Application of Fuzzy Sets in Elevator System Control

Copyright © IFAC Artificial Intelligence in Real-Time Control, Bled, Slovenia, 1995

APPLICATION OF FUZZY SETS IN ELEVATOR SYSTEM CONTROL

Nadja Hvala and Vladimir Jovan

J. Stefan institute Jamova 39, 61111 Ljubljana e-mail: [email protected]

Abstract: The paper considers the elevator group control problem which is actual in large premises where a group of co-ordinated cars is necessary to serve the transport of passengers. Efficient elevator control requires low passenger waiting and transport times, together with low energy consumption, under different traffic conditions. In the paper two algorithms based on fuzzy sets are proposed to perfonn this task. The first algorithm acts as a "soft switch" between two classical algorithms, each covering a specific traffic situation. The second algorithm is entirely based on fuzzy sets and is appropriate for all situations. The perfonnance of the algorithms in tested case studies gave promising results so that the algorithms will be additionally tested, optimised and statistically evaluated in different case studies. Keywords: Fuzzy control, control algorithms, supervisory control, traffic control.

1. INTRODUCTION ease of inclusion of expert knowledge in the algorithm, reduction of the number of rules necessary to cover different problem situations, short computation times, realisation of the fuzzy algorithm on the microcomputers by the aid of fuzzy processors.

Elevator systems represent one of the fields ""here fuzzy sets methodology proves to be useful for solving real-world problems. The elevator system control is classically considered as an optimisation problem. However, using conventional optimisation methods the problem could not be solved efficiently in all situations due to the time-variable traffic conditions in buildings. In such cases the problem becomes too complicated and requires the use of specific evaluation functions in different situations.

When fuzzy sets methodology is used in an actual system, special attention is addressed on how it should be applied. Hence, the emphasis is on the problem fonnulation rather than on the research of methodology itself. From the literature review in the area of elevator group controL different approaches to the problem fonnulation can be found (Yamaguchi, et al. . 1988; Umeda, et aI. , 1989: Tobita, et al., 1991). Recently, Hikita (1993) reported about the control procedure based on fuzzy rule base method. In this approach the overall control algorithm is based on fuzzy rules, and by computing the degree of applicability, only one of the rules is selected for execution.

On the other hand, the available experts knowledge can improve the control perfonnance if used in a control strategy. This encouraged the use of AI methods in this area (Al-Sharif, 1993). There are many publications where expert systems are considered for application (Tsuji, et al., 1989: Pang and Nandy, 1989), while in the last years specially fuzzy sets methodology is gaining popularity in this area. The following advantages of the fuzzy approach are reported: 143

In this paper we approach this problem in a different way. The main idea is to design the control strategy based on already established and well-known elevator group control algorithms that have proved their efficiency also in practice. The strategy is designed so that it preserves the advantages of these algorithms while improving their weak points.

lem of efficient allocation of individual cars to incoming calls within the system. The algorithms fall into two major classes, namely those minimising the waiting time, and those minimising the energy consumption. The majority of installed elevator systems apply algorithms which combine the characteristics of the two basic classes.

The paper first gives a short description of problems related to elevator control and transport organisation in buildings. Then it presents two algorithms based on fuzzy sets methodology and shows their efficiency as examined by simulation.

Algorithms developed so far are capable of fulfilling the desired criteria successfully in normal circumstances, thereby applying the well-known assembly regime (Cavazza and Faldella, 1980). However, problems are perceived in irregular transport situations, most of all in periods of predominant incoming or predominant outgoing transport. In these cases, the cars tend to become clustered within a narrow area, and then eX"pedient servicing of calls from further away is not possible. Large hindrances are observed in irregular situations such as a concentration of calls in one section of the building, increased calls for transportation in one direction, loss of cars due to failures, etc.

2. PROBLEMS OF TRANSPORT ORGANISATION IN BUll..DINGS Large commercial, tourist and residential premises depend on systems of passenger elevators to provide efficient transport of passengers within the building. Recently, systems have been conceived in such a manner, that the cars do not operate in isolation but rather in a co-ordinated system, controlled by a computer. In this way, the total number of cars required for passenger transport in buildings may be reduced.

To cope with such circumstances, producers have tried to improve the efficiency of the control systems by upgrading the basic assembly regime, adequate for ordinary situations, with supplementary algorithms, which are activated when specific situations are detected in the building. Very often a supplementary algorithm is used which amends the basic algorithm in the periods of the filling or emptying the building.

The economics of new construction of large buildings dictate the installation of as few elevator cars as possible. Criteria for estimating the adequacy of an elevator system have been established around the world. Based on these criteria, one can determine the minimum number of cars of given capacity and velocity. The main criteria are as follows :

3. DESIGN OF ELEVATOR GROUP CONTROL ALGORI1HMS BASED ON FUZZY APPROACH

the average time of arrival of a car at the main floor has to be below 30 seconds, the elevator system has to be capable of transporting at least 12 percent of the building population in five minutes, the cycle period of a car participating in the assembly regime has to be below 150 seconds.

Although the mentioned classical group control algorithms perform reasonably well in many traffic situations, aware of the deficiencies in some cases the developers still search for the new improvements. In the last years, specially the advantages of new methodologies are considered and compared to the classical solutions.

The efficient control of transport in a building requires the linking of the elevator cars and control components into a unified system, on-line monitoring of the transportation requests and an algorithm which sensibly allocates individual cars to the pending calls. By efficient dispatching of the group of cars, the total elevator system throughput may be significantly improved, resulting in faster transportation in the building, and in reduced waiting times.

In this section we present two algorithms based on fuzzy sets. The first algorithm acts as a "soft switch" avoiding sharp transitions between the basic assembly regime and the regime of filling. It on-line determines the necessity of activating the filling regime and the number of cars to be involved in this regime. The second algorithm is based entirely on the fuzzy set methodology. Although partially relying on the algorithm for dynamic sector allocation in the classical approach, it completely changes the basic control algorithm and is appropriate for all traffic situations.

The producers of elevator systems are well aware of the advantages of efficient car control, so it is not surprising that large sums have been invested in the development of various control algorithms. The result is a number of algorithms for solving the prob144

3.1.

Fuzzy algorithm for dynamic calculation of the transitions between the regimes

As mentioned in the second section, the problem of predominant transport in a certain direction, e.g. , the morning rush of employees arriving at offices, is classically solved by activating the built-in algorithm which then prevails over the basic assembly regime as long as the transport situation requires. The switch between the regimes is perfonned when the control system detects an increased frequency of calls from the main floor (e.g. , the ground floor) towards upper floors. The usually established criterion for the switch is two consecutive departures of 75percent occupied cars from the main floor within a pre-set interval of time, e.g. , within two minutes. In this way, the intensified traffic from the main floor can be indirectly estimated. During the regime of filling, the algorithm allocates the cars only to the up-directed calls, and when the car deploys its passengers at the highest destination floor in the ride, it is returned directly to the main floor, to remain there waiting with door open.

culation. The number of cars is dynamically calculated according to the present transport situation. The input variables of the algorithm are: the number of cars departing from the main floor in two minutes (f}), and the average load of the cars (f2)' The output variable is the number of cars to participate in the regime of filling (f3). Fig. I shows the membership functions of the input and output variables and the decision rules.

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The classical solution to this problem does not allow a smooth transition between the basic assembly regime and the building filling regime. The tendency to minimise the number of cars installed dictate the involvement of all cars in the regime of filling, when the conditions to activate it are detected. Thus any nonnal down-going and inter-floor transport within the building is disabled during the filling regime. Switching from the ordinary regime to the filling regime, switching back, and the delays incurred by the switching, represent sharp transients in the elevator system operation, and the utilisation of the cars during these transients is reduced, resulting in increased waiting times. Sometimes, even a small number of up-going calls may trigger the filling regime, although the actual situation does not justify it. Such a switch is then only an inconvenience in the elevator system operation.

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Fig.I . Membership functions and fuzzy rules for calculating the number of cars in the filling regime. 145

As a first approximation, three membership functions were found to be sufficient to represent each variable. The shape of the membership functions is based on suggestions of an elevator control expert. The top of these functions and the asymmetry in some cases was chosen to achieve the desired nonlinearity in switching between the regimes, i.e., to fasten the transition to the filling regime when a great increase in the number of departures is detected.

a small portion of the building. This may appear also in case of normal traffic conditions. In classical regime with the algorithm of dynamic sector allocation this means that the majority of calls is assigned to one car and the waiting and transport times are prolonged. To avoid such situations the classical regime includes an additional, so called zoning algorithm, which disperse the cars throughout the building so that an approximately equal number of possible calls is assigned to each car. Reallocation of cars is performed if there is no hall calls in a certain time interval. This opens again the problem of setting the optimal time interval. If the interval for activating the zoning regime is too long, there is no car reallocation and the cars are not optimally positioned for serving the calls in the building. On the other hand, short time interval often means too high frequency of reallocation as during reallocation the cars are not available for passenger transport. Ideally, the time interval should adapt to the current traffic density in the building, although from the energy consumption point of view the reallocation of cars is always undesirable.

To calculate the required number of cars in the filling regime the min-max composition method is applied. The centroid method is used for defuzzification. When, e.g ., three 75-percent occupied cars depart from the main floor during 2 minutes, the calculated result of the fuzzy algorithm is 2.867. This means that 3 cars are needed to support the regime of filling in this case. The advantages of this approach are, besides the variable number of cars participating in the filling regime, also the soft transitions of each conditional variable and the variety of different cases that can be considered in this way.

3. 2. Fuzzy algorithm in basic regime In fuzzy control algorithm the size of the sector is one of the input variables which has an important impact on the value of the unsuitability coefficient. The fuzzy rules are constructed in such a way that, depending on the value of this variable, the unsuitability coefficient has an appropriate value so that grouping of cars is prevented in advance. Hence, no special reallocation algorithm is necessary. E.g. ,

The second algorithm was designed to cover all traffic situations and is completely based on fuzzy sets. The algorithm calculates the unsuitability coefficient which determines how suitable is the car to serve the call. When the new hall call is registered this coefficient is calculated for each car, and the car with the lowest value is then chosen to answer the current call.

IF the size of the sector associated to the car is big AND the number of calls already assigned to the car is small AND the distance of the call from the current car position is small TIIEN the unsuitability coefficient of the car is small.

To calculate the unsuitability coefficient as an output variable, the following input variables are used: the size of the sector which is currently associated to the given car, the number of calls that are already assigned to the car, and the distance of the call from the current car position.

Each variable is presented by three membership functions, while the algorithm is based on 21 fuzzy rules.

The first input variable, i.e. , the size of the sector, is determined as in already well-known classical algorithm of dynamic sector allocation. In this algorithm, each car serves the hall calls in the currently associated area which includes the floors from the current car position to the next car in a clockwise direction. The size of the sector of a given car is determined as the maximum number of hall calls possibly appearing in this sector.

4. SIMULATION TESTS The first algorithm, i.e. , the fuzzy set-based method for the dynamic calculation of the required cars, was tested by simulation and compared to the classical way of activating of the filling regime. A case study was a simulation of the filling of a 1200 employee commercial building in the period between 7 and 8 in the morning, with a Gaussian distribution of arrivals, by a system of 5 cars of 13 person capacity.

This input variable can be related to the concentration of cars in the building. If a large sector is allocated to a certain car, the other cars tend to group in 146

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Fig. 2. Comparison of the number of passengers that were not transported during 2 minutes.

The resulted passenger waiting times in both cases are shown in Fig. 2 for comparison. In the classical case, the filling regime is activated already after 6 minutes, and is abandoned in the 56th minute. The cars took part in the filling regime 112 times, and 114 passengers were compelled to wait for more than 2 minutes for their ride. Interfloor transport was held up for 50 minutes.

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The fuzzy set-based activation of the filling regime resulted in the reduction of the participating cars (l09 cars), and a reduction in the number ofpassengers waiting for more than 2 minutes, by 10 percent (99 passengers). The duration of all cars involved in the regime of filling was reduced to 26 minutes, thus improving significantly the situation for inter-floor transport.

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The case study chosen for presenting the performance of the second algorithm, i.e., the fuzzy algorithm in basic control regime, is shown in Figures 3 to 6. This case study addresses a typical traffic situation which is often considered in papers to test the performance of the algorithms. The example represents the building, e.g. , a hotel, where in certain time periods more intensive traffic appears to a certain floor, e.g. , to the floor with the dining room. The case study considers the assignment of cars (A, B and C) to the passenger calls (I, 11,.. ., XI), triggered in different floors (9-th floor, 7-th floor, ... , 5th floor) . All passenger calls require the transportation to the first floor. Figures 3 and 5 represent the travelling of each car in classical and fuzzy control algorithm, respectively. It can be seen that after triggering a call, one of the cars is chosen to serve the call. Figures 4 and 6 represent the waiting times of each passenger.

Fig. 5. Arrangement of traffic in fuzzy control algorithm.

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no additional algorithms are necessary to cover specific traffic situations.

Comparing the results of both algorithms it can be seen that the fuzzy algorithm significantly reduces the average passenger waiting time (from 21 to 11 seconds). The first difference is noticed in serving the IV-th call. The classical algorithm decided on car B, while the fuzzy algorithm decided that car C is most appropriate to serve this call. This is due to the fact that much greater area (greater number of possible calls) is in this situation assigned to car B. Deciding on car C, however, increases the waiting time of this passenger. In the new situation after triggering the V-th call, car B is also assigned to serve this call in classical case, while fuzzy algorithm decided for an additional car A. From then on the differences of both algoritluns become larger so that only statistical comparison is reasonable. In general it can be seen that the fuzzy algorithm activates additional cars for serving the calls. Hence it primarily tends to reduce the passenger waiting and transport times and gives less attention to energy consumption.

Our future work will continue by seeking optimal membership functions and fuzzy rules used in the algorithms. Also, some additional input variables will be considered for inclusion in the second algorithm. These tasks will be performed by the aid of simulation and in close co-operation with the specialists from the elevator control area. The algoritluns will be also tested and statistically evaluated in additional case studies before they will be adapted for application in a real elevator control system.

REFERENCES Al-Sharif, L.R. (1993). Applications of artificial intelligence in lift systems. Elevator, 45-49. Cavazza, S. and E. Faldella. Microcomputercontrolled lift system. Microprocessors and Microsystems,4, 137-140. Hikita, S. (1993). Elevator control using a fuzzy rule base. In: Industrial Applications of Fuzzy Technology (ed. K. Hirota), Springer-Verlag, Tokyo. Pang, G.K.H. and B, Nandy (1989). Intelligent scheduling of a group of elevators. IEEE Int. Symp. on Intelligent Control, Albany, NY, USA, 144-149. Tobita, T., A. Fujino, H. Inaba, K. Yoneda and T. Ueshirna (1991). An elevator characterized group supervisory control system. Proc. IECON'91 Inter. Con! of Industr. Electron. , Control and Instrument, 1972-1976. Tsuji, S., M. Arnano and S. Hikita (1989). Application of the expert system to elevator groupsupervisory control. IEEE Fifth Conf on ArtifiCial Intell. Appl., Washington, USA. 288294. Umeda, Y. , K. Uetani, H. Ujihara and S. Tsuji (1989). Fuzzy theory and intelligent options. Elevator World, 86-91. Yamaguchi, T., T. Endo and K. Haruki (1988). Fuzzy predict and control method and its application. lEE International Con! on Contro/'88, 287-292.

5. CONCLUSION The paper presents two fuzzy algorithms for elevator group control. The first algorithm was designed in order to assure soft transitions between two well known regimes in elevator control. Both regimes, i.e., the assembly regime and the filling regime, use classical algorithms and were designed to cover normal and specific traffic conditions, respectively. The second algorithm is entirely based on fuzzy calculations and covers all traffic situations. The results of testing the algorithms for different traffic situations can be considered promising. Simulation of the building filling situation demonstrated that the application of the fuzzy set theory renders possible more favourable transitions among the various regimes of the system operation, reduces the number of cars required to participate in the regime of filling, and accommodates more passengers in such a situation. Similarly, better results of passenger waiting and transport times are observed when the whole algorithm is based on fuzzy sets and

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