PLC IMPLEMENTATION OF A FUZZY SYSTEM

Transcription

1 The 6 th edition of the Interdisciplinarity in Engineering International Conference Petru Maior University of Tîrgu Mureş, Romania, 202 PLC IMPLEMENTATION OF A FUZZY SYSTEM Adrian-Vasile DUKA # # Department of Electrical Engineering and Computer Science, Petru Maior University of Tg. Mureş No. N.Iorga St., Tg. Mureş Romania adrian.duka@ing.upm.ro ABSTRACT This paper investigates the implementation and design of a fuzzy system on an industrial controller. Programmable Logic Controllers (PLCs) are key devices used in many industrial processes. Most of the time they implement discrete control functions involving sequential control, but the availability of basic features like arithmetic operations, floating point units etc. allow for more complex algorithms to be implemented. The fuzzy system, in this paper, uses two inputs and one output, triangular shape membership functions and a rule base made of if-then type rules and it is implemented on a Siemens S7-200 PLC. Keywords: Fuzzy System, Programmable Logic Controller, PLC. Introduction Programmable Logic Controllers (PLC) are very effective and reliable devices well suited for applications involving discrete control actions in the manufacturing, chemical and process industries. The availability of PLCs with features like: floating point math, data handling, advanced functional instructions and the improvement of graphical user interfaces (GUI) in programming these controllers have created the premises for the implementation of complex control algorithms.[3,] Early PLCs were able to perform only logical operations, but with the evolution of hardware and software the future of PLCs lies not only in traditional discrete process control, but also in the area of demanding continuous and, particularly, batch processes, which are a combination of continuous and discrete processes. Thus, today a typical PLC-based application deals with several hundreds of analog and digital inputs and outputs, while performing quite complex control procedures.[5] Despite the fact that programmable controllers have become much more sophisticated, functions, like fuzzy logic, are not at all available for micro- PLCs. They are available only for the more advanced and expensive PLCs. For example, PLC manufacturer Siemens provides a software tool named Fuzzy Control++, which allows the user to configure and generate fuzzy systems for Simatic S7-300 and S7-400 PLCs as runtime modules which can be executed on the corresponding target platform.[2] Rockwell Automation offers the FuzzyDesigner option for RSLogix 5000 as an editor for creating custom fuzzy systems to be used by the Logix5000 family of controllers.[8,0] While these tools allow the development of fuzzy systems, they are not compatible with the micro-plcs families produced by the two manufacturers. There is little literature regarding the implementation of fuzzy systems on micro-plcs. However, fuzzy system implementations on Siemens S7-200 micro-plcs have been denoted in [5,9,4]. In [9], the PLC is part of a SCADA system, but the fuzzy algorithm is not computed on the PLC itself, but as a subprogram of SCADA applications. In [5] the fuzzy system is part of a control structure implemented on S7-24 CPU which uses a very small number of rules. In [4] a fuzzy controller is realized on the basis of the more complex Siemens S7-300 PLC and programmed in ladder diagram for a sewage disposal system, and in [] a fuzzy logic system is part of a superblock in Simatic library. This article describes the implementation of a fuzzy system on a Siemens S7-224 PLC with an EM- 235 analog I/O unit. The fuzzy system uses two inputs and one output, triangular shape membership functions and a rule base made of 25 if-then type rules. The structure of the proposed fuzzy system is discussed in section The Fuzzy System A fuzzy system with two antecedent variables and one consequent parameter is assumed. It can be given a set of rules in the form: R n : if x is A i and x 2 is B j then y is U k () 37

2 where n denotes the number of fuzzy rules. The variables x and x 2 denote the two inputs of the fuzzy system and variable y denotes the output. The antecedent variable x is connected to five fuzzy sets A i, and each fuzzy set A i (i=:5) is associated with a membership function ( x ): R [ 0,] that produces a membership degree of the variable x with respect to the fuzzy set A i. The same structure is considered for the second antecedent variable x 2, which is defined over a universe of discourse made of five fuzzy sets B j (j=,5) characterized by their membership function Bj ( x2 ): R [ 0,] and for the consequent variable y which is connected with U k fuzzy sets and their membership function. Figure shows the general structure of the considered fuzzy system. Fig. The Fuzzy System The system in fig. with the rule base () can be described as: y ( x g x g ) y = g f (2) x, 2 x2 where f represents the input-output mapping of the fuzzy system and g x, g x2, g y are the scaling gains of the fuzzy variables. A standard choice for the input mf was considered. That is, five symmetric triangular shape mf were used, overlapping at 50% which uniformly cover the universe of discourse for the input variables. [2,7] Figure 2 shows the design choice for two adjacent membership functions. Fig. 2 Two membership functions in the universe of discourse for the variable x In fig.2 c and c + denote the centers of the two adjacent membership functions. The degree of membership of a crisp value a to fuzzy sets A i and A i+ is computed as follows: [2,7] ( a) + ( a) c+ a = c+ c a c = c c + (3) For the output variable y singleton membership functions were used. With these design choices a rule base made of 25 (=5 2 ) rules results and a maximum of 4 rules can be activated at any given time. The consequences of these rules, and the position of the singletons, are chosen as the sum of the centers of the input membership functions and cover all possible combinations. The resulting fuzzy rules are given as: R n : if x is A i and x 2 is B j then y is c +c Bj (4) The and connective in the rules is implemented by the algebraic product. This means that the strength for the antecedent in rules (4) is given by: = ( a) Bj ( b) (5) The crisp output value is computed using the weighted average as follows: where # rules n= y = # rules n= U U is defined as in (5) and (6) U is the output value for rule n, which is a singleton. The resulting structure of the fuzzy system assures a linear behavior of this system.[2,6,5] 3. The PLC Implementation of the Fuzzy System The linear fuzzy system presented in section 2 was implemented using STEP 7-Micro/Win in ladder programming on a Siemens S7-224 PLC with an EM235 analog I/O module. EM235 is a 4 Input / Output analog extension module with a maximum input / output range of ±0V and 2 bit analog-todigital and digital-to-analog converters.[3] As input variables of the fuzzy system, two bipolar voltages on AIW0 and AIW2 were considered. The resulting crisp value, which is also a voltage, was applied on AQW0. A sampling rate of 00ms was implemented using SMB34 timed interrupt. The associated interrupt service routine was used to collect the input crisp values and to compute the real values of the input voltages. In the main program, on each interrupt, the scaling gains are applied to these voltages, then their degree of membership to the corresponding fuzzy sets are computed using eq. (3). In the end, after applying inference (5) and defuzzification (6) the output crisp value is determined and applied on the analog output channel. Figure 3 shows a flowchart representing the fuzzy system algorithm implemented on the PLC. 38

3 { 20, 5, 0, 5,0,5,0,5,20} U (8) k - the three scaling gains g x, g x2, g y were considered equal to - the rule table expresses rules of the form shown in (4) and is given in Table. Table. Rule table for the Fuzzy System input: x output: y A A 2 A 3 A 4 A 5 B B input: B x 2 B B Fig. 3 The Fuzzy System algorithm For each of the two inputs two arrays are used. The first one is made of 5 double-word variables (5x4Bytes=20Bytes) and contains the centers of the input membership functions, while the second one, having the same size, contains the computed values of the membership functions for a given input. The degree of membership is computed based on equation (3) by knowing the centers of the membership functions and the input value. After performing the fuzzification, the structure of the fuzzy system considered in this paper allows that, at any given time, at most two of the 5 membership function values are not equal to zero. 00 bytes of memory are used for expressing the rule base which is implemented as a look-up table in the V memory of the controller. Each rule is introduced by its consequence, which is a real value, corresponding to the singleton membership function associated to the output variable. Table I summarizes one of the possible rule tables for the fuzzy system. To validate the PLC implementation of the fuzzy system the following structure was considered: - for both of the inputs: 5 symmetric triangular shaped membership functions overlapping at 50% were used and were centered at: c { 0, 5,0,5,0} (7) cbj { 0, 5,0,5,0} - 9 singletons were considered for the output variable and were positioned as follows: The fuzzy system is not limited to the choices mentioned above, regarding the number and position of membership functions (for both input or output), the type of rules and the structure of the rule base. Small changes to the PLC program allow for other fuzzy system structures to be considered. To verify the effectiveness of the PLC fuzzy system design a Matlab model having the same structure was considered and the results of the two models (Matlab and PLC) were compared. Figure 4 shows the Matlab model, which for a given input pair (x, x 2 )=(2.2, 6.3) produces the crisp output y=8.5. Fig. 4 Matlab Implementation of the Fuzzy System The same results are produced by the PLC implementation of the fuzzy system as shown in the Status Chart presented in fig

4 Fig. 5 PLC Implementation of the Fuzzy System. Step 7-Micro/Win Status Chart With the design choices specified above, the total amount of V memory needed for the implementation of the fuzzy system on the PLC is 268Bytes which were used as follows Memory 00Bytes 40Bytes 40Bytes 20Bytes 2Bytes 2Bytes 44Bytes Table 2. Memory usage Usage 25 rules. Each consequence introduced by a floating-point value representing the singleton Centers of the membership functions for both inputs Fuzzification values for both inputs Various pointers needed for indexed addressing of the variables x,x 2 and y crisp values g x, g x2, g y scaling gains Iterators, intermediary results used by the algorithm The execution time of the algorithm is situated between 4 and 2ms. This means that the system can be successfully applied with sampling rates greater than 25ms, which can be achieved using the timed interrupts SMB34 or by other PLC specific means. These results were compared to that of a fuzzy system implemented using FuzzyControl++ on the more advanced S7-300 and S7-400 CPUs taken from [2]. Table 3 summarizes these results. Table 3. Runtime measurements CPU S7-200 S7-300 S7-400 Inputs m.f. 5 each 5 each 5 each Rules Outputs m.f Runtime av. 7.5ms 3.5ms.8ms The execution of fuzzy functions requires computationally intensive operations. The execution speed depends on the performance of the CPU used. However, the results shown in Table 3 are quite satisfactory given the difference in performance between the considered CPUs. 4. Conclusion This paper presented the implementation results of a fuzzy system on a micro-plc. The device used for implementation was Siemens S7-224 PLC with an EM235 analog input/output extension unit. When compared to the more expensive and advanced PLCs the fuzzy system implemented here shows promising results. The accuracy of the implementation is demonstrated by the comparative analysis between the PLC version of the fuzzy system and a Matlab model with the same structure. The implementation of the fuzzy system relied very much on the PLC s capability to perform floating point operations and indirect addressing. Basically, all the components of a fuzzy system require floating point computations. This issue influences directly the necessary amount of memory needed by the fuzzy system implementation, as shown in Table 2. By changing the initialization values for the centers of the input membership functions, the gains and the rule base, in the program s data block, other configurations of fuzzy systems can be obtained. The next step in the development of this system would be the implementation of a Fuzzy Logic Controller. References [] Bogdan, S.; Kovačić, Z.; Krapinec, D. (2007), Sensitivity-based Self-learning Fuzzy Logic Controller as a PLC Super Block, Proceedings of the 5 th Mediterranean Conference on Control & Automation [2] Brehm, Thomas; Rattan, Kuldip (995) A classical controller: a special case of the fuzzy logic controller, Fuzzy logic and intelligent systems, Kluwer Academic Publishers 320

5 [3] Bryan, L.A.; Bryan, E.A. (2003), Programmable Controllers: Theory and Implementation, 2 nd ed., Amer Technical Pub [4] Kang Sun; Yan-min Song; Guo-chuan Feng (2009), The Application of the Fuzzy Controller Based on PLC in Sewage Disposal System, Proceedings of the 2009 International Conference on Artificial Intelligence and Computational Intelligence, Vol. 02, pp [5] Karasakal, Onur; Yeşil, Engin, Guzelkaya, Mujde; Eksin, Ibrahim (2005), Implementation of a New Self-Tuning Fuzzy PID Controller on PLC, Turkish Journal of Electrical Engineering & Computer Sciences, Vol.3, No.2, pp [6] George K. I. Mann; Bao-Gang Hu (999), Analysis of Direct Action Fuzzy PID Controller Structures, IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, Vol. 29, No. 3, p [7] B.M. Mohan, Arpita Sinha (2006), The simplest fuzzy PID controllers: mathematical models and stability analysis, Soft Computing no. 0, pp , Springer Verlag [8] Neamţu, O. (2008), Motion Control with Fuzzy Logic in an High Speed PLC System, Journal of Electrical and Electronics Engineering, pp [9] Nikolić, Vlastimir; Ćojbašić, Žarko; Ćirić, Ivan; Petrović, Emina (200), Intelligent Decision Making In Wastewater Treatment Plant Scada System, Automatic Control and Robotics Vol. 9, No, pp [0] Rockwell Automation Inc. (2007), RSLogix 5000 Fuzzy Designer [] Nordin Saad; M. Arrofiq (202), A PLC-based modified-fuzzy controller for PWM-driven induction motor drive with constant V/Hz ratio control, Journal Robotics and Computer- Integrated Manufacturing, Vol. 28 Issue 2, pp. 95-2, Pergamon Press, Inc. [2] Siemens AG (2003), FuzzyControl++ User s Manual [3] Siemens AG (2008), SIMATIC S7-200 Programmable Controller System Manual [4] Yanmin Song, Zhongwei Bi, Kun Liu (2007), The PLC System of Egg Powder Treatment Based on Fuzzy Control Algorithm, Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007), Vol.4, pp [5] Hao Ying (2005), Conditions for analytically determining general fuzzy controllers of Mamdani type to be nonlinear, piecewise linear or linear, Soft Computing, no. 9, pp , Springer Verlag 32