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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 3, JUNE 2006 941

Water Bath Temperature Control by aRecurrent Fuzzy Controller and

Its FPGA ImplementationChia-Feng Juang, Member, IEEE, and Jung-Shing Chen

AbstractA hardware implementation of the TakagiSugenoKan (TSK)-type recurrent fuzzy network (TRFN-H) for waterbath temperature control is proposed in this paper. The TRFN-His constructed by a series of recurrent fuzzy ifthen rules builton-line through concurrent structure and parameter learning.To design TRFN-H for temperature control, the direct inversecontrol configuration is adopted, and owing to the structure ofTRFN-H, no a priori knowledge of the plant order is required,which eases the design process. Due to the powerful learning abil-ity of TRFN-H, a small network is generated, which significantly

reduces the hardware implementation cost. After the networkis designed, it is realized on a field-programmable gate array(FPGA) chip. Because both the rule and input variable numbersin TRFN-H are small, it is implemented by combinational circuitsdirectly without using any memory. The good performance of theTRFN-H chip is verified from comparisons with computer-basedproportionalintegral fuzzy (PI) and neural network controllersfor different sets of experiments on water bath temperaturecontrol.

Index TermsDirect inverse control, fuzzy chip, fuzzy control,neural network, structure/parameter learning.

I. INTRODUCTION

F UZZY logic controllers (FLCs) have been widely appliedto both consumer products and industrial process control.For temperature control problems, we usually encounter the

problem of time delays, i.e., the current output is a function of

plant input or past input or both. When feedforward networks,

like feedforward neural and neural fuzzy networks, are applied

to this type of problem, we should know the order of the plant

and decide the proper controller input variables [1][4]. This is

obviously an inefficient approach, and the inclusion of too many

variables in the network input will increase the network size and

decrease learning speed. Owing to these problems, a recurrent

neural fuzzy network controller should be a better choice

in temperature control problems. In [5], we have proposed

a TakagiSugenoKang (TSK)-type recurrent fuzzy network

(TRFN), and the superiority of TRFN over existing recurrent

Manuscript received October 10, 2003; revised January 3, 2006. Abstractpublished on the Internet March 18, 2006. This work was supported bythe National Science Council, Taiwan, R.O.C., under Grant NSC 94-2213-E-005-014.

C.-F. Juang is with the Department of Electrical Engineering, NationalChung Hsing University, Taichung 402, Taiwan, R.O.C. (e-mail: [email protected]).

J.-S. Chen was with the Department of Electrical Engineering, NationalChung Hsing University, Taichung 402, Taiwan, R.O.C. He is now withthe Logic Department, Magic Pixel Inc., Hsinchu, Taiwan, R.O.C. (e-mail:

[email protected]).Digital Object Identifier 10.1109/TIE.2006.874260

networks has been demonstrated. In this paper, based on the

structure of TRFN, a modified version of TRFN for hardware

implementation, which is denoted as TRFN-H, is proposed and

realized on a field-programmable gate array (FPGA) chip.

For time-delayed plant control, one generally adopted ap-

proach is the generalized predictive control (GPC) [6]. GPC

is originally presented based upon a linear model so it is not

suitable for nonlinear plant control. To cope with this problem,

some nonlinear controller model designs based on GPC areproposed [7], [8], most of which belong to fuzzy-model-based

predictive control. The drawback of this model is that we should

know in advance the order of input and output terms of the

linear GPC model in the fuzzy consequence. Other controller

design configurations based upon neural learning approaches

include the direct inverse, direct and indirect adaptive control,

etc. [9]. Among them, the direct inverse control configuration

requires no emulation of the plant and is simpler in imple-

mentation. Because the adopted TRFN-H is characterized with

powerful learning ability, which can model the inverse of the

plant accurately, we will design a TRFN-H controller based

upon direct inverse control configuration. When TRFN-H is

applied to temperature control problems, only the current plantstate and reference state are fed as TRFN-H inputs because both

the past plant states and controller signals can be memorized

by internal variables. This significantly reduces the following

hardware implementation cost.

In recent years, many hardware implementations, including

analog and digital, of FLCs have been proposed. For design

flexibility and ease of programmability [10][18], a digital

implementation of TRFN-H is proposed here. The digital hard-

ware of FLC originates from [10]. Then, Watanabe et al. [11]

proposed an FLC with dynamically reconfigurable cascadable

architecture. In [12], a fuzzy processor using single-instruction

multiple-data (SIMD) is proposed. Lee and Bien [13] de-signed an expandable fuzzy inference processor consisting

of IF modules and THEN modules for implementing fuzzy

IFTHEN rules. Whereas in [14], fuzzy inference is performed

by sequential processing of the antecedents of the fuzzy rules.

In [18], the implementation uses the dynamic membership

function generator, as well as the high-speed integration capa-

bility afforded by very large scale integration (VLSI). To our

knowledge, most previous works on FLC intended to improve

the inference performance for real-time applications to expand

the capacity for processing more input and output variables

and focus on the implementation of a feedforward fuzzy logic

system. However, there has been no attempt to design a

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942 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 3, JUNE 2006

Fig. 1. Structure of TRFN-H.

hardware-based TSK-type recurrent fuzzy system. With the

recurrent structure of TRFN-H, both the numbers of input vari-

ables and rules are small in temperature control experiments.

So, we will design TRFN-H in combinational circuits directly

without using any memory and then, realize TRFN-H on anFPGA chip. The TRFN-H control chip is then applied to water

bath temperature control.

This paper is organized as follows: Section II presents

the structure and learning of TRFN-H. Section III presents

the control configuration of TRFN-H. Section IV presents the

hardware implementation of TRFN-H. The experimental results

are presented in Section V. Finally, conclusions are drawn in

Section VI.

II. STRUCTURE AND LEARNING OF TRFN-H

A. Structure of TRFN-H

The structure of TRFN-H is shown in Fig. 1. Like TRFN,

each rule in TRFN-H is of the following form:

Rule i :

IF x1(t) is Ai1 and and xn(t) is Ain and hi(t) is G

THEN y(t + 1) is ai0 +

nj=1

aijxj(t) + aij+1hi(t)

and h1(t + 1) is w1i and and hr(t + 1) is wri

where A and G are fuzzy sets, w and a are the consequentparameters for inference output h and y, respectively, n is the

number of external input variables, and r is the number of rules.The consequent part for the external output y is of the TSK

type. For the consideration of easy hardware implementation,

the functions of TRFN-H are different from those of TRFN. To

give a clear understanding of the mathematical function of each

node, we will describe the functions of TRFN-H layer by layer.

For notation convenience, the net input to the ith node in layerk is denoted by u

(k)i and the output value by O

(k)i .

Layer 1: No function is performed in this layer. The node

only transmits input values to layer 2.

Layer 2: Two types of membership functions are used in this

layer. For external input xj , a local membershipfunction is used, and the following isosceles trian-

gular function is adopted:

O(2)i =

0, u(2)j mij ij

1 u(2)j

mij

ij , mij ij u(2)j mij + ij

and u(2)j = O

(1)j

0, u(2)j mij + ij

(1)

where mij and ij are the center and the width ofthe triangle membership function of the ith term ofthe jth input variable xj, respectively. For internalvariable hi, a global membership is used, and thefollowing piecewise linear function is adopted:

O(2)i =

1, u(2)i 2.8125

u(2)i

+2.8125

5.625 , 2.8125 u(2)i 2.8125

and u(2)i = hi

0, u(2)i 2.8125

(2)

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JUANG AND CHEN: WATER BATH TEMPERATURE CONTROL BY RECURRENT FUZZY CONTROLLER AND ITS FPGA 943

where the parameters 2.8125 and 5.625 are chosen

for easy digital implementation. Links in layer 2 are

all set to unity.

Layer 3: The output of each node in this layer is determined

by fuzzy and operation. Here, the minimum oper-

ation is utilized to determine the firing strength of

each rule. The function of each rule is

O(3)i =

n+1minj=1

O

(2)j

. (3)

The link weights are all set to unity.

Layer 4: Nodes in this layer perform a linear summation.

The mathematical function of each node i is

O(4)i =

n+1j=0

aiju(4)j = aio +

nj=1

aijxj + ain+1hi. (4)

Links from this layer to layer 6 are all equal tounity.

Layer 5: The context node functions as a defuzzifier for

the fuzzy rules with inference output h. The linkweights represent the singleton values in the con-

sequent part of the internal rules. The simple

weighted sum is calculated in each node as

hi = O(5)i =

rj=1

O(3)j wij . (5)

As shown in Fig. 1, the delayed value of hi isfed back to layer 1 and acts as an input variableto the precondition part of a rule. Each rule has

a corresponding internal variable h and is used todecide the influence degree of temporal history to

the current rule.

Layer 6: The node in this layer computes the output signal

y of the TRFN-H. The output node together withthe links connected to it acts as a defuzzifier. The

mathematical function is

y = O(6) = rj=1 O

(3)j O

(4)jr

j=1 O(3)

j

. (6)

B. Learning of TRFN-H

The task of constructing the TRFN-H is divided into two sub-

tasks, namely 1) structure learning and 2) parameter learning.

Because there are no rules initially in TRFN-H, the first task

in structure learning is to decide when to generate a new rule.

Clustering on the external input x, which represents the spatialinformation, is used as the criterion. Based on this concept, the

spatial firing strength

Fi(x) =n

mink=1

O(2)k [0, 1] (7)

Fig. 2. Configuration of the TRFN-H-based control.

is used as the criterion to decide if a new fuzzy rule should be

generated. For each incoming data x(t), find

I = arg max1ir(t)

Fi(x) (8)

where r(t) is the number of existing rules at time t. If FI 2.8125.

Here, the processing can be ignored. The reason is that

the succeeding inference processing unit will take the

minimum operation from the outputs of these modules

and those from the input fuzzifier module, whose output

values always lie between 0 and 1. Thus, whether the

output values in this module are larger than 1 or not do

not affect the output values of the minimum operation.

3) Inference processing unit: The main function of thismodule is to perform the minimum operation in (3). Fig. 4

shows a block diagram of the inference processing unit,

where each MIN module performs minimum selection

from two inputs.

4) Internal defuzzifier: This module implements the defuzzi-

fier operation in (5). All the parameters wij are fixed con-stants in the hardware implementation. For this reason,

each multiplier is implemented by distributed arithmetic

[19], [20] to reduce the cost. The module (for one internal

variable) is shown in Fig. 5. After multiplication, it still

needs an adder to summate them. For TRFN-H consisting

ofr

rules, in this module, there will ber

2 multipliers

and r adders in total.5) Output signal defuzzifier: This module implements the

defuzzifier operation in (6). As shown in (6), for a single-

output TRFN-H system, a single divider is sufficient to

compute the defuzzified value. The defuzzifier module is

shown in Fig. 6. First, we must calculate the value of

TSK-type linear summation in (4). Because the values

of aij are all fixed, we can implement the correspondingmultipliers by distributed arithmetic. For the multipliers

with inputs O(3)i and O

(4)i , we cannot implement them by

distributed arithmetic because the inputs are not fixed; we

implement them by finite state machines (FSMs) instead.

As to the divider, it is implemented by the binary divisionalgorithm [20].

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Fig. 4. Circuits that implement the precondition part of TRFN-H. (a) Input fuzzifier. (b) Recurrent fuzzifier. (c) Inference processing unit.

V. EXPERIMENTS

The experiment is performed on a real water bath temper-

ature control system. The water bath is an example of animportant component in a batch-reactor process. A schematic

diagram of the experimental setup is shown in Fig. 6. It contains

four components, namely: 1) a pump that works as a stirrer;

2) an FPGA-implemented TRFN-H control chip; 3) a tem-

perature sensor; and 4) a heater based on silicon-controlled

rectifier (SCR). A brief description of the four components

follows. The submersible pump pumps 180 L/h, and its function

is to ensure even temperature distribution. The volume of

the water bath is 12 L. The device of the FPGA is Altera

FLEX EPF10K50EQC240-1, which contains 50 000 typical

gates [logic and random-access memory (RAM)] and 2880

logic elements. In order to be compatible with sensor and

controller plant, analog-to-digital (AD) and digital-to-analog(DA) converters are needed. The AD converter we used is

the 12-bit AD1674. The DA converter is the 8-bit monolithic

DAC0808. We used the 12-bit AD converter for more accurate

measurement. For the temperature measurement, a PT100 sen-

sor is used. The maximum power of the heater is 1000 W. For

a discrete-time control system, it is necessary to decide on the

sampling period. Here, we first chose TS = 30 s as the sam-pling period.

To obtain data for training of TRFN-H, a sequence of random

input signals u(k) limited to 0 and 5 V is injected directly tothe system. The water temperature reaches about 95 C when

85 input signals are injected and remains at that temperature

when more input signals are injected. In the same way, another

85 training patterns are collected so that there is a total of

170 training patterns for off-line training. For TRFN-H train-

ing, the inputs are yP(k) and yP(k + 1), and the desired

output is u(k). After training, only four rules are generated,and the learning curve is shown in Fig. 7. Then, the hardware

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Fig. 5. Circuits that implement the consequent part of TRFN-H. (a) Internal defuzzifier. (b) Output signal defuzzifier.

implementation of TRFN-H is realized using Quartus II soft-

ware and Verilog language. The designed TRFN-H controller

can work at a clock frequency of 51.28 MHz. The total gatecount of the designed TRFN-H is 11 383.2533 (using a Synop-

sys Design Compiler with Avant .35 cell library).

To test the control performance of the TRFN-H control chip,

the following three set points are to be followed:

yref(k) =

40 C, k 4055 C, 40 < k 8070 C, 80 < k 120.

(11)

The controlled result for these set points is shown in Fig. 8,

and the corresponding sum of absolute error (SAE) is shown

in Table I.

For comparison, a personal computer (PC)-based back-propagation neural network (BPNN) controller designed by the

Fig. 6. Schematic diagram of the water bath temperature control system.

same configuration is experimented. BPNN is a feedforward

network and consists of one hidden layer. As we have noa priori knowledge of the plant order, we should first decide the

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Fig. 7. Trained error curve of TRFN-H (solid line) and BPNN withtwo ( ), six (), and eight ( ) input variables.

TABLE ISUM OF ABSOLUTE ERROR (SAE) BETWEEN TRFN-H, PI, AN D

FLC IN DIFFERENT KINDS OF EXPERIMENTS WHERESAE(m,n) =

nk=m

|yref(k) yp(k)|

variables fed as BPNN input. An experimental method basedon trying several combinations of input variables is adopted

to accomplish this decision task. During the off-line training

process, BPNN with 2, 6, and 8 input variables are tried, and

the corresponding input variables are

Net. 1: [yp(k), yp(k + 1)],Net. 2: [yp(k1),yP(k),yP(k+1),u(k2),u(k 1), u(k)]Net. 3: [yP(k 2), yP(k + 1), yP(k), yP(k + 1), u(k 3),

u(k 2), u(k 1), u(k)].

For fair comparison, the number of parameters in each net-

work is set to be the same as that in TRFN-H. The learning

curve of each network is shown in Fig. 7, from which we see

that it is only when the number of input nodes is augmentedto 8 and after 107 iterations of training can we achieve a goodtraining result. The control result for these three set points in

(11) using the PC-based BPNN with 8 input variables is also

shown in Fig. 8, from which we see that the performance of

TRFN-H obviously outperforms that of BPNN.

Other than that of the BPNN controller, the performance of

PC-based proportionalintegralderivative (PID) and FLCs are

compared. For the PID control, a positional form discrete PID

controller [21] is used. In order not to aggravate noise in the

plant, only a two-term PID controller is used, i.e., the derivative

parameter is set to zero. After numerous experiments, the

best proportional parameter and integral parameter are found

to be 50 and 0.15, respectively. The reference set points in(11) are used to test the control performance of the PC-based

Fig. 8. Performance of the BPNN controller with 8 input variables (solid line)and TRFN-H (broken line).

proportionalintegral (PI) controller, and the SAE is shown in

Table I. For the FLC, we specify the input variables as the per-

formance error e(k), which is the error between the referenceoutput and actual temperature of the water bath system, and

the rate of change of the performance error e(k). The outputvariable u(k) is the voltage between 0 and 5 V . We partitioneach of the two input variables into three fuzzy sets, which

yields nine fuzzy rules. Triangle membership functions are cho-

sen for the fuzzy sets of the two input fuzzy variables. For the

output variable u(k), we quantify it into six fuzzy singletons:0.0, 1.0, 2.0, 3.0, 4.0, and 5.0 V. The SAE for the reference

set points control by the FLC is also shown in Table I. For the

FLC, we have tried our best to achieve its best performancethrough several trial-and-error experiments. Even so, as shown

in Table I, we see that TRFN-H not only costs the least design

effort but also achieves better performance than FLC.

To test the performance of the aforementioned controllers

(TRFN-H, PI, and FLC) under different control conditions,

another two sets of experiments are conducted on the water

bath temperature control system. The two experiments include

variation of the sampling period TS and variation of the watervolume.

In the first set of experiments, we change the original sam-

pling period TS = 30 s to other sampling periods, including

TS = 2 and 60 s. The control performance of the threecontrollers for all of these new sampling periods are shown inTable I, from which we see that the TRFN-H control chip has

fewer SAE than the other two controllers in all the sampling

periods experimented. For clarity, some control results are

shown in Fig. 9. Although the parameters of the TRFN-H

control chip were obtained at TS = 30 s, owing to its recurrentproperty, it still performs well at other sampling periods

without changing any network parameters.

In the second set of experiments, the volume of the water

is doubled. The control result by the TRFN-H control chip is

shown in Fig. 10. The controlled SAE by TRFN-H, PI, and

FLC are shown in Table I. The performance of the TRFN-H

control chip outperforms those of the two other controllersfrom Table I.

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Fig. 9. Experiments on variation of sampling periods. (a) Performance of PI

(solid line) and TRFN-H (broken line) when the sampling period is changed to2 s. (b) Performance of FLC (solid line) and TRFN-H (broken line) when thesampling period is changed to 60 s.

Fig. 10. Control performance of TRFN-H when the volume of water isdoubled.

VI. CONCLUSION

Temperature control by hardware implementation of a recur-rent neural fuzzy controller, the TRFN-H, was presented. The

design is based on the direct inverse modeling approach withouta priori knowledge of the plant order. Owing to the powerful

learning ability of TRFN-H, only four rules are required in

the temperature control problem, which efficiently reduces thehardware design cost. The designed TRFN-H controller was

realized on an FPGA chip. Several sets of experiments were

performed on a practical water bath temperature control. Com-

pared with the generally adopted controllers, including PC-

based BPNN, PI, and FLC, the TRFN-H control chip hasshown superior performance both in controller design effort

and control performance. Overall, these advantages of the

TRFN-H control chip motivate further applications to other

temperature control problems in the industry.

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Chia-Feng Juang (M00) received the B.S. andPh.D. degrees in control engineering from theNational Chiao-Tung University, Hsinchu, Taiwan,R.O.C., in 1993 and 1997, respectively.

From 1999 to 2001, he was an Assistant Profes-sor in the Department of Electrical Engineering atthe Chung Chou Institute of Technology. In 2001,he joined the National Chung Hsing University,

Taichung, Taiwan, R.O.C., where he is currently anAssociate Professor of electrical engineering. Hiscurrent research interests are computational intel-

ligence, intelligent control, computer vision, speech signal processing, andchip design.

Dr. Juang is a member of the IEEE Computational Intelligence Society andthe IEEE Signal Processing Society.

Jung-Shing Chen received the B.S. degree in elec-trical and control engineering from the NationalChiao-Tung University, Hsinchu, Taiwan, R.O.C.,in 2001, and the M.S. degree in electrical engi-neering from the National Chung Hsing University,Taichung, Taiwan, R.O.C., in 2003.

In 2003, he joined Magic Pixel Inc., Hsinchu,Taiwan,R.O.C., as an Engineer, where he is currently

with the Logic Department. His research interests areintelligent control and chip design.

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