Fuzzy system for an automatic door’s control

In this page you will find a fuzzy system for an automatic door’s control. 

You can play around with the applet, push “+” or “-“ to vary the indoor expected temperature and the real temperature, press “ Pasar Persona” for you cross a person and “Pasar 5 Personas” for you cross five persons, You can see the results using the Mandami, Product and Lucasiewicz fuzzy logics and try the product result, also you can  read a paper describing the theory behind it. 

NOTE: You need Java Plug-in to run this applet. If it does not work, get the latest Java Plug-in here.

Download jar here

  

It has been developed by Joaquin Gayoso Cabada as a final project for the course "Razonamiento aproximado y con incertidumbre" in the Facultad de Informática of Universidad Complutense de Madrid. 

Here is the complete paper of this project: 

Fuzzy System for Intelligent Automatic Door’s Opening Control

 

joaquin Gayoso Cabada, luis garmendia salvador

gayoxo@gmail.com, lgarmend@fdi.ucm.es

Dpto. Ingeniería Software e Inteligencia Artificial. Facultad de Informática, Universidad Complutense de Madrid, 28040-Madrid, Spain

1.                Abstract

This paper describes an automatic door control fuzzy system based on the stream of people who walk through the door and on the difference of degrees between the indoor temperature and the outdoor temperature. The motivation of the system is to save energy by using as least as possible the door's motor and by reducing the heating waste. An implementation of the system is available in the web.

 

2.                Introduction

In the present world where the efficiency and the ecology are now on top, this system tries to save on the usage of the motor by means of an automatic control system, minimizing the impact on the environment and reducing the energetic cost. Nowadays, when we examine usual automatic doors, we see a manual timing system which is only controlled by the men who are designated to set it up. In other cases, the door´s adjustment is based on the experience of the worker who assembled the door. As a result, we may see that automatic doors do not work properly. This common and extended used way is not intelligent at all, because automatic doors opens too slow when there are a lot of people walking through, or they are continuously opening and closing. There are also situations in which the doors are closed and the air conditioner or heating are working, while indoor and outdoor temperature is the same. As well as open doors in midwinter when there are not too many people walking through.

 Therefore, our proposal to improve and maximize the performance of automatic doors is an automatic fuzzy system that regulates the opening and closing based on the following variables to set the period of time in which the door should be keeping open.

The implementation in a Java Applet and executable java jar file  is available on the web at http:/www.fdi.ucm.es/profesor/lgarmend/SC/DoorControl/

 

3.                Problem description

The problem is based on three variables that represent our system: the people walking through the door, the difference of degrees between indoor and outdoor-temperature of the building and the waiting time of opening and closing. Normally, as we explained above, this time is adjusted by employees without using an optimal technical method , so the system does not work at its fullest potential, because sometimes the doors are very quick or too slow, and its opening and closing time is longer or shorter than needed. It also happens the same when the indoor and outdoor-temperature difference is too big or too small and the automatic doors are keep open or closed uselessly.

4.                Problem description with fuzzy sets

The problem description is a simplified model of the real world door, with the following variables in the system [see Klir G. and B. Yuan, 1995; Pedrycz, 1992; Lewis, H.W. 1997].

·         Input Variables:

o    Stream of people

o    Difference of temperature degrees

 

·         Output variables:

 

o    Waiting time between closing and opening.

 

The goal is to set a waiting time between opening and closing that minimizes the use of the motor without reducing the functionality of the door.

The following subsections describe some fuzzy sets [Zadeh, 1965] for different linguistic variables on the input and output variables.

4.1. Stream of People

The stream of people is modeled as a number of weighted people that walk through the door in a minute, it is bounded between zero and sixty. There are three linguistic variables modeled with fuzzy sets to represent the item what is represented within the figure 1.  Those fuzzy sets are evaluated from a counter of people within a minute that adds one people per second when the laser of the door cuts.

The three modeled fuzzy sets to evaluate the stream of people are defined like:

 

§  “ Low stream” (‘Poca’ in Spanish, in figure 1): Sigma function with center in ten and amplitude least two.

§   “Medium stream” (‘Medio’ in Spanish): Bell function with center in fifteen and amplitude seven.

§  “High stream  (‘Mucho’ in Spanish): Sigma function with center in thirty and amplitude least seven.

 

Figure 1. Fuzzy sets “low stream”, “medium stream” and “high stream” to evaluate the amount of people stream within a minute.

 

 

4.2. Difference of temperature ( in centigrade degrees)

The difference of temperature in centigrade degrees is a simple subtraction between the desired indoor temperature and the real temperature out of the building. The domain of this variable is bounded between zero and thirty. To model this variable, it is used  four fuzzy sets because it is the most important variable, is represented within the figure 2 and his function set are defined like:

§  “Very low” (‘Poca’ in figure 2): Bell function with center in zero and amplitude five.

§  “More or less low” (‘LBaja’ in firure 2): Bell function with center in ten and amplitude five.

§  “More or less high” (‘LAlta’ in figure 2): Bell function with center in fifteen and amplitude five.

§  “High” (‘Mucho’ in figure 2): Sigma function with center in twelve and amplitude three.

 

 

Figure 2. Fuzzy sets “very low”, “More or less low”, “more or less high”, and “high” to evaluate the difference of temperature in centigrade degrees.

 

4.3. Open waiting time between closing and opening the door

The waiting time between closing and opening of the door is designed to model a  subjective vision of  the waiting time concept in seconds. It can be readjust by experts based on air cooling and warming on temperature differences.

 We use five fuzzy sets represented within figure 3 to model this variable:

 

§  “Very low” (‘Bajo’ in Spanish): Bell function with center in zero and amplitude one.

§  “Low” (‘Leve’ in Spanish): Bell function with center in two and amplitude one.

§  “Medium” (‘Medio’ in Spanish): Bell function with center in four and amplitude one.

§  “Some  (Moderado’ in Spanish): Sigma function with center in six and amplitude two.

§  “High” (‘Alto’ in Spanish): Isosceles function with center in thirty and amplitude thirty.

 

Figure 3. Fuzzy sets “Very Low”, “Low”, “Medium”, “Some”, “High” for the waiting time ins seconds.

 

 

 

5.                Fuzzy Rules for door’s control

Once we have modeled the fuzzy sets, we define rules that represent the desired functionality to learn how many seconds to maintain open the door from the people stream and the difference of temperature.  Twelve rules are represents in an adjacency table (figure 4), where DifTemp= Difference of temperature, Personas= Stream of People, (X, Y) = Waiting Time Door.

Figure 4. FuzzyRules of the system.

For example, the rule described in (first row, first column) is the fuzzy rule:  IF ‘the people stream is Low’ AND ‘the difference of temperature is Very Low’ THEN ‘the opening time is high”

6.                Results of applying our control to a door

We apply our control to a door and we realize that the door can save so much energy if the difference of temperature is too high and modeled if the difference is middle based on the stream of people.

The AND operator in the premise is tested for different continuous t-norms [B. Schweizer and A.Sklar, 1960]. We only test continuous t-norms because we want a ‘soft’ behavior, in the sense that if the difference of temperature is increased a little bit, the door´s open wait must be decreased just a little bit, so we do approximate reasoning. After testing the AND operator with several t-norms we find that the minimum t-norm ignores one of the two input variables loosing then some king of information. The Lucasiewicz t-norm gives a too low premise evaluation when both variables are not close to one, so it is chosen  an `in between’  product t-norm, which also provides a softer behavior and  its bound results represent better the problem.

The chosen implication operator is Mandami´s operator [Mandami, 1977].

With the chosen operators, a summary of the fuzzy inference results are shown in figure 5.

 

Figure 5. Waiting time learned from people stream and temperature difference using the product t-norm in the premise conjunction and the Mandami´s implication operator.

 

 

7.                Fuzzy System VS Singleton System

We implement a classical rule inference system to compare the difference between the fuzzy approach and the classical rule system approach. The crisp sets are defined with the same names that in the fuzzy case, but they only have nitide values 0 or 1. The crisp sets are used in the classical rule systems are shown in figures 6, 7, 8.

 

Figure 6. Three stream of people classical sets for  low stream”, “medium stream” and “high stream”.

 

Figure 7. Four Difference of temperature classical sets for “very low”, “More or less low”, “more or less high”, and “high”.

 

Figure 8. Five waiting time classical sets for  Very Low”, “Low”, “Medium”, “Some”, “High” for the waiting time ins seconds.

 

Then we apply the same rules described in figure 4, now considered nitide rules and we reach the following learned waiting time described in figure 9.

Figure 9. Opening waiting time learned from classical rules of inference.

 

8.                Conclusions

The given intelligent  system to learn  how long a door must be open  can save a lot of energy used by the motor of the door and preserving indoor temperature if the door is implanted in cities with a medium fluctuating temperature and different streams of persons along the time that the building is opened.

A fuzzy and a classical rule of inference systems have been compared. Examining the figures 5 and 9 we find that in extreme conditions (nitide values) both systems behave in a similar way, but when somehow uncertainty appears,  the fuzzy system reaches a big  improvement , and  have a much ‘softer’ behavior than the classical modus ponens inference system, that produces some ‘jumps’ in the inference results. When the premise conjunction is implemented with the product t-norm operator, softness of the system is increased when it is compared with other continuous conjunction operators.

The implementation in Java of the fuzzy inference engine can be tested at http://www.fdi.ucm.es/profesor/lgarmend/SC/DoorControl/

 

9.                References

1.     IMSE Centro Nacional de Microelectrónica. Herramientas de CAD para Lógica Difusa. Xfuzzy 3.0. http://www.imse.cnm.es, 2003.

2.     Klir G. and Yuan, B. “Fuzzy Sets and Fuzzy Logic Theory and its Applications” Prentice Hall. 1995.

3.     Pedrycz, W.: Modelling with fuzzy sets in fuzzy control. Fuzzy Days, 3-34, 1992.

4.     Lewis, H.W. “The Foundations of Fuzzy Control”, Springer. 1997.

5.     E. H. Mamdani, "Applications of Fuzzy Set Theory to Control Systems: A Survey," in Fuzzy Automata and Decision Processes, M. M. Gupta, G. N. Saridis and B. R. Gaines, eds., North-Holland, New York, pp. 1-13, 1977.

6.     B. Schweizer and  A.Sklar, Probabilistic Metric Spaces. North-Holland, 1960.

5.    E. Trillas and L. Valverde, Approximate reasoning in expert systems, North-Holland, 157-166, 1985.

7.    L.A. Zadeh, Information and Control, 8, 338-353, 1965.