
Research Article


Optimal Design of Neural Fuzzy Inference Network for Temperature Controller 

Nisha Jha,
Udaibir Singh,
T.K. Saxena
and
Avinashi Kapoor



ABSTRACT

In this study, a Neural Fuzzy Inference Network (NFIN) for controlling the temperature of the system has been proposed. The NFIN is inherently a modified fuzzy rule based model possessing neural network’s learning ability using hybrid learning algorithm which combines gradient descent and least mean square algorithm. In contrast to the general adaptive neural fuzzy networks where the rules should be decided in advance before parameter learning is performed, there are no rules initially in the NFIN. The rules in the NFIN are created and adapted as online learning proceeds via simultaneous structure and parameter identification. The NFIN has been applied to a practical water bath temperature control system, designed and developed around Atmel’s 89C51 microcontroller. In the above system, four experiments were conducted on water bath each for 250 and 500 mL min^{1} flow of water for different volume of water and power of heater. The performance of NFIN has been compared with Fuzzy Logic Controller (FLC) and conventional Proportional Integral Derivative (PID) controller. The three control schemes are compared through experimental studies with respect to set point regulation. It is found that the proposed NFIN control scheme has the best control performance of the three control schemes.





Received: January 18, 2011;
Accepted: May 10, 2011;
Published: July 02, 2011


INTRODUCTION
The ProportionalIntegralDerivative (PID) controller (Yazdizadeh
et al., 2009) has been commonly used in process industries, since
it has many advantages such as simple designing technique, easy application
and parameter design methods and so on. It is well known that appropriate values
of PID parameter are the most important aspect which influences the PID controller
performance and is hard to get especially for large timedelay or timevariation
uncertain system. Some kinds of selftuning PID controller have been presented
to solve these problems (Wu et al., 2005; Wen
and Liu, 2004; Huapeng and Handroos, 2004; Astrom
et al., 1993; Astrom and Hagglund, 1995; Chu
and Teng, 1999; Ho and Xu, 1998). In this study,
we use the neurofuzzy based tuning formula of PID controller for developing
Neural Fuzzy Inference Network (NFIN) system.
The concepts of fuzzy logic and artificial neural network for control problem
have been developed into a popular research topic in recent years (Hsu,
2007; Fakhrazari and Boroushaki, 2008; Lin
and Xu, 2006). The reason is that the classical control theory usually requires
a mathematical model. The inaccuracy of mathematical modeling of the plants
usually degrades the performance of the controller, especially for nonlinear
and complex control problems (Astrom and Wittenmark, 1989).
On the contrary, the advent of the Fuzzy Logic Controllers (FLC’s) (Driancov
et al., 1996; Harris et al., 1993; Sugeno,
1985; Tareghian and Kashefipour, 2007) and the neural
network controllers (Miller et al., 1990; Yabuta
and Yamada, 1991) based on multilayered Back Propagation Neural Networks
(BPNN’s) has inspired new resources for the possible realization of better
and more efficient control (Kosko, 1992; Lin
et al., 1996; Hourfar and Salahshoor, 2009)
over traditional adaptive control systems (Narendra et
al., 1991). That is, they do not require mathematical models of the
plants. The traditional neural networks can learn from data and feedback but
the meaning associated with each neuron and each weight in the network is not
easily understood. For a BPNN, its nonlinear mapping and selflearning abilities
have been the motivating factors for its use in developing intelligent control
systems (Yabuta and Yamada, 1991). However, slow convergence
is the major disadvantage of the BPNN. Alternatively, the fuzzy logic systems
are easy to appreciate because it uses linguistic terms and the structure of
ifthen rules (Miller et al., 1990). The simplicity
of designing these fuzzy logic systems has been the main advantage of their
successful implementation in a lot of industrial process (Islam
et al., 2007). There has a lot of fuzzy PI, fuzzy PD and fuzzy PID
control schemes were proposed in literature (Visioli, 2001;
Haiguo and Zhixin, 2007; Juang and
Lin, 1998). Despite the advantages of the conventional FLC over traditional
approaches, there remain a number of drawbacks in the design stages. Even though
rules can be developed for many control applications, they need to be set up
through expert observation of the process. The complexity in developing these
rules increases with the complexity of the process. FLC’s also consist
of a number of parameters that are needed to be selected and configured in prior,
such as selection of scaling factors, configuration of the center and width
of the membership functions and selection of the appropriate fuzzy control rules.
In contrast to the pure neural network or fuzzy system, the neural fuzzy network
(Nurnberger et al., 1999; Azeem
et al., 2003; Chopra et al., 2005;
Kasabov, 1996; Caswara and Unbehauen,
2002; Munasinghe et al., 2005; Ouyang
et al., 2005; Arbaoui et al., 2006)
representations have emerged as a powerful approach to the solution of many
problems (Lin et al., 2001).
In this study, a Neural Fuzzy Inference Network (NFIN) is proposed to combine
the advantages of fuzzy logic and neural networks. The NFIN is a fuzzy rulebased
network possessing neural network's learning ability. A major characteristic
of the network is that no preassignment and design of the rules are required.
The rules are constructed automatically during the online operation. Two learning
phases, the structure identification as well as the parameter learning phases
(Lin and Lin, 1996), are adopted online for the construction
task. The structure identification determine the proper number of rules needed
i.e., finding how many rules are necessary and sufficient to properly model
the available data and the number of membership functions for input and output
variables. Parameter learning phase is used to tune the coefficients of each
rule (like the shape and positions of membership functions). In this study,
a Neural Fuzzy Inference Network (NFIN) is proposed to overcome the disadvantages
of the BPNN and FLC.
Temperature control is an important factor in many process control systems
(Khalid et al., 1993; Khalid
and Omatu, 1992; Tsai et al., 2008). If the
temperature is too high or too low, the final product is seriously affected.
Therefore, it is necessary to reach some desired temperature points quickly
and avoid large overshoot.
Since the processcontrol systems are often nonlinear and tend to change in an unpredictable way, they are not easy to control accurately. In the present study we conducted four sets of experiments, each for 250 and 500 mL min^{1} continuous flow of water with different volume of water and power of heater. In these experiments, the tracking performance of the three controller’s i.e., NFIN controller, FLC controller and conventional PID controller in respect of controlling a set point temperature of 50°C are studied under the same training process via a simulation of above water bath temperature control systems. This study shows that the NFIN has good control performance of the three temperaturecontrol system and is able to cope with the disadvantages of the BPNN. NEURAL FUZZY INFERENCE NETWORK (NFIN) NFIN learning: The learning scheme is mainly composed of two steps. In the first step, the number of rules nodes (hence the structure of the network) and initial rule parameters (weights) are determined using structure identification; in the latter all parameters are adjusted using parameter identification as shown in Fig. 1.
To start the structure tuning, a training set composed of inputoutput data
which contains n inputs and one output must be provided. The data points have
been assumed to be normalized in each dimension and they consider as a possible
cluster center which define a measure of the potential of data point (Chiu,
1994). To extract the set of initial fuzzy rules, firstly data is separated
into groups according to their respective classes. Subtractive clustering is
then applied to the input space of each group of data individually for identifying
each class of data. Each cluster center may be translated into a fuzzy rule
for identifying the class.
A fuzzy rule of the following form is adopted in our system:
• 
Rule 1: If X_{1 }is A_{i1 }and X_{2}
is A_{i2} and... then class is c_{1} 
where, X_{i} is the i’th input variable and A is the membership
function (Gaussian type).

Fig. 1: 
Steps of learning scheme for NFIN 
For each rule, the first antecedent corresponds to the first input, the second antecedent corresponds to the second input etc. and for output we use centroid defuzzification method. The parameters of the initial fuzzy rules are tuned by using neural network techniques through parameter identification. A neural network with four layers is designed based on the fuzzy rules obtained in first phase. To realize the described fuzzy inference mechanism, the operation of a neural network is shown in Fig. 2 and structure of NFIN described below. Structure of the NFIN: The NFIN consists of nodes, each of which has some finite fanin of connections represented by weight values from other nodes and fanout of connections to other nodes as shown in Fig. 3. Associated with the fanin of a unit is an integration function f which serves to combine information, activation or evidence from other nodes. This function provides the net input for this node:
where, u_{1}^{(k)}, u_{2}^{(k)}, ..... u_{p}^{(k)}
are inputs to this node and w_{1}^{(k)}, w_{2}^{(k)},
..... w_{p}^{(k)} are the associated link weights.
The superscript (k) indicates the layer number. A second action of each node
is to produce an activation value as a function of its netinput:
where, a (.) denotes the activation function. In a standard form:
Now the functions of the nodes in each of the layers are described below (Farivar
et al., 2009).
Layer 1: No computation is done in this layer. Each node in this layer which corresponds to only one input variable, transmits input values to the next layer directly. That is: In the above equation, the link weight (w_{i}) in layer one is unity. Layer 2: Units in this layer receives the input value (X_{1}, X_{2}… X_{n}) and acts as the fuzzy sets representing the corresponding input variable. Nodes in this layer are arranged into j groups; each group representing the IFpart of a fuzzy rule. Node (i, j) of this layer produces its output H^{(2)}_{ij}, by computing the corresponding Gaussian membership function: where, m_{ij} is center (or mean) and σ_{ij} is width (or variance) of the membership function. Layer 3: The number of nodes in this layer is equal to the number of fuzzy rules. A node in this layer represents a fuzzy rule; for each node, there are n fixed links from the input term nodes representing the IFpart of the fuzzy rule. Node H_{ij}^{(3)} of this performs the AND operation by product of all its inputs from layer 2. For instance: Layer 4: This layer contains only one node whose output O^{(4)} represents the result of centroid defuzzification, i.e.,: where
Where, c_{j} is the class of data as discussed above and it is also
called the fuzzy singletons defined on output variables. Apparently, m_{ij},
σ_{ij} and c_{j} are the parameters that can be tuned to
improve the performance of the system. The above parameters have been tuned
by using parameter learning. After that a hybrid learning algorithm which combines
the gradient descent method and the Least Square Estimator (LSE) method is used
to refine these parameters. Since gradient descent method is generally slow
and likely to become trapped in local minima when it can be apply to identify
the parameters in an adaptive network.
The following parameter learning is performed on the whole network after structure
learning. The idea of backpropagation (Rumelhart and McClelland,
1986) is used for this supervised learning. The goal is to minimize the
error function:
where, y^{d }(t) is the desired output and y (t) is the current output. For each training data set, starting at the input nodes, a forward pass is used to compute the activity levels of all the nodes in the network. Then starting at the output nodes, a backward pass is used to compute ∂E/∂y for all the hidden nodes. Assuming that adjustable parameter w is m_{ij} and σ_{ij} in a node, the general learning rule used is: where, η is the learning rate and: To show the learning rule, we shall show the computations of ∂E/∂w, layer by layer, starting at the output nodes and we will use the membership functions with centers m_{i}’s and widths σ_{i}’s as the adjustable parameters for these computations. These adjustable parameters are updated by the backpropagation algorithm. Using the chain rule, we have: where, And m_{ij}^{(2)} is updated by: Similarly, we have: Where: And σ^{(2)}_{ij} is updated by: EXPERIMENTAL AND SIMULATION STUDIES
Problem statement: The continuoustime temperature control of a water
bath system (Tanomaru and Omatu, 1992) is described
as:
where, y (t) is system output temperature in °C, u (t) is heating flowing inward the system, Y_{o} is room temperature, R and C are the equivalent thermal resistance and capacity between the system borders and surroundings respectively. We assume both quantities to be constant; now rewrite the above Eq. 22 into discrete time form as: where,
Equation 23 models a real water bath temperaturecontrol
system, where α and β are some constant values describing R and C.
The system parameters used in this example are α = 1.00151e^{4};
β = 8.67973e^{3}, γ = 40.0 and y_{o} =25.0°C
which were obtained from a real water bath. The plant input u (k) is limited
between 0 volt and 5volt. The sampling period is T_{s} = 30 sec. The
system configuration is shown in Fig. 4, where y^{d}
is the desired temperature of the controlled plant.
Experimental setup: To see whether the proposed NFIN can achieve good
performance and overcome the disadvantages of the BPNN, we compare it with the
BPNN under the same aforementioned training procedure on a simulated water bath
temperaturecontrol system. The schematic diagram of the experimental setup
of the water bath temperature controller is shown in Fig. 5.
The hardware for controlling the temperature of the bath has been designed and
fabricated around the Atmel microcontroller 89C51. The temperature of the bath
is acquired with the help of PRT. When the PRT is excited with a constant current
source of 1mA current, it gives the output in voltage form. The voltage is so
amplified that the value of the amplified voltage is equal to the temperature.
This voltage is then fed to the 4½ digit ADC. This digitized voltage
is then sent to the PC by microcontroller through RS232C interface. The program
in PC does the calculations using the NFIN algorithm. After doing all the calculations
it generates the firing angle to control the energy in the water bath and sends
the same to the microcontroller.

Fig. 4: 
Block diagram of NFIN controller 

Fig. 5: 
Schematic diagram of the experimental setup 

Fig. 6: 
Block diagram of FLC 
Thereafter, microcontroller triggers the triac accordingly. The NFIN program
in PC continuously monitors the temperature and accordingly controls the same
in the bath. In case it senses any change in the temperature, it automatically
modifies the parameters of the temperature controller. The NFIN program in PC
has been written in Visual BASIC5.0 language. The program stores the data in
the user defined file as well as plots the online data in the form of graph
on the screen. A specially designed varying environment is created by continuous
flow of fresh water in such a way that the level of the water inside the bath
remains constant even if the hot water is removed at random outflow rates. Uniform
heat distribution is maintained using the circulator and the isolated system
is used to minimize external disturbance. The cooling is achieved at a constant
rate using the refrigeration system of the bath.
Experimental results: In this study, we compare the NFIN controller to the FLC and PID controller. Each of the three controllers is applied to the water bath temperature control system. The comparison performance measures include setpoints regulation and parameter variation as change in volume of water and change in power of heater in the system.
The discrete form of PID controller can be described by well known expression
(Lin et al., 2006; Anderson,
1987). In this control system K_{p} and K_{i} are set as
2.5 and 100, respectively and K_{d }is kept at constant value of 10.
For the Fuzzy Logic Controller (FLC) as shown in Fig. 6,
the input variables are chosen as e(t) and ce(t), where e (t) is the performance
error indicating the error between the desired water temperature and the actual
measured temperature and ce(t) is the rate of change in the performance error
e(t).

Fig. 7: 
Membership functions for e (t), ce (t) and u (t) 

Fig. 8: 
Temperature response of a water bath having 5 L volume at
0.5 KW for 250 mL min^{1} flow using NFIN, FLC and PID controller 
The output or the controlled linguistic variable is the voltage signal u (k)
to the heater. Seven fuzzy terms are defined for each linguistic variable. These
fuzzy terms consist of Negative Large (NL), Negative Medium (NM), Negative Small
(NS), Zero (ZE), Positive Small (PS), Positive Medium (PM) and Positive Large
(PL). Each fuzzy term is specified by a Gaussian membership function as shown
in Fig. 7. According to common sense and engineering judgment,
49 fuzzy rules are specified in Table 1. Like other controllers,
a fuzzy controller has some scaling parameters to be specified. They are GE,
GCE and GU, corresponding to the process error, the change in error and the
controller’s output, respectively.
In the water bath, four sets of experiments were conducted, each for 250 and
500 mL min^{1} continuous flow of water. In these experiments, the
tracking performance of the three controllers i.e., NFIN controller, FLC controller
and conventional PID controller in respect of controlling a setpoint temperature
of 50°C are studied. The four systems of these two flows of water are categorized
in terms of volume of water and power of heater as shown in Table
2.

Fig. 9: 
Temperature response of a water bath having 10 L volume at
1.0 KW for 250 mL min^{1} flow using NFIN, FLC and PID controller 
Table 1: 
Fuzzy rule base 

Table 2: 
Different values of system parameters 


These are: (1) 5 L with 0.5 KW, (2) 10 L with 1.0 KW, (3) 10 L with 1.5 KW
and (4) 15 L with 1.5 KW. In this way overall eight experiments were conducted
in the water bath.
The simulation results for 250 mL min^{1} continuous flow rate of
water for 5 L with 0.5 KW, 10 L with 1.0 KW, 10 L with 1.5 KW and 15 L with
1.5 KW are shown in Fig. 811, respectively.
In these graphs the temperature response of three controllers are shown simultaneously
for comparison. It is clear from these figures that there is always large overshoot
and settling time for conventional PID controller and also for all the systems.
The temperature control performance of FLC controller is also not satisfactory
as it takes large settling time. These problems with both the controllers happen
because on implementing the FLC, the numbers of rules and membership functions
have to be decided and tuned by hand and PID controller needs proper tuning
of K_{p}, K_{i} and K_{d} parameters.

Fig. 10: 
Temperature response of a water bath having 10 L volume at
1.5 KW for 250 mL min^{1} flow using NFIN, FLC and PID controller 

Fig. 11: 
Temperature response of a water bath having 15 L volume at
1.5 KW for 250 mL min^{1} flow using NFIN, FLC and PID controller 
Altogether we say that both controllers require a long time in design for
achieving good performance. On the other hand NFIN controller takes much less
settling time and overshoot as compare to FLC and PID controller, to achieve
desired temperature of 50°C. This occurs because on implementing the NFIN
controller, no controller parameters have to be decided in advance. We only
need to choose proper training patterns and the input vector of the NFIN controller.
When we compare the results of Fig. 9 with 10 having same
volume of water as 10 L but different power of heater than it is observed that
10 L with 1.0 KW system gives best result for controlling desired temperature.

Fig. 12: 
Temperature response of a water bath having 5 L volume at
0.5 KW for 500 mL min^{1} flow using NFIN, FLC and PID controller 

Fig. 13: 
Temperature response of a water bath having 10 L volume at
1.0 KW for 500 mL min^{1} flow using NFIN, FLC and PID controller 
It means, for good tracking control of the system using NFIN, the volume of
water should be increased through proportion of 0.5 L with 0.5 KW power of heater.
The same trend of results, as discussed in above section, is obtained for the
remaining four systems with 500 mL min^{1} flow rate of water as shown
in Fig. 1215, respectively. It is also
noticeable that systems of 250 mL min^{1} flow rate of water gives
better result with less settling time and overshoot as compare to systems of
500 mL min^{1} flow rate of water with same configuration.
One can say that in our temperature controller the NFIN tracked well the set
point temperature of 50°C by the optimal design of PID parameters using
neural network in combination with fuzzy inference rules.

Fig. 14: 
Temperature response of a water bath having 10 L volume at
1.5 KW for 500 mL min^{1} flow using NFIN, FLC and PID controller 

Fig. 15: 
Temperature response of a water bath having 15 L volume at
1.5 KW for 500 mL min^{1} flow using NFIN, FLC and PID controller. 
It means among the three controllers, NFIN controller has the shortest risetime
and the best regulationcontrol performance with smallest errors in the tracking
path.
CONCLUSION
In conclusion, in this study, a temperature controller based on Neural Fuzzy
Inference Network (NFIN) has been proposed to control precisely the desired
temperature of water bath. The NFIN is a fuzzy rulebased network possessing
neural network's learning ability. The four experiments were conducted, each
for 250 and 500 mL min^{1} flow of water for different volume of water
and power of heater. The experimental results of NFIN controller has been compared
with FLC and conventional PID controllers, through implement on above systems.
These results show that NFIN controller has better control performance in terms
of less settling time with minimum overshoot and error than the other two controllers.

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