|Publication number||US5918221 A|
|Application number||US 08/638,370|
|Publication date||Jun 29, 1999|
|Filing date||Apr 26, 1996|
|Priority date||Apr 28, 1995|
|Also published as||DE69522313D1, DE69522313T2, EP0740260A1, EP0740260B1|
|Publication number||08638370, 638370, US 5918221 A, US 5918221A, US-A-5918221, US5918221 A, US5918221A|
|Inventors||Nicolo Manaresi, Eleonora Franchi, Dario Bruno, Rinaldo Poluzzi|
|Original Assignee||Stmicroelectronics, S.R.L.|
|Export Citation||BiBTeX, EndNote, RefMan|
|Patent Citations (28), Non-Patent Citations (14), Referenced by (3), Classifications (6), Legal Events (4)|
|External Links: USPTO, USPTO Assignment, Espacenet|
This invention relates to an analog processor, and in particular to a fuzzy logic analog processor.
In recent years, the analog processing of signals has grown in importance, especially with the advent of neural networks and fuzzy logic, and many attempts have been made, with varying degrees of success, at implementing and integrating processors which could carry out such processing.
Among the different problems posed by the making of processors which can perform well and, therefore, be of real commercial value, are the need for the processing to be unaffected by changes in temperature and variations in process parameters, and the programmability of the type of processing as identified by the values of processing coefficients.
The former problem has already been addressed, for example, by M. Sasaki and F. Ueno in an article "A Novel Implementation of Fuzzy Logic Controller Using New Meet Operation", Proceedings of the Third IEEE International Conference on Fuzzy Systems, Jun. 26-29, 1994, pages 1676-1681. The solution proposed there is based on the use of two independent reference signals, namely a current signal and a voltage signal. This is not easy to implement in any reliable manner if high performance is sought; the problem of programmability, moreover, is not addressed, nor is that of how to compensate for variations in the processing coefficients.
The latter problem has already been addressed, for example, by J. W. Fattaruso, S. S. Mahant-Shetti and J. Brock Barton in an article "A Fuzzy Logic Inference Processor", IEEE Journal of Solid-State Circuits, Vol. 29, No. 4, April 1994. This approach involves the use of at least one memory of the RAM type in which several processing coefficients are programmed by a "master" digital processor in digital form, as well as of various digital-to-analog converters. If a processor is to process analog input signals analogically and to output analog signals, storing the coefficients in digital form does not seem to be the natural and more convenient choice.
It is an object of this invention to provide an analog processor which can perform high-quality processings, unaffected by operating temperature and process parameters, in a reliable manner using fairly simple circuitry.
To provide unaffected performance as indicated, the processor according to one aspect of this invention is implemented and integrated with transistors of the MOS type, has voltage inputs and outputs, and includes a biasing section which supplies voltage bias signals of which at least one is substantially the combination of a voltage proportional to the threshold voltage of the MOS transistors and a reference voltage.
This reference voltage can be obtained from a reference potential which is stable to temperature and process parameters, such as the voltage generated by a bandgap type of generator.
A noteworthy feature of the processor according to the invention is the linearity of its input-output characteristic with respect to the reference voltage. This suggests that it may be advantageous to extract the reference voltage by division from a signal indicating how wide the range of variation of the input signals may be, to thereby achieve compensation for or independence of variations in this range.
The invention can be more clearly appreciated from the following description, to be taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a block diagram of an analog processor according to one aspect of the invention;
FIG. 2 is a block diagram of the processing section of the processor of FIG. 1;
FIG. 3 is a circuit diagram of the fuzzyfier circuit and the evaluation circuit of the processing section shown in FIG. 2;
FIG. 4 is a circuit diagram of the defuzzyfier circuit of the processing section shown in FIG. 2;
FIG. 5 is a block diagram of the storage section of the processor shown in FIG. 1;
FIG. 6 is a circuit diagram of the power supply section for the processor in FIG. 1;
FIG. 7 is a circuit diagram of the biasing section of the processor in FIG. 1;
FIG. 8 illustrates a membership function as determined by various programming signals;
FIG. 9 illustrates the processing carried out by the fuzzyfier circuits and evaluation circuits according to programming parameters stored in the storage section of the processor in FIG. 1; and
FIG. 10 is a graph of an output of the processor of FIG. 2.
The term "coupling" will be used hereinafter to comprehensively indicate a direct coupling, or an indirect coupling (i.e. one established with the intermediary of circuit elements).
In FIG. 1, the architecture of this analog processor FUZ of the fuzzy type is shown to include a set AI of analog voltage inputs and a set AO of analog voltage outputs, and comprises: an analog processing section PROC connected to the inputs AI and the outputs AO; a storage section MEM which is connected to the section PROC to transfer programming signals PP and to control its operation; and a biasing section BIAS which is connected to the section PROC to transfer bias signals VG and to enable it to operate. It will be appreciated that the section MEM would become unnecessary where no programmability of the processor FUZ is sought, and that the degree of complexity of the section BIAS would vary with the level of its expected performance.
It is understood that digital-to-analog converters are provided upstream and analog-to-digital converters are provided downstream from the processor FUZ, if digital signals are to be received and generated.
The processor FUZ further comprises a power supply section AL connected to the section MEM to transfer supply signals VI for selective storage thereinto.
The processor FUZ may additionally include a voltage generator BG, specifically of the bandgap type, which would be connected to the section BIAS and the section AL in a suitable way to have them supplied with a stable reference potential VBG which is unaffected by temperature and the processor integration process. Any well-known bandgap circuit may be used. While many bandgap circuits are based on bipolar technology, those based on MOS technology may also be used. One such MOS technology based bandgap circuit is described in "A CMOS Bandgap Reference for Differential Signal Processing" by G. Nicollini and D. Senderowicz in IEEE Journal of Solid-State Circuits, Vol. 26, No. 1, January, 1991, pages 41-42. Alternatively, the potential VBG could be provided by external circuitry of the processor FUZ, or be extracted by division from a supply potential VDD, as more clearly explained hereinafter.
Processors of this type can be integrated and implemented to advantage with transistors of the MOS type. More complicated fabrication methods are available which admit of integration of both MOS and BJT transistors, so that such circuits may also include junction transistors, if necessary. A major advantage of integration is that transistors of one type can have similar performance and their characteristics determined by an area factor.
It will be appreciated that the architecture shown in FIG. 1 is a universal one which could also be used with other types of analog processors.
Illustrated in greater detail by FIG. 2 is the architecture of the section PROC shown in FIG. 1 for the specific instance of the set AI consisting of first and second analog voltage inputs, I1 and I2, and the set AO consisting of a single analog voltage output, OUT.
A fuzzy processor, and precisely the analog processing section PROC, can usually process a plurality of rules (numbered 0 to N), and in any case at least one rule. The diagram of FIG. 2 shows one horizontal circuit block for each rule, and for simplicity, only the first and last rule blocks have been respectively indicated. These rule blocks are connected together in parallel, both input- and output-wise. Where two outputs are provided, a first set of rule blocks would have their outputs connected together in parallel and to a first of such outputs, and a second set of rule blocks have their outputs paralleled and connected to the second of such outputs. The construction of just one rule block will, therefore, be described hereinafter. The rule block for fuzzy logic rule 0 in FIG. 2 comprises a pair of membership function or fuzzyfier circuits MF and one complement or evaluation circuit RE which process the antecedent part of rule 0, and a defuzzyfier circuit OTA which processes the consequent part of rule 0. As will become apparent from the discussion of circuits that follows, the output of the rule block is responsive to the threshold voltage of the MOS transistors, the bias signals VG, temperature and the integration process parameters.
In general, for each input of the set AI there is provided a corresponding fuzzyfier or membership function circuit MF, input-wise connected thereto and effective to output an electric signal which depends on the value of a corresponding membership function of the fuzzy type. Thus, in the particular instance of a single input, there will be a single circuit MF provided for each rule block.
The circuit MF can be input programming signals PP which establish the shape of the membership function. It is fairly common practice to select membership functions of trapezoidal shape. In this case, the programming parameters can determine the locations of the trapezoid corners.
The membership function is of such a type that, for each value of the electric signal input to the circuit MF, a single value of the electric signal is output from the circuit MF.
For each block, an evaluation or complement circuit RE is provided which has inputs connected to the outputs of the rule block circuits MF and is effective to output an electric signal which is tied to the truth level of the corresponding rule.
Finally, for each block, a defuzzyfier circuit OTA is provided which has a control input IG connected to the output of the circuit RE and an output 0 connected to the output OUT. This defuzzyfier OTA has a first signal input LS receiving one of programming signals PP and a second signal input LD which is coupled to its output 0. The signal PP supplied to the input LS determines the weight of the rule evaluated within the rule block relative to the output.
FIG. 2 illustrates diagrammatically the fact that the biasing section BIAS supplies the bias signals VG in particular to the circuits MF and RE. As shown in FIG. 2, the outputs of all defuzzyfier circuits are connected together to define an output node OUT. The symbol AI stands for Analog Input and corresponds to a set of inputs for respective analog signals and symbol AO stands for Analog Output and corresponds to a set of outputs for respective analog signals; in FIG. 2 symbol AO is associated to a big arrow to which a number of electrical connections arrive but only two are depicted; all the single outputs of the "N" Operational Transconductance Amplifiers OTA are electrically connected together to the same single electrical connection; other electrical connections may arrive from other sets of OTA not depicted in FIG. 3.
FIG. 3 shows a circuit diagram of the fuzzyfier circuit MF and the evaluation circuit RE associated with the first rule block.
The circuit MF comprises two substantially identical (but for mismatch of the circuit elements) differential transconductor circuits, each consisting of two N-channel input MOS transistors having source terminals connected to each other and to a current generator, control terminals connected to the differential inputs, and one drain terminal connected to a supply potential VDD, the other drain terminal being connected to the output of the transconductor circuit. The current generator consists of two N-channel MOS transistors having main conduction paths connected in series between a ground potential GND and the source terminals of the input transistors. By having two MOS transistors connected in series, a current generator can be provided which has a very high output resistance, when one of the transistors is operated within the linear range and the other operated within the saturation range.
The first analog input I1 is connected to a first voltage differential input of both transconductor circuits. The second voltage differential inputs of the transconductor circuits receive, respectively, a first programming voltage signal PP-0 and a second programming voltage signal PP-1 from the section MEM, the value of the two programming signals determining the horizontal location of the midpoint of each oblique side of the trapezoid corresponding to the membership function. In principle, the section MEM is to generate two programming signals PP for each circuit MF contained in the processor FUZ.
The control terminals of the current generator transistors respectively receive a first bias voltage signal VG-2 and second bias voltage signal VG-1 from the section BIAS. The value of the first signal VG-2 determines the current of the current generator, that is the transconductor circuit bias current that corresponds to the height of the trapezoid, while the value of the second signal VG-1 should be adequate to hold the associated transistor at saturation. In principle, it will be sufficient that the section BIAS only generates two signals VG for all the circuits MF of the processor FUZ. Furthermore, where the output resistance is no parameter of interest, a single MOS transistor, and hence a single signal VG, would suffice. However, different signals VG may be provided for different rule block circuits MF, if desired.
The current outputs of the two transconductor circuits are connected together and to the output of the circuit MF, and are selected to be complementary of each other, that is, not on the homologous side. Thus, when the voltage at the input I1 is lower or higher than the voltage of both signals PP-0 and PP-1, the current output to the circuit MF will be the same as the current generated by the current generator.
FIG. 3 shows a second circuit MF, identical to the first, which is connected to the input I2 and is input two additional programming signals, PP-3 and PP-4.
The outputs of the two circuits MF are input to the circuit RE.
The circuit RE basically comprises a transistor G-0 of the MOS type. In the circuit of FIG. 3, the transistor G-0 is a P-channel type and has its source terminal connected to the supply potential VDD and its drain terminal connected to a summing node SN. The node SN is connected to the circuits MF.
The control terminal of the transistor G-0 receives a bias voltage signal VG-0 from the section BIAS. The value of the signal VG-0 should be such that the current generated by the transistor G-0 at saturation is slightly less than the current generated by the current generators of the transconductor circuits of the circuits MF; a factor of 0.8 would undoubtedly provide a safe margin.
The node SN is connected to the output of the circuit RE via a diode D-0 which is used as a unidirectional conduction circuit element. This may be implemented, for example, by a diode-connected transistor of the MOS type. A current will appear at the circuit RE output which has a non-zero value equal to that of the current generated by the transistor G-0, when all the output currents of the circuit MF are zero, i.e. all of the conditions for membership are met.
In principle, it will be sufficient for the section BIAS to only generate one signal VG-0 for all the circuits RE of the processor FUZ. If desired, however, different signals VG-0 may be provided for different rule block circuits RE.
Shown in FIG. 4 is a circuit diagram of the defuzzyfier circuit OTA associated with the first rule block.
This basically comprises a transconductance operational amplifier and includes a current output O-0, a first signal voltage input LS-0, a second signal voltage input LD-0, and a control current input IG-0. The input IG-0 is connected to the output of the circuit RE, the input LD-0 is connected to the output O-0, and the input LS-0 receives a programming signal PP-2 from the section MEM. The value of the signal P-2 determines the weight of the rule evaluated within the rule block relative to the output.
The transconductance operational amplifier comprises two input transistors of the N-channel MOS type which have control terminals respectively connected to the inputs LS-0 and LD-0. These transistors are connected to a load consisting of a first current mirror locked up to the supply potential VDD, and are biased by a second current mirror locked up to the ground potential GND. The output of the second current mirror is then connected to the input transistors, and its input connected to the input IG-0.
In the present embodiment, all of the plural outputs O-0, . . . , O-N are connected together and to the single output OUT of the processor FUZ. The potential which develops at the output OUT will be of such value that the sum of the currents generated and drawn by the circuits OTA of the various rule blocks is nil. Accordingly, it will be necessary for that output OUT to be connected to a high-impedance load, or alternatively, that an output buffer be used.
FIG. 5 is a block diagram of the storage section MEM.
This section MEM has a plurality of inputs which receive supply voltage signals, denoted by VI-0, . . . , VI-K, and a plurality of outputs to generate programming voltage signals, denoted by PP-0, . . . , PP-L, and is effective to supply, in connection with information stored therein, one of the signals VI to each output. The number of the signals VI and the signals PP is quite variable and dependent on the individual application, being of one as a minimum.
The section MEM comprises a plurality of controlled switches SW-00, . . . , SW-LK, equal in number to the product of the number of signals VI and signals PP. These switches are implemented, for example, by transistors of the MOS type. The section MEM further comprises a corresponding plurality of storage elements E-00, . . . , E-LK having outputs respectively connected to the control terminals of the switches SW. In FIG. 5, both the switches SW and the elements E are arranged into a logical and preferably physical matrix having an equal number of columns to the inputs and equal number of rows to the outputs.
According to the contents of the storage elements E, some of the switches SW will be closed and some open.
Each switch is connected on one side to an input and on the other side to an output, so that when closed, the input signal can be transferred to the output. Proper operation requires that one switch only in each row be closed, whereas several switches may be closed at one time in each column.
Assuming K+1 different values for the supply voltage signals VI, the programming signals PP will take one of the K+1 values in accord with the contents of the elements E.
It would be possible for the elements E to be simple links to either the supply potential VDD or the ground potential GND.
In a still simpler way, the aggregate of a switch SW and an element E could consist of a direct link between an input and an output. Thus, the section MEM would be made up of a first set of leads for the columns and a second set of leads for the rows, as well as of connection contacts between the rows and the columns at locations dependent on the type of processing sought by the processor FUZ.
Alternatively, the elements E may comprise flip-flops of the D type, connected together into at least one shift register; in this way, storing contents into the elements E through simple control circuitry and a minimum number of terminals (for the processor) becomes a straightforward matter. One shift register may be provided for each row, so that the value of one signal PP at a time can be modified.
In a further alternative, the elements E could be memory cells connected into a matrix; in this way, the circuit complexity of the elements E would be alleviated, but at the expense of increased complexity of the control circuitry for the address, write and, possibly, read functions, and of an increased number of terminals (for the processor).
A compromise between the two alternatives just described consists of using memory cells connected into a matrix and address circuitry including one or more counters so as to simulate in part a shift register by means of the matrix.
FIG. 6 is a circuit diagram of the power supply section AL.
This section AL comprises a voltage divider formed of a plurality of resistors R-0, . . . , R-K which have a corresponding plurality of intermediate taps from which supply voltage signals VI-0, . . . , VI-K can be output.
The voltage divider is connected on one side to the ground potential GND and on the other side to the output of a first current mirror locked up to the supply voltage VDD.
The input of the first current mirror is driven by the drain terminal of a transistor DR of the N-channel MOS type which has its source terminal connected to the ground potential GND.
The section AL further comprises a comparator consisting of a second current mirror locked up to the supply voltage VDD and connected to ground via two input transistors of the N-channel MOS type. The control terminal of one of the two input transistors receives the reference potential VBG, while the control terminal of the other is connected to an intermediate tap of the divider and, in the specific instance of FIG. 6, receives the supply voltage signal VI-0. A comparator such as this ensures that, in steady state operation, the corresponding potentials to its two inputs be the same.
A feedback loop is then formed by connecting the control terminal of the transistor DR to the output of the second current mirror of the comparator, whose operation will not, therefore, be significantly altered by virtue of the low drain from the transistor DR.
If the drain of current at the outputs of the section AL is negligible compared to the current flowing through the divider (an easily met condition because the load on such outputs is formed by gating currents of MOS transistors), then the current at the mirror output is given by the ratio of the reference potential VBG to the resistance of the resistor R-0. Thus, the values of the signals VI are easily calculated and quite stable because they are dependent on a resistance ratio; in general, they will be selected equispaced from the ground potential GND and the supply potential VDD.
FIG. 7 shows a circuit diagram of the biasing section BIAS.
The bias circuit section BIAS receives the reference potential VBG as input and outputs the bias signals VG for the section PROC. As shown in FIG. 7, three bias signals are generated, VG-0, VG-1, VG-2, and the section BIAS is preferably only formed of transistors of the MOS type. The three bias signals are used to bias the current generators of the membership function circuits MF and the complement circuits RE as described in more detail below.
The section BIAS includes an N-channel transistor N8 which receives the potential VBG on its control terminal, and has its source terminal connected to the ground potential GND and its drain terminal connected to the input of a first current mirror formed of two P-channel transistors P9 and P10 and being locked up to the potential VDD. The output of this first current mirror is connected to the control terminal of an N-channel transistor N6 and to the drain terminal of an N-channel transistor N7 having its source terminal connected to the potential GND. The source terminal of the transistor N6 is connected to the control terminal of the transistor N7 and to the source terminal of a P-channel transistor P8 having control and drain terminals connected together and to the potential GND, and a substrate terminal connected to the source terminal to prevent any body effect. The drain terminal of the transistor N6 is connected to the input of a second current mirror formed of two P-channel transistors P3 and P4 and being locked up to the potential VDD. The output of this second mirror is connected to the source and substrate terminals of a P-channel transistor P7 having its drain terminal connected to the potential GND. The output of the second mirror is also connected to the control terminal of an N-channel transistor N5 having its source terminal connected to the potential GND. The control terminal of the transistor P7 is connected to the control terminals of an N-channel transistor N4 having its source terminal connected to the potential GND and of an N-channel transistor N2 having its source terminal connected to the potential GND. The drain terminal of the transistor N5 is connected to the input of a third current mirror with a double output which is formed of P-channel transistors P2, P5, P6 and locked up to the potential VDD; a first output of this third mirror is connected to the drain and control terminals of the transistor N4, and the second output of this third mirror is connected to the drain and control terminals of an N-channel transistor N3 having its source terminal connected to the potential GND. The control terminal of the transistor N3 is connected to the control terminal of an N-channel transistor N1 having its source terminal connected to the drain terminal of the transistor N2. The drain terminal of the transistor N1 is connected to the drain and control terminals of a P-channel transistor P1 having its source terminal connected to the potential VDD.
The signals VG-0, VG-1, VG-2 correspond to the potential (as related to the potential GND) of the control terminals of the transistors P1, N1, N2, respectively.
The signal VG-2 determines the bias current of the differential transconductor circuits of the circuits MF, and has a value substantially equal to the sum of a first voltage proportional to the potential VBG and a second voltage proportional to the threshold voltage of the N-channel MOS transistors.
The value of the signal VG-1 is of no great importance, provided that it can, under all conditions, hold the transistors it is driving within their saturation range.
Relatively unimportant is also the value of the signal VG-0; in fact, a consideration of the transistor P1 and the transistors G-0, . . . , G-N of the various circuits RE reveals that these form N current mirrors all of which are input the same current, i.e. the current which is flowing through the two transistors N1 and N2. Thus, the important proportional relationship between the current of the two differential transconductor circuits of the circuits MF and the current of the MOS transistor of the circuit RE will be ensured by the fact that the signals VG-1 and VG-2 are supplied both to the control terminals of the transistors N1, N2 and to the control terminals of the transistors which make up the current generators of the differential transconductor circuits.
The processor FUZ just described has an input-output characteristic which is compensated for temperature and absolute variations in the process parameters, this being achieved by the use of a single reference signal, namely the reference potential VBG.
This may be justified by the inputs AI and outputs AO being adapted to handle voltage signals; furthermore, the programming signals PP and bias signals VG also are voltage signals.
In addition, the fact that the inputs AI and outputs AO handle voltages makes for easier cascade interconnection of several processors.
That the reference signal must be a voltage one is an advantage because stable potentials are much easier to generate than stable currents.
It will be appreciated that, for the purpose of providing compensation, it is necessary that the membership function "breakdown" points (in the example shown, the corners of the trapezoid) be kept at fixed points of the input range.
It will be apparent, therefore, that if the input voltage values at which the rules become active are not constant, variations are bound to occur in the input-output characteristic of the processor.
In the example shown, for this condition to be met, it is necessary that the bias current for the transconductor circuits of the circuit MF be steadily proportional to the common factor k' of the N-channel MOS transistors, and that the current generated by the P-channel MOS transistor of the circuit RE be steadily proportional, i.e. tied by a steady factor of proportionality, to that bias current. Furthermore, this factor should be less than unity.
With this bias current being generated by a transistor of the N-channel MOS type, the voltage VGS of that transistor is required to be proportional to the sum of a voltage which is stable from all aspects, such as the voltage at the output of a bandgap generator, and a voltage proportional to its threshold voltage.
Where programmability of the processor is sought, it is further necessary that the programming voltage signals be also stable from all aspects, if the input-output characteristic is to be compensated. This can be achieved by extracting such signals from the output of a bandgap type of generator.
A highly interesting feature of this processor is that, if a supply potential VDD (which usually is not stable) is used to generate the reference potential VBG and passed to a voltage divider (e.g., a resistive one in view of the division ratio being eminently controllable and constant), the input-output characteristic would closely retain its shape as the supply potential varies. Where the input signals and output signals are to be tied to the supply potential, the absolute variations would be null relative variations; this is, in fact, no rare occurrence.
More generally, if a signal is provided which indicates the width of the variation range of the input signals, and which varies linearly with that width, then the signal can be used to generate the potential VBG which controls in a linear fashion the "size" of the input-output characteristic of the processor, and as a result, the width of the variation range of the output signals as well. Thus, a processor can be provided which is compensated for such variations in width.
One example will now be given to illustrate the inventive concept; this is for illustration only and not to limit the scope of the invention. With reference to FIG. 2, I1 and I2 are voltage signals linked in general to inputs AI (e.g., A1 and A2) by way of an operation of shifting and bufferization and therefore may vary with continuity within a certain range. In this example, inputs AI vary between 0 volt and 2 volt, signals II between 1.8 volt and 3.8 volt. IG-N are current outputs of the blocks RE each evaluating the antecedent part of a different rule.
The processing carried out by these blocks is shown in FIG. 9; the output of each MF block has the shape of a trapezoid with concavity pointing upwardly. The maximum value of the output is fixed by the value of the current flowing in the current generators of the blocks MF controlled by the signals VG-1 and VG-2. The position of both edges of the trapezoid is determined by the programming parameters PP (particularly PP-0 and PP1 in FIG. 3). In block RE the output currents of blocks MF are summed and complemented to a reference value. The value of the reference current of block RE is fixed by transistor G-0 biased by voltage V-0 (in FIG. 3 only two MF blocks are depicted though more blocks may be presented).
The output AO is linked to the value of the potential of node OUT by way of an operation of shifting, amplification and bufferization. In particular AO varies between 0 volt and 2 volt, OUT between 2 volt and 3.5 volt. In stable condition the voltages LD-i are all equal to the voltage OUT. The output currents 0-i are such that their sum equal 0, and they are a function of IG-i and of the difference between LS-i and LD-i. The value LS-i represents the value, that is programmable, of the "consequence" associated to the rule and is derived from block MEM. There is a programming value for each rule (PP-2 in FIG. 4). Therefore each rule requires a number of programming parameters PP equal to one (1) plus the number of inputs (AI) multiplied by 2; the global number of parameters is equal to said last calculated number multiplied by the number of rules.
The values E-Ik in FIG. 5 may be 0 or 1 corresponding to the status OFF or ON of the switches SW-Ik. Particularly, in each row only one switch may be ON so establishing the connection between signal PP-I and a predetermined value VI-k. In FIG. 6 the values VI-Ik are determined by the series connection of resistors whose extreme terminals are connected to potentials having a value independent from temperature derived from a bandgap (VBG). In this example, VI-k=4.16 volt, VI-0=1.44 volt, K=136, and the step is therefore 20 mV.
The circuit may be used for implementing an ARCSIN or SIN-1 function. The measured output is represented in FIG. 10 with one input and seven rules.
Values of programming parameters are given by the following:
______________________________________Antecedent part: PP-0 PP-1First Rule: 1.60 2.12Second Rule: 2.04 2.42Third Rule: 2.20 2.62Fourth Rule: 2.46 3.12Fifth Rule: 2.96 3.38Sixth Rule: 3.12 3.54Seventh Rule: 3.48 3.90Consequent part: PP-2First Rule: 2.00Second Rule: 2.08Third Rule: 2.32Fourth Rule: 2.74Fifth Rule: 3.16Sixth Rule: 3.40Seventh Rule: 3.50______________________________________
Values of coefficients E in the storage device MEM with K=136:
______________________________________1111111111111111111111111111111011111111111111111111111 . . .1111111111111111111111111111111111111111111111111101111 . . .0111111111111111111111111111111111111111111111111111111 . . .1111111111111111111111111111111111111111111111111111110 . . .. . .______________________________________
From the foregoing it will be appreciated that, although specific embodiments of the invention have been described herein for purposes of illustration, various modifications may be made without deviating from the spirit and scope of the invention. Accordingly, the invention is not limited except as by the appended claims.
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|U.S. Classification||706/9, 706/1, 706/8|
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