases (Lee). (1) The control processes are too complex to analyze by conventional quantitative techniques. (2) The available sources of information are interpreted qualitatively, inexactly, or uncertainly. El control convencional La teoria del control convencional se caracteriza por: Modelos matematicos de un proceso Linealizacion en un punto de operacion y controladores Lineales Metodos de diseño basados en la planta ideal 12-abr-17

5 Los problemas reales Los sistemas reales son complejos
Conventional control theory uses a mathematical model of a process to be controlled and specifications of the desired closed-loop behaviour to design a controller. This approach may fall short if the model of the process is difficult to obtain, (partly) unknown, or highly nonlinear. The design of controllers for seemingly easy everyday tasks such as driving a car or grasping a fragile object continues to be a challenge for robotics, while these tasks are easily performed by human beings. Yet, humans do not use mathematical models nor exact trajectories for controlling such processes. Many processes controlled by human operators in industry cannot be automated using conventional control techniques, since the performance of these controllers is often inferior to that of the operators. One of the reasons is that linear controllers, which are commonly used in conventional control, are not appropriate for nonlinear plants. (Babuska, 2002) The FLC is considered as a good methodology because it yields results superior to those obtained by conventional control algorithms. In particular the FLC is useful in two cases (Lee). (1) The control processes are too complex to analyze by conventional quantitative techniques. (2) The available sources of information are interpreted qualitatively, inexactly, or uncertainly. Los problemas reales Los sistemas reales son complejos No linealidades Modelos dificiles de obtener Las fuentes de informacion son Cualitativas Inexactas El control tipicamente es manual El conocimiento “experto” del operador 12-abr-17

6 Proposito del control fuzzy
Fuzzy logic is much closer in spirit to human thinking and natural language than the traditional (classical) logical systems. Basically, it provides an effective means of capturing the approximate, inexact nature of the real world. Therefore, the essential part of the fuzzy logic controller (FLC) is a set of linguistic control strategy based on expert knowledge into an automatic control strategy. The early work in fuzzy control was motivated by a desire to: mimic the control actions of an experienced human operator (knowledge-based part) obtain smooth interpolation between discrete outputs that would normally be ob-tained (fuzzy logic part) Proposito del control fuzzy Proponer otro paradigma de diseño Imitar las acciones de control del operador humano Interpolacion suave de la salida bajo condiciones distintas 12-abr-17

7 Diseño clasico del sistema de control
Metodos de diseño: Basado en señal: el modelo solo se usa en la etapa de diseño basado en modelo: el modelo hace parte del algoritmo de control 12-abr-17

8 Diseño clasico del sistema de control
Problemas del control Regulacion, Seguimiento 12-abr-17

9 Pasos del diseño clasico
Estudio del proceso. Selección de sensores y actuadores Modelado del sistema. Identificacion. Selección de las especificaciones Selección y diseño del controlador Simulacion. Posible mejora. Selección del HD y SW Experimentos en tiempo real. Sintonia De Sousa, 2000 12-abr-17

10 Metodologia del diseño clasico
Diseño del controlador Root-Locus Control PI Modelo analitico Identificacion Algoritmo de control Modelo Dinamico Satisface Analisis de requerimientos Performance Specifications

11 El control fuzzy Pretende controlar sistemas complejos
Usa estrategias de control basadas en conocimiento Representado en la base de reglas Y la base de datos 12-abr-17

12 Bases del control fuzzy
Diseño basado en sistemas fuzzy en lugar de ecuaciones matematicas Ventajas Utilizacion del conocimiento experto Aproximacion de funciones no lineales Eficiente: numero de parametros, local, metodos de identificacion transparente 12-abr-17

13 Pasos de diseño del control fuzzy
Comparing the design of a conventional fuzzy controller to a classical controller, the steps concerning the modeling and the choice of design specifications are not explicitly present in the FLC. The If–Then rules contain implicitly the performance criteria and the choice and settings of the controller meeting the desired specifications. Fuzzy logic controllers are usually tuned by a trial-and-error method using simulations or experiments on the system. Unfortunately, experience shows that this design methodology has some significant drawbacks. Expertise to be extracted from operators is usually difficult to express in a rule-base form, and it is a time-consuming task. Moreover, in an industrial environment, the in-line trial-and-error controller tuning is often not acceptable for e.g. safety, economical and environmental reasons. Furthermore, the performance of the FLC mimics the control actions performed by the operator, and therefore does not perform better than the best operator. However, this control is consistent, and independent from the “condition” of the operator. It is questionable whether the control actions performed by the operator are the most desirable ones, given the possible changes in the process behavior. Pasos de diseño del control fuzzy Estudio del sistema. Selección de sensores y actuadores Modelado del sistema. Identificacion. Selección de las especificaciones Selección y diseño del controlador Simulacion. Posible mejora. Selección del HD y SW Experimentos en tiempo real. Sintonia 12-abr-17

14 Modelado de la planta en el control fuzzy
El modelo la planta puede ser no lineal 12-abr-17

15 Controlador proporcional difuso
18 de septiembre del 2003 Controlador proporcional difuso

16 Controladores proporcionales
En el sistema de control El controlador fuzzy construye una funcion monotona P: Cuanto mas error, mayor accion de control 12-abr-17

17 Controladores proporcionales
Mapeo de entrada salida Controlador fuzzy 12-abr-17

18 Base de reglas del controlador proporcional
If error is NB then control input is NB If error is Zero then control input is Zero If error is PB then control input is PB 12-abr-17

19 Controlador fuzzy: ejemplo
Matriz asociativa fuzzy Consecuente Regla 12-abr-17

20 Controlador fuzzy: ejemplo
Activacion de las reglas Regla 4 12-abr-17

21 Controlador fuzzy: ejemplo
Superficie entrada-salida 12-abr-17

22 18 de septiembre del 2003 Controlador PD difuso

23 Controlador PD convencional
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24 Controladores PD difusos
Controlador PD fuzzy 12-abr-17

25 Controladores PD difusos
Comparacion entre el PD convencional (izq.) y el PD fuzzy (der.) 12-abr-17

26 18 de septiembre del 2003 Controlador PI difuso

27 Estructura del controlador PI difuso
The fuzzy rules contained in the conventional fuzzy controller do not include any dynamics. The dynamic behavior is provided by an external dynamic filter, that computes the variables needed as inputs in the FLC. Examples of these variables are the errors between the references r and the output y, the rate of change or the cumulative sum of these errors, or other dynamic time shift operations such as regressions of inputs and outputs. 12-abr-17

28 Base de reglas del controlador PI
IF e(k) is P AND Δe(k) is P THEN Δu(k) is P IF e(k) is P AND Δe(k) is N THEN Δu(k) is Z IF e(k) is N AND Δe(k) is P THEN Δu(k) is Z IF e(k) is N AND Δe(k) is N THEN Δu(k) is N 12-abr-17

29 18 de septiembre del 2003 Control Difuso VS. PID

30 Control PID convencional
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31 Control PID fuzzy 12-abr-17

32 Controlador fuzzy dinamico
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33 Obtencion de la base de reglas
18 de septiembre del 2003 Obtencion de la base de reglas

34 Comportamiento del error
Respuesta transiente tipica 12-abr-17

35 Tres meta-reglas Si e(k) y De(k) son cero entonces mantener el control presente (sea Du(k) o u(k)); Si e(k) tiende a cero a una velocidad satisfactoria, entonces mantener el control presente; Si e(k) no tiende a cero, entonces la accion de control es distinta de cero y depende del signo y la magnitud de e(k) and De(k). 12-abr-17

36 Base de reglas PI Salida 12-abr-17

37 analisis de los controladores fuzzy
Tomado de [Reed A., 2002 ] analisis de los controladores fuzzy

38 Introduccion de la dinamica en un controlador fuzzy
El sistema fuzzy es una relacion de entrada-salida estatica Los filtros introducen la dinamica crisp-fuzzy interface inference engine fuzzy-crisp interface Input(s) output Knowledge base Data base Rule base informations Dynamic filter The fuzzy rules contained in the conventional fuzzy controller do not include any dynamics. The dynamic behavior is provided by an external dynamic filter, that computes the variables needed as inputs, or outputs, in the FLC. Examples of these variables are the errors between the references r and the output y, the rate of change or the cumulative sum of these errors, or other dynamic time shift operations such as regressions of inputs and outputs. The fuzzy control scheme in Fig does not include the disturbances explicitly, but they are usually present as shown in the general control scheme (See Fig. before). The FLC must be designed such that it can cope with these disturbances, but unfortunately this problem is not always considered. 12-abr-17

39 Los factores de escala son parametros de sintonia importantes
Normalizacion Usualmente Los universos de entrada y salida estan normalizados. Calculo de los factores de escala Los factores de escala son parametros de sintonia importantes 12-abr-17

40 Diagrama tipico de un control fuzzy
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41 Pre-procesamiento Filtro dinamico Escalamiento de la señal
The pre-filter processes the controller’s inputs in order to obtain the inputs of the static fuzzy system. It will typically perform some of the following operations on the input signals: Signal Scaling. It is often convenient to work with signals on some normalized domain, e.g., [ .1 ,1]. This is accomplished by normalization gains which scale the input into the normalized domain [ .1 ,1]. Values that fall outside the normalized domain are mapped onto the appropriate endpoint. Dynamic Filtering. In a fuzzy PID controller, for instance, linear filters are used to obtain the derivative and the integral of the control error e . Nonlinear filters are found in nonlinear observers, and in adaptive fuzzy control where they are used to obtain the fuzzy system parameter estimates. Feature Extraction. Through the extraction of different features numeric trans-formations of the controller inputs are performed. These transformations may be Fourier or wavelet transforms, coordinate transformations or other basic operations performed on the fuzzy controller inputs. Pre-procesamiento Filtro dinamico Escalamiento de la señal Extraccion de caracteristicas 12-abr-17

42 Pos-procesamiento Escalamiento de la señal Filtro dinamico 12-abr-17
The pre-filter processes the controller’s inputs in order to obtain the inputs of the static fuzzy system. It will typically perform some of the following operations on the input signals: Signal Scaling. It is often convenient to work with signals on some normalized domain, e.g., [ .1 ,1]. This is accomplished by normalization gains which scale the input into the normalized domain [ .1 ,1]. Values that fall outside the normalized domain are mapped onto the appropriate endpoint. Dynamic Filtering. In a fuzzy PID controller, for instance, linear filters are used to obtain the derivative and the integral of the control error e . Nonlinear filters are found in nonlinear observers, and in adaptive fuzzy control where they are used to obtain the fuzzy system parameter estimates. Feature Extraction. Through the extraction of different features numeric trans-formations of the controller inputs are performed. These transformations may be Fourier or wavelet transforms, coordinate transformations or other basic operations performed on the fuzzy controller inputs. Pos-procesamiento Escalamiento de la señal Filtro dinamico 12-abr-17

43 : papel de los conjuntos fuzzy
Numero y posicion de los conjuntos fuzzy Division lineal division logaritmica 12-abr-17

44 : papel de los conjuntos fuzzy
Numero y posicion de los conjuntos fuzzy Traslapamiento Con traslapamiento de mas de dos conjuntos fuzzy, la superficie de salida se suavisa El cambio de los consecuentes no tiene mucha consecuencia: el efecto es filtrado por las otras reglas activas The higher the density of the fuzzy sets on a certain part of the universe of discourse, the more complex the controller output as function of the controller inputs can be defined. 12-abr-17

45 : papel de los conjuntos fuzzy
Numero y posicion de los conjuntos fuzzy Traslapamiento Forma Usando MFs no lineales se introducen caracteristicas no lineales La no linealidad deberia ser definida por las reglas 12-abr-17

46 : papel de los conjuntos fuzzy
Numero y posicion de los conjuntos fuzzy Traslapamiento Forma Conjuntos fuzzy de salida Normalmente se usan conjuntos equidistantes Parece razonable usar consecuentes constantes o funcionales 12-abr-17

47 : papel de los operadores
Negadores en las premisas de las reglas 12-abr-17

48 : papel de los operadores
Negadores en las premisas de las reglas Conector logico and El uso del operador min resulta en no-linealidades El operador producto es conveniente desde este punto de vista 12-abr-17

49 : papel de los operadores
Negadores en las premisas de las reglas Conector logico and Conector logico Or El numero de reglas puede decrecer usando el operador Or (not) No se recomienda 12-abr-17

50 Propiedades de la base de reglas
Continuidad Reglas con premisas “adjacentes” tienen consecuentes “adjacentes” Consistencia Se refiere a la consistencia del conocimiento representado por la base de reglas Completitud Todas las situaciones del espacio de entrada (a un nivel semantico) tienen una salida definida 12-abr-17

51 Estructuras de controladores fuzzy tipo pid
18 de septiembre del 2003 Estructuras de controladores fuzzy tipo pid Cortesía de Jan Jantzen, Technical University of Denmark, 2002

52 Controlador Fuzzy Proporcional
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53 Controlador Fuzzy PD 12-abr-17

54 Controlador Fuzzy PI 12-abr-17

55 Controlador Fuzzy PD + I
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56 Controlador hibrido Fuzzy-lineal P + ID
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57 Fuentes Robert Babuska. Course Fuzzy and Neural Control, 2001/2002.
Andrii Riid, Transparent Fuzzy Systems: Modeling and Control. PHD Thesis. 2002 Joao Miguel da Costa Sousa, “Fuzzy Model-Based Control” , Technical University of Lisbon, 2000 12-abr-17

58 Fuentes René Jager, Fuzzy Logic in Control. PHD thesis, 1995.
Antonio Sala P., Validacion y aproximacion funcional en sistemas de control basados en logica borrosa. Tesis PHD. 1998 L.X. Wang, “A course in Fuzzy Systems and Control”, Prentice-Hall, 1997 Kevin Passino, Intelligent Control, The Ohio State University, 2000 12-abr-17

59 Robert Babuska. Course Fuzzy and Neural Control, 2001/2002.
Fuentes Kwang-Hyung Lee, Textbook CS670 Fuzzy Theory, septiembre 2001. Robert Babuska. Fuzzy and neural control. DISC Course Lecture Notes (October 2001) Robert Babuska. Course Fuzzy and Neural Control, 2001/2002. 12-abr-17

60 The end