Synthesis of Nonlinear Control of Switching Topologies of Buck-boost Converter Using Fuzzy Logic on Field Programmable Gate Array (fpga)

An intelligent fuzzy logic inference pipeline for the control of a dc-dc buck-boost converter was designed and built using a semi-custom VLSI chip. The fuzzy linguistics describing the switching topologies of the converter was mapped into a look-up table that was synthesized into a set of Boolean equations. A VLSI chip–a field programmable gate array (FPGA) was used to implement the Boolean equations. Features include the size of RAM chip independent of number of rules in the knowledge base, on-chip fuzzification and defuzzification, faster response with speeds over giga fuzzy logic inferences per sec (FLIPS), and an inexpensive VLSI chip. The key application areas are: 1) on-chip integrated controllers ; and 2) on-chip co-integration for entire system of sensors, circuits, controllers, and detectors for building complete instrument systems.


Introduction
The design of control laws for power converters and inverters has been based mainly on linear control theory.However, most power electronics switching topologies have variable structures which are non-linear, characterized by discontinuities, and are therefore more difficult to model.The three most popular control methods used are state-space averaging technique [1], variable structure control (VSC) [2], and sliding mode control [3].The state-space technique may lead to instability, the VSC control has hysteresis as drawback, and the sliding-mode control is very complicated.The implementation of the above-mentioned control laws are complicated, high cost and almost not practical.
Fuzzy logic controllers (FLCs) are very suitable for variable structures but current applications of FLCs use software for implementation.However, hardware implementation will be cheaper and faster.The proposed method combines hybrid linguistic models used in FLCs and computational paradigms of Boolean algebra.The knowledge base of the converter switching topologies is used to form a look-up table which is described by Boolean equations which are easily implemented using FPGA.Results showed that the size of the FPGA is in-dependent of the number inference rules in the knowledge base, speeds in giga FLIPS are achieved because it is hardware based, and very fast control response.

Single-Input-Single-Output (SISO) Fuzzy Controller
Consider the generalized buck-boost converter shown in Figure 1.This is a single-input-single-output (SISO) system.The input variable is the capacitor voltage (v C ) and the output variable is the duty ratio D. It can be shown that the average model has the following equations: The membership functions for v C and D are shown in Figure 2. The SISO system of Figure 1 has a single fuzzy input V (v C ) and a single fuzzy output D.
The fuzzy membership sets V and D are represented by five linguistic qualifiers L (low), ML (medium low), OK (okay), MH (medium high), and H (high). Hence there  are 5x5=25 possible combinations that can generate 25 possible rules.However, the following 5 rules are sufficient to describe the membership values of Figure 2.

Logic Synthesis of Fuzzy Controllers
Consider a SISO fuzzy controller with input universe of discourse A 1 and output universe of discourse B 1 .Manzoul [4] showed that the number of unique fuzzy inputs (ufi) is equal to the dimension of the input universe of discourse.That is: In the fuzzification on (5) Each fuzzy input ha fo process, each input is mapped into ly one value (one element) in the input universe of discourse and zero value to all other values (elements).The objective here is to use a look-up table.Therefore, the number of rows in the look-up table is equal q 1 .It was also shown in [4] that the total least integer number of binary bits X for all the inputs is given by X=log 2 q 1 s only one output value and therere the maximum number of distinct output values is also equal to q 1 .In the defuzzification process only one element is selected in the output universe of discourse.It is therefore, easier and economical to use the defuzzified

Synthesis of Nonlinear Control of Switching Topologies of Buck-Boost Converter
Using Fuzzy Logic on Field Programmable Gate Array (FPGA) 38 outputs in the look-up table.If the there are p elements (p <q 1 ) in the output universe of discourse, the dimension of the output universe of discourse is given as The total least intege th Y=log 2 p (7)

Buck-Boost Con
er to control the output voltage From (5) the least th 29=5 r number of binary bits Y for all e outputs is given by verter Fuzzy Controller

Fuzzy Controller
Consider a SISO controll of the buck-boost converter of Figure 1.The input variable is the voltage and output variable is the duty ratio.The duty ratio maintains the voltage at a selected value.The ranges of capacitor voltage (v C ) and duty ratio D are (5.2 to 10.8) V and (0.33 to 0.47) respectively.The membership values are in the interval [0, 1], where 0 denotes no membership and 1 denotes full membership.Assume that 1 1 number of binary bits to represent e input values is given as Similarly, using (6) the least number of binary bits to represent output values is given as In Appendix I the 5 rules of (3) are expressed numerically.The fuzzy relation obtained is too big to be shown here because of the size (29x29 matrix).Table 1 of Appendix I shows the summary of the complete computations of the controller.0.0, ., ., 1.0, ., ., ., 0.0 *,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5,.5 .5,.58,.

Co
In m e ion

FPGA Implementation
The FPGA configuration is implemented by u inx's X95 (XC9536-10-PC44 CPLD) 05XL FPGA) boards.Both boards come with 8051 microcontroller with 12 MHz speed.The Xilinx's development system is used to implement the Boolean equations, which also represents the fuzzy controller.Figure 3 shows the semi-custom VLSI chip of the FPGA functional block diagram.

Instrument
Figure 4 shows the diag

On-Chip Cointegration
Microsystems technology has made inroads in instrumentation and measurement (I&M) applications.The fuzzy logic FPGA controller chip can be fabricated to have compact size.The FLC chip of this paper provides an interesting fabrication technique that has been identified in I&M applications: cointergration of control/sensors/detectors and circuits for building complete instrument systems.Th a compact FPGA chip, which can be fabricated as part of an integrated system of sensors, circuits, controllers, and detectors squeezed onto nanometer wafer.Such microchips can be used in a variety of applications in different environments and requirements.Beside e on-chip controller mentioned in the paper uses tion of these microchips, there ar cheaper parts and assembly of instruments, better functionality, lower mass and size, speed of control, lower cost, and higher efficiency.Some companies are now using multi fuzzy logic controller-based (MFLC) chips in some of their new dryers, dishwashers, and washing machines.

Results
The output voltage of Figure 1 is regulated at about 8.0 V through a feedback loop using the fuzzy controller on FPGA chip for adjusting the duty ratio D. The input voltage V s =12 V and the circuit parameters are L=100 H, C=330 F.The steady-state voltage is about 8.0 V when the load R is changed from 10  to 5 . Figure 5 shows the test results of a fuzzy controller chip.shows the effect on the output voltage when changing the load resistance.Figure 5 shows that the output voltage v c (t) can respond instantaneously to changes in the duty ratio D. The hardware implementation is cheaper and faster than using software.

Conclusions
The fuzzy controller implemented on an FPGA was used to control a dc-dc buck-boost switching converter.The size of the semi-custom VLSI was independent of the number of rules in the k emory space was required to store the large of rules.t aspect of the controller is that it was ed and consequently speeds over giga circuits to provide a complete co-integration system.

Figure 2 .
Figure 2. Membership functions for (a) voltage and (b) duty ratio

Figure 3 .
Figure 3. Semi-custom VLSI fuzzy controller chip Synthesis of Nonlinear Control of Switching Topologies of Buck-Boost ConverterUsing Fuzzy Logic on Field Programmable Gate Array (FPGA) 40 Legend : PGND = Tie pin to GND for additional ground path or leave unconnected VCC = Dedicated Power Pin GND = Dedicated Ground Pin TDI = Test Data In, JTAG pin TDO = Test Data Out, JTAG pin TCK = Test Clock, JTAG pin TMS = Test Mode Select, JTAG pin PROHIBITED =

Figure 4 .
Figure 4. (a) FPGA pin out; (b) input and output waveforms of FLC chip

Figure 1. Buck-boost switching converter with a fuzzy controller
Synthesis of Nonlinear Control of Switching Topologies of Buck-Boost ConverterUsing Fuzzy Logic on Field Programmable Gate Array (FPGA) 37

Table
The look-up table representing the fuzzy controller is given in Table2.The input universe of discourse has dimension of 29 and the output universe has dimension of 29.The look-up can be described by 7-variable Boolean equations.That is,

Table 2 . Look-up table for fuzz
Synthesis of Nonlinear Control of Switching Topologies of Buck-Boost ConverterUsing Fuzzy Logic on Field Programmable Gate Array (FPGA) 41