Download 5 Acknowledgment

Implementation of CMOS MIN-MAX
Circuit for the Rule-Base Block of Fuzzy
Logic Temperature Controller
Srismrita Basu , Subhodip Maulik, Sayan Samanta
Abstract-The paper proposes the realization of a CMOS min –max circuit for the Rule-Base block of Fuzzy Logic Temperature
controller using P-SPICE. Here, we mainly deal with the analog implementation of VLSI circuit and we compare the digital
implementation along with the analog implementation and also show the advantages of the analog one in this case. Now, analog
implementation is popular mainly because of their continuous-time-processing and high frequency and low power implementation.
Index Terms—
Fuzzy logic, Analog implementation, Digital implementation, VLSI, Current mode, Current Mirror, Bounded
difference.
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1
Introduction
Fuzzy logic is a mathematical system that
analyzes analog input values in terms of fuzzy
variables that takes continuous values between
0 and 1, in contrast to classical or digital logic,
which operates on discrete values of either 0 or
1. Fuzzy logic was first proposed by Lotfi A,
Zadeh of the University of California at
Barkley in 1965 paper and the idea was
elaborated in 1973 paper that introduced the
concept of Fuzzy set. Here, we used TakagiSugenos type controller. Now, in this
controller we are mainly concern about the
Rule Base block, where, a set of rules
specifying
the
combination
of
input
membership values are stored. The controllers
here for used by the inference mechanism, can
therefore be applied to multi-input-multioutput problems and single- input- singleoutput problems.
The block diagram of Fuzzy controller is
shown below in fig-1.
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 Srismrita Basu is currently working as Asst.Professor in electronics and
communication engineering department in Greater Kolkata College of
Engineering and Management, Baruipur, West Bengal. Country-India,
E-mail: [email protected]
 Co-Author name Subhodip Maulik is currently working as Asst. Professor
in Camellia institute of technology, West Bengal. Country-India,
E-mail: [email protected]
 Co-Author name Sayan Samanta completed B.Tech in applied electronics
and instrumentation engineering from future institute of engineering and
management, West Bengal. Country-India.
E-mail:[email protected]
Fig-1 Block diagram of Fuzzy logic controller
To design the Rule base block we consider the
analog implementation of CMOS over digital
implementation.
2 Digital Implementation
VLSI digital implementation of Fuzzy Logic
systems offers several advantages issued from
the sound knowledge of digital circuit design
and technology. Several mature CAD
(Computer Aided Design) tools allow
relatively easy design automation (synthesis
and simulation) reducing consequently time
and cost of development. The automatic
regeneration of logic levels involves high noise
immunity and low sensitivity to the variances
of transistors characteristics. This proves
accurate and reliable data and signal
processing. Binary data can be easily stored
and allows realizing programmable and
multistage fuzzy processing.
Complex
representation of fuzzy vector and parallel
structures is however required to obtain
accurate and fast processing. Digital
implementation of common fuzzy operation
leads unfortunately rapidly to complicated,
enormous VLSI circuits. The density and
speed of these circuits are nevertheless
continually
increasing
according
to
technological advances, so that they will
continuously
increasing
according
to
technological advances, so that they become
more efficient to implement fuzzy logic
systems.
Digital fuzzy processors are generally
designed for multipurpose applications. They
should thus implement a great and various
numbers of fuzzy operators, membership
functions and inference rules. These make
them efficient for a large range of applications,
provided that appropriate programming is
possible. Now, combined with an appropriate
programming environment, linguistic rules
derived from a human expert can be directly
translated into an implementation on a chip.
Digital implementation is used in control,
expert systems, robots, image recognitions,
diagnosis etc.
3 Analog implementation
Analog circuits present several advantages
towards digital ones, especially regarding the
speed of processing, power dissipation and
functional density. They can moreover
perform continuous time processing and have
the particularities to be well compatible with
sensors, actuators and all other analog signals.
Therefore they are indicated to deal with fuzzy
values which are analog by nature. Some
continuous representations of symbolic
membership functions and non-linear fuzzy
operations can be easily synthesized by
dealing with transistor characteristics. There is
no need of A/D or D/A converters when
implemented in a real system, provided that
no specific digital signal processing is
required. Analog circuits can then supplant
digital controllers for some applications
requiring low-cost, low-consumption, compact
and high-speed stand-alone chips. They suffer
nevertheless of the lack of reliable memory
cells. They are consequently not well
appropriate to pipeline structures and have
very restricted programmability possibilities.
Fortunately, the nature of fuzzy variable
systems requires extensive parallelism which
makes analog circuit s well appropriate to
precede high-speed numerous inferences and
also limits the problem of error accumulation.
Analog implementation is used in stable and
low-noise analog technologies (n-well CMOS,
Bi-CMOS) having sufficient accuracy with
wide frequency range.
During the last decade a growing interest in
low voltage, low power circuit in standard
CMOS technology can be observed because of
the portable electronic devices and sensors.
Current mode circuits’ shows great future
since using current as signal carriers enables it
to be unrestricted by supply voltage.
Now, analog implementation consists of two
mode of operations- 1) Voltage Mode
and 2) Current Mode
3.1 Voltage Mode
It is attractive because it makes easy to
distribute a signal in various parts of a
circuit. Non-linear operators such as
the MIN, MAX and truncation ones
are quite easy to implement in voltage
mode. Multiple-input MIN & MAX
circuits are constructed with bipolar
transistors and these circuits are
called Emitter coupled fuzzy logic
gates. These basic non-linear gates
present good characteristics and
robustness.
Such
circuits
are
impractical with MOS transistors
which cause an acceptable error
associated with the transition region
in which multiple devices are active.
CMOS multiple-input MIN & MAX
circuits using gain-enhanced voltage
followers based on differential
amplifiers.
They
are
more
complicated but have frequency and
accurate performance.
But, voltage-mode fuzzy circuit implies a large
stored energy into the parasitic capacitances
and speed is limited by charge delays of
various capacitors. They are moreover
penalized by a certain lack of precision
because signals are sensitive to changes of
supply voltages. The problems mainly lie in
the sizing of some components and also
several functions are very difficult to build in
voltage-mode.
Now,
this
type
of
implementation needs resistors to achieve
additions and to convert voltages into
currents. But, the integrated resistors are
inaccurate,
cumbersome
and
involve
significant
parasitic
capacitances.
The
truncation of consequent and the defuzzification pose an important problem as
regards the parallelism of the Inference engine
(especially when the number and size of
output sets is large). This approach implies
high-power dissipation and large chip area
and leads to high cost. These problems can
remove by the Current mode operation.
3.2 Current Mode
These circuits do not need resistors
and can achieve summation and
subtraction in the simplest way, just
by wire connections. This leads to
simple and intuitive configurations,
which exhibits high speed and great
functional density. They are used
mainly for systems requiring a high
level of interconnectivity.
The main advantages of the current
mode circuits are(i) Low power dissipation
(ii) Low supply voltage
(iii) Good insensitivity to the supply
voltage fluctuation.
Since, current mode circuits have a
single fan-out, current repeatability is
of prime importance and the
distribution of signals requires
multiple-output current mirrors.
3.2.1 Current Mirror
It is a circuit designed to circuit
designed to copy a current through
one active device by controlling the
current in another active device of a
circuit, keeping the output current
constant regardless of loading.
An ideal current mirror is simply an
ideal current amplifier.
There are 3 main specifications that
characterize a current mirror(a) The current level it produces
(b) Its ac output resistance
which determines how much the
output current varies with the voltage
applied to the mirror.
(c) The minimum voltage drops
the mirror necessary to make it work
properly.
Fig-2
An n-channel MOSFET
Current Mirror
Previously the transistors are used to
develop the current mirror but now a
day, the transistors are replaced by
the MOSFET as the speed of MOSFET
is much higher and the power
dissipation is low. The n-channel
MOSFET current mirror with a
resistor to set the reference current
IREF is shown in fig.2.
A basic realization of multiple-output CMOS
current mirror is shown below in fig-3.
Fig-3
Basic n-output CMOS current
mirror and symbolic represemtation
The circuit is however not suitable for
synthesizing accurate functions since each
output current is slightly modulated by output
voltage throughout the Early conductance. The
output current should be independent of the
output voltage, which is obtained by reducing
the conductance as for the 3 common mirrors
shown in fig-3. The drain voltage of the
transistor which imposes the current is then
independent of the output voltage of the
circuit. Multiple-output cascade mirrors are
often used but Wilson ones are preferable for
low power applications because they require a
single polarization voltage instead of two
superposed voltages. The Mod-Wilson mirror
is obtained by adding a transistor to the
Wilson mirror to improve its symmetry. This
mirror provides good accuracy and input
current is well reproduced with perfectly
matched identical transistors. The precision of
all these mirrors depends on their output
resistance and on the matching of their
transistors.
Current mirror can be used as building block
to synthesize fuzzy logic operation and
relevant processing. In this way, nine basic
fuzzy operations can be easily implemented on
the monolithic ICs with standard CMOS
technologies. This current mode basic logic
cells exhibit good linearity which cannot be
easily achieved in voltage mode and lead to
fuzzy integrated systems which are globally
smaller than in voltage mode.
3.2.2 MIN-MAX circuit
Minimum (MIN) and Maximum (MAX)
operators are typically employed to define the
sentence connectives in any kind of fuzzy
controller. In MAMDANI controller they also
define the fuzzy implication and aggregation
mechanism. They are also used in the
fuzzification operation using membership
functions. The building block of these circuits
is known as bounded difference circuit which
is defined as
X Θ y={x-y; if x ≥ y
0; if x < y
[where, x, y are two
variables]
Fig-4
A Bounded Difference Circuit
Input and output of Bounded difference circuit
is given below in fig-5.
The bounded difference circuit can be obtained
by the combination of a current mirror and a
diode. Now, the diode can easily be realized in
the CMOS circuit either by a single FET in
which gate and drain is connected together
Fig-5
Input and output of Bounded difference circuit
Now, as bounded difference and algebraic
sum are sufficient to realize all fuzzy
functions, fuzzy circuits can be designed only
by specifying connections between difference
sub-circuits.
MIN function of two inputs x and y can be
derived by using bounded difference operator
as follows:
MIN (x, y) = x Θ (x Θ y)
And the circuit is given in fig-6.
Fig-8
Fig-6
A two input MIN circuit
A two input MAX circuit
The input and output of MAX circuit is given
below.
The input and output of MIN circuit is given
below.
Fig-9
Input and output of MAX circuit
4 Conclusion
Fig-7
Input and output of MIN circuit
MAX function of two inputs x and y can be
derived by using bounded difference operator
and Add (+) operator as follows:
MAX (x, y) =(x Θ y) + y
And the circuit is given in fig-7.
An attempt has been made here to initiate
work on analog realization of fuzzy circuits,
but the implementation involves a large
number of MIN-MAX circuits, which is time
consuming and needs elaborate simulation
and testing. Research and development is also
continuing on fuzzy applications in software,
as opposed to firmware, design, including
fuzzy expert systems and integration of fuzzy
logic with neural network and so called
adaptive “genetic” software systems, with the
ultimate goal of building “self-learning” fuzzy
control systems.
5 Acknowledgment
The authors wish to thank Prof. Dr. P.K. Sinha
Roy, Ex. Professor of BESU, Shibpur, Prof. of
ECE department of Institute of Engineering
and Management, Salt Lake, West Bengal,
India, for his enormous support and guidance
throughout this paper.
6 References
[1] “NEURAL NETWORKS, FUZZY LOGIC AND
GENETIC ALGORITHM”-S. Rajasekhran, G. A.
Vijayalakshmi Pai
[2]Design of Fuzzy Controllers:
http://faculty.petra.ac.id/resmana/private/fuzzy/design.
pdf
[3]Fuzzy control system:
http://en.wikipedia.org/wiki/Fuzzy_control_system
[4]Current Mirror:
http://en.wikiepedia.org/wiki/Current_mirror
[5] PID Controller-Wikipedia
[6] Fuzzy Logic:
http://faculty.petra.ac.id/resmana/private/matlabhelp/pdf_doc/fuzzy/fuzzy_tb.pdf
[7]MIN and MAX Circuit:
http://portal.acm.org/citation.cfm?id=79828.79833
[8]CMOS Circuit design, Layout and Simulation - R.
Jacob Baker, Harry W. Li, David E. Boyee
[9] Design of Analog CMOS Integrated Circuits –
Behzad Razavi