Programmable Membership Function Circuits Using Analog MOS Technology

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Programmable Membership Function Circuits Using Analog MOS Technology

    Reconfigurable Analog Fuzzy Controller Design

    Part 1: Fuzzifier Circuit

     12 Faizal A. Samman , Rhiza S. Sadjad

    Department of Electrical Engineering Hasanuddin University

    Jl. Perintis Kemerdekaan Km. 10 Makassar 90245 12E-mail: ,

    Abstract Reconfigurable membership function circuit using MOS analog electronics is

    presented in this paper. Fuzzification circuit, which is also called membership function circuit,

    is very important in fuzzy logic controller circuit. It has function to fuzzify or convert a crisp

    input into fuzzy input based on membership function of fuzzy linguistic term related to the input.

    This paper proposes fuzzification circuit, which can be reconfigured in term of its membership

    form, as well as its membership location in universe of discourse of the input voltage domain.

    Those main features result in flexible membership function circuit and place the circuit

    functions in wider application areas. This paper is the branch of the project to design analog

    fuzzy logic controller chip resembling standard-cell-like technique as in digital design

    technology, where membership function circuit is one of the important cells in the chip.

    Keywords: Fuzzy logic circuit, Fuzzification circuit, electronic design, circuit simulation.

    topics in this paper) will be presented. Both input1 and 1. INTRODUCTION

     input2 have three membership functions. The basic Fuzzy Logic Controller (FLC) as one of the theory of the topics such as fuzzy sets, fuzzy terms, and intelligent control systems has been extensively used in membership function will be briefly described.

    some electronic equipment such as in air conditioner,

    vacuum cleaner, rice cooker, washing machine, and as 1.1. Fuzzy Sets

    automatic transmission controller and cruise control in

    automotive. FLC has also intensively applied in process In classical set theory, which is based on bivalent control system both in evaporation control and logic, a number or object is either a member of a set or distillation control. FLC applications in chemical not. For example, an object is either big or small. In process are for examples in sterilizing process of CPO theoretic terms, it says that the same object cannot (crude palm oil) production, pH control in simultaneously be a member of a set and its

    pharmaceutical production, food processing, and so on. complement. With fuzzy set theory, an object can be a Even fuzzy controller is suitable to handle chemical member of multiple sets with a different membership process control with multiple distillation columns. degree of membership in each set. It might be able to In industrial practices, fuzzy logic is used especially allow the same object be considered “big” to some in the systems that have complicated mathematical degree and be considered “small” to another degree. model even in the system whose model is extremely The degree of membership of an object in a fuzzy set difficult to be derived. As an alternative and non-expresses the degree of compatibility of the object with conventional control system, fuzzy logic controller the linguistic term represented by the fuzzy set

    emerges not to replace or eliminate all conventional

    control system. Sometimes fuzzy controller is used to 1.2. Fuzzy Linguistic Term

    complement an existing PID controller, where FLC

    control the parameters of the PID controller, or A linguistic term is characterized by its term set. The supervised PI, PD or PID control action signals. This linguistic term weight can be defined by the term set T experiment has been investigated in reference [8]. This in the following way: T(weight)={heavy, medium,

    paper is part 1 of three parts. Part 2 will discuss light}. T(weight) denotes the term set of weight, that is, reconfigurable fuzzy inference circuit, and part 3 will the set of names of linguistic values of weight, with discuss defuzzifier circuit. In this paper, fuzzifier circuit each value being a fuzzy variable, ranging over a for FLC architecture of two-input one output (discussed universe of discourse.

Three to seven terms are often appropriate to cover a 2. Fuzzy inference mechanism circuit.

    linguistic term. Rarely, one uses less than three terms, 3. Defuzzification circuit.

    since most concepts in human language consider at least

    the two extremes and the middle in between them. On In this part 1 of the paper, we will mainly concern the other side, one rarely uses more than seven terms with membership function circuit (MFC) or because humans interpret technical figures using their fuzzification circuit. Before fuzzy inference process is short-term memory. The human short-term memory can undertaken, signals from sensor devices in crisp values only compute up to seven symbols at a time. Another are fuzzified by MFC to be fuzzy values. The fuzzy observation is that most linguistic variables have an odd values are taken from the grade values related to any number of terms. This is due to the fact that most membership form of the crisp inputs. The understanding linguistic terms are defined symmetrically, and one term of fuzzy sets is basic knowledge to surf the fuzzy logic describes the middle between the extremes. Hence, most theory. Reference [1] and [4] give basic explanations of fuzzy logic systems use 3, 5, or 7 terms. fuzzy sets and fuzzy logic theory. Figure 1 shows fuzzy Fuzzy linguistic terms can be of several types: sets or membership function of the input terms, and it

    also shows how fuzzified inputs are calculated from its fuzzy predicates, such as heavy, large, old, small,

    related membership forms. medium, normal, expensive, near, smart, and the like;

    Input 1 has three membership functions called low, fuzzy truth values, such as true, false, fairly true, or

    med and high. And Input 2 also has three membership somewhat true;

    functions called slow, med and fast. The form and the fuzzy probabilities, such as likely, unlikely, very number membership functions can be freely specified likely, or extremely unlikely; by the user/designer. However, the emerging of fuzzy quantifiers, such as many, few, most, or all. adaptive neuro-fuzzy system makes the membership forms of the FLC are specified by itself through training 1.3. Membership Function and The Fuzzification the input-output data of system/plant to be controlled. For a continuous variable, the degree of membership

     (u)is expressed by a function called membership function. IN 1

    The fuzzy concept (or linguistic term) “level” is LowMedHighrepresented by the fuzzy sets (or terms) “low”, 1.0“medium” and “high”. And The fuzzy concept (or (In1) Medlinguistic term) “speed” is represented by the fuzzy sets

    (or terms) “slow”, “medium” and “fast”. The (In1) Lowmembership functions of the terms of level and speed (In1) Highare represented in figure 1(a) and 1(b) respectively. The

    In1functions show the degree of membership with which a person belongs to the fuzzy sets low, medium, high, (a) slow and fast. The membership function Low assigns to (v)IN 2 each element, x (Input 1), of the universal set X, a

    number, (x), which characterizes the degree of lowSlowMedFast1.0membership of the element in the fuzzy set Low, as in

    equation (1). (In2) Fast (In2) Med (1) ,:;;Lowx,xx|XLOW (In2) Slow In2The degree of membership in a normal set is based on a scale from 0 to 1, with 1 being complete (b)

    membership and 0 being no membership. At 80 km/s

    speed and below, a vehicle does not belong to the class Fig.1. Fuzzification processes for each fuzzy term of fast. At 150 km/s and above, a vehicle speed fully input 1 and input 2.

    belongs to the class fast. Between 80 km/s and 150 km/s

    the membership increases linearly between 0 and 1. The For every one crisp signal of the input 1 in the membership function is not limited to values between 0 universe of discourse, the MFC will give three fuzzified and 1. values in accordance with the three membership

     function forms. This process is also valid for input 2. As

    2. MEMBERSHIP FUNCTION CIRCUIT shown in figure 1, MFC will give (In1), (In1) lowmed and (In1) for input 1, and (In2), (In2) and highslowmedIn general, Fuzzy logic controller hardware consists (In2) for input 2. Thus fuzzy logic controller fastof three main components: architecture as shown in figure 2, the MFCs will feed 1. Membership function circuits, or fuzzifier six fuzzified inputs (MFC outputs) to nine minimum components. operation circuit of the fuzzy inference circuit, three

signals from input 1 and three signals from input 2. Based on figure 3, parameter T or the half-length of

    Each one signal from MFC output will be fed together membership slope is determined by following equation:

    with one from another MFC to two-input min circuit.

     2IssT,ProgrammableProgrammablej(AntecedentsRules Switchingj

    th (1) jdiffrensialpairjMFCMinβconductanceparameterofNMOSIN 1Min MFCIf triangular function is preferred then following Minequation must be fulfilled MFC Min

    VrefTVrefT,ProgrammableMaximum matriks crcuit1122 (2) AntecedentsMinifTTT,VrefVref2T.1221Min MFCIf trapezoidal function is preferred then following MinIN 2Maximum Column Circuitequation must be met. MFC MinMaximum Column CircuitVrefTVrefT,1122 (3) MFCMinMaximum Column CircuitifTTT,VrefVref2T.1221OUT Maximum Column CircuitIf Z-form function is preferred then I=0, and if S-SS1Maximum Column Circuitform function is required then I=0. SS2

    The circuit shown in figure 4(a) has output range Defuzzifier Circuit

    between 4 to 5 volts. Therefore, two-stage level shifter Sub circuitcircuit as in figure 4(b) is coupled to the output of MFC

    circuit. Thus the result will give MFC that gives ideal ProgrammableSub circuitConsequencesrange of membership grade, i.e. the output with range between 0 to 1 volts. Sub circuit Fig.2. The architecture of the proposed programmable Sub circuitanalog fuzzy logic controller, colored/in dashed

    line box components are the scope of this paper. Sub circuit

    Figure 3 shows the general criteria for membership form. There are four membership types and they have their own criteria. The four membership forms are S-form, Z-form, trapezoidal and triangle form. MFC is constructed by two-pair differential amplifier configuration coupled with two-stage level shifter circuit.



    Membership GradeT1T2



    Inputs’ Universe of Discourse (b) Fig.3. General criteria for the shape of the membership-Fig.4. (a) Two-differential amp pair of MFC schematic, function circuit. (b) two-stage level shifter circuit.

    Figure 7(a) shows the triangular membership 3. SIMULATION RESULTS

    function forms with different slopes. The inner curve

    In this section, the simulation results of the MFC shows membership function with transconductance 2will be described. Figure 5(a) and 5(b) exhibits , as well as V=2.4 V and parameter (=0.00003 A/Vref1triangular and trapezoidal membership function forms V=3.6 V. And the outer curve shows another form ref22with different slope references performed by the MFC. with transconductance parameter (=0.00001 A/V, as The trapezoidal form is obtained by setting Vref1 well as V=2 V and V=4 V. ref1ref2somewhat further than V. And the triangular form is ref2Figure 7(b) shows the S-forms with different slopes, obtained by setting Vquite close to V. However, ref1 ref2but they have the same reference voltages, i.e.V=2 V. ref1criteria as in (2) and (3) must be concerned. Figure 7(c) shows Z-forms with different slope, but they

     have the same reference voltages, i.e.V=3 V. ref2

     (a) (a)

     (b) (b) Fig.5. (a) The triangular and (b) trapezoidal forms.

Figure 6 shows the S-form and the Z-form

    membership function respectively with different

    reference voltages. The S-form is obtained by setting

    I=0, thus differential pair 1 does not work, and V=2 ss1ref2

    V (left-side curve) and V=3 V (right-side curve). And ref2

    the Z-form is obtained by setting I=0, thus the ss2 differential pair 2 does not work, and V=2 (left-side (c) ref1curve) and V=3 V (right-side curve). ref1

     Fig.7. (a) Triangular forms (b) S-form, and (c) Z-form

    membership function with different slopes.


    Membership function circuit (MFC) proposed in this

    manuscript comprises two-pair of differential amplifier

    configuration with its output is coupled with two-stage level shifter configuration, thus it gives ideal (a) membership function output range between 0 to 1 volt.

    The MFC can be programmed or reconfigured by

    sending external signals to the MFC, which adjusting its

    membership function type, membership center location

    in the universe of discourse and the slope of the

    membership function form.

    Because of using metal oxide silicon (MOS) transistors and less-resistor, the MFC is suitable to be (b) implemented in an IC (integrated circuit). The MFC also utilize small number of MOS, thus the full-costume Fig.6. (a) S-form and (b) Z-form membership function. IC design technique is of a little problem. Full-costume

    IC design gives high performance IC product. The

    circuit layout is not presented in this paper, for readers who familiar with IC layout will not have problem to design and simulate it layout results. Then comparing the results with ones presented in section 3 of this paper. The study and analysis about power consumption and the processing speed of the circuit is not presented. The quantitative and qualitative analysis about both performances is important and open to the following researches of this paper.


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