Online Adaptive Control for Non Linear Processes Under Influence of External Disturbance

Nisha Jha, Udaibir Singh, T.K.Saxena & Avinashi Kapoor
International Journal of Artificial Intelligence and Expert System (IJAE), Volume (2) : Issue (2) : 2011 36
Online Adaptive Control for Non Linear Processes Under
Influence of External Disturbance
Nisha Jha nishajha2010@gmail.com
Department of Electronic Science
University of Delhi South Campus
New Delhi, 110021, India
Udaibir Singh uday_mac2001@yahoo.co.in
Department of Electronics
Acharya Narendra Dev College
University of Delhi
Govindpuri, Kalkaji, New Delhi, 110019, India
T.K. Saxena tushyks@gmail.com
National Physical Laboratory
Dr. K.S. Krishnan Road
New Delhi, 110 012, India
Avinashi Kapoor avinashi_kapoor@yahoo.com
Department of Electronic Science
University of Delhi South Campus
New Delhi, 110021, India
Abstract
In this paper a novel temperature controller, for non linear processes, under the influence of
external disturbance, has been proposed. The control process has been carried out by Neural
Network based Proportional, Integral and Derivative (NNPID). In this controller, two experiments
have been conducted with respect to the setpoint changes and load disturbance. The first
experiment considers the change in setpoint temperature in steps of 10oC from 50oC to 70oC for
three different rates of flow of water. In the second experiment the load disturbance in terms of
addition of 100ml/min of water at three different time intervals is introduced in the system. It has
been shown that, in these situations, the proposed controller adjusts NN weights which are
equivalent to PID parameters in both the cases to achieve better control than conventional PID. In
the proposed controller, an error less than 0.08oC have been achieved under the effect of the
load disturbance. Moreover, it is also seen that the present controller gives error less than
0.11oC, 0.12oC and 0.12oC, without overshoot for 50oC, 60oC and 70oC, respectively, for all
three rate of flow of water.
Keywords: Neural Network Based PID (NNPID) Controller, Temperature Controller, Back-
propagation Neural Network, Load Disturbance.
1. INTRODUCTION
Temperature control is an important factor in chemical, material and semiconductor
manufacturing processes [1]-[3]. To design a general purpose temperature controller with good
response time, smaller error and overshoot with load disturbance for the industrial implementation
is still a challenge in the control research field. Over the past several years the on-off control and
PID control schemes have been employed in commercial products with reasonable success.
A PID controller is the classical control algorithm in the field of process control. It still
predominates in the process industries due to its robustness and effectiveness for a wide range
of operating conditions and partly to its functional simplicity [4]. For the existing controllers, there

are three important parameters, namely, Kp, Ki and Kd which need to be evaluated [5]. The
problem associated with the PID controller is to choose optimal value of these parameters so that
the desired output is yielded for the appropriate process inputs. Usually, process engineers tune
PID controller manually for an operation which, if done diligently, can take considerable time.
Therefore, it is hard to establish an accurate dynamic model for a PID controller design. When the
system has external disturbances, such as the variations of loads and changing process
dynamics, then the transient response may go down. For this reason, free intelligent control
schemes have gained the researcher attention.
In order to overcome the above disadvantages [4], [6], [7], researchers have proposed some
adjusting rules for the self tuning controllers (STC) [8]-[19]. They have considerable potential for
the process control problems since STCs provide a systematic and flexible approach for dealing
with uncertainties, nonlinearities, and time varying parameters. A basic model structure for static
nonlinearities is the back-propagation neural network (BPNN) [20]. The major advantages of
BPNN over the traditional controller is that it can tune the three PID parameters on-line without
requiring the prior knowledge of the mathematical model of different plants. Besides, the other
advantages include its nonlinear mapping and self-learning abilities in various control processes,
such as temperature control. It may be mentioned that the time varying and complex nonlinearity
problems associated with PID controllers have been addressed by other researchers also using
different algorithms [21], [22].
Neural Networks (NN) [23], which is the focus of the current work, is a better alternative to solve
control engineering problems. It can be applied in two different ways: one is to use the NN to
adjust the parameters of PID controller and the other is to use it as a direct controller. PID
parameter values can also be adjusted by creating NN system based on the system output error
signal [24]-[26], [27]-[30]. Prominent among them are the inverse model neuro-control approach
by Widrow and Steams [29] and Psaltis, et al. [30] and further modified by other researchers [31]-
[34].
In the present paper we have investigated two conditions viz the change in setpoint temperature
and the load disturbance using Neural Network PID (NNPID) controller. In both the cases NN
weights equivalent to PID parameters, are trained to achieve better control than existing
conventional PID.
2. PROPOSED DESIGN APPROACH AND EXPERIMENTAL DETAILS
Fig.1 shows the block diagram of the proposed approach followed in the present work. According
to this block diagram, the actuating error, Terr, can be expressed as
Terr = Ts- To (1)
Where Ts and To are the setpoint temperature and observed temperature respectively and Terr is
the error in terms of temperature.
The design of NNPID is shown in Fig. 2. It consists of three layers which are input layer, hidden
layer and output layer. The input layer has two neurons represented by I1 and I2.The output layer
FIGURE 1: Block Diagram of the approach followed

FIGURE 2: Neural Network tuning of PID Controller
has one neuron represented by O1. The hidden layer has three neurons and they are symbolized
as H1 (P-neuron), H2 (I-neuron) and H3 (D-neuron) respectively.
In the present case weights for the different layer combinations are taken as follows:
Weights between input layer and hidden layer are
, (2)
Weights between hidden layer and output layer are taken in terms of PID parameters as
, and , (3)
Then, input to hidden layer nodes are defined as
(4)
(5)
(6)
where , and are the inputs of the hidden layer nodes.
The outputs of the hidden layer nodes are equal to their inputs, which can be expressed as
function of proportional, integral and derivative as mentioned below:
(7)
(8)
(9)
Then, input to output layer becomes
(10)
(11)
where , and are output part of hidden layer nodes, and is the input part of
output layer.
Thus eq. (11) illustrates that PID parameters, which compared with weights as given in eq. (3),
are tuned by using NNPID algorithm. It is well-known that most neural networks cannot be
practically used in a controller because the initial connective weights of the neural networks are
randomly selected. The randomized selection procedure imparts instability to the system.
Therefore, it demands more experience to choose or tune PID parameters in order to ensure the
stability. This can be achieved via training and learning capability of NNPID algorithm. The simple
and prevalent algorithm which we have used in our work is BPNN algorithm [20] for weighting
coefficients.
In the present controller, the main aim of the above algorithm is to minimize the error as given in
eq. (12) in order to recover the system quickly from the effects of the external disturbance by
tuning of PID parameters.

(12)
The weights of NNPID controller are adjusted by BPNN algorithm based on steepest descent on-
line training process. It is done in terms of adjusted weights of hidden-to-output layer [ and
input-to-hidden layer [ ] [35]. The increments of weight in hidden-to-output connection are
updated by using the gradient descent method as
(13)
(14)
where η and α are learning coefficient and momentum, respectively. Here the values of these
terms are taken to be η = 0.005 and α = 0.5.
Further eq. (14) can be rewritten as [35]
(15)
(16)
Where we have defined
(17)
Similarly, the incremental weights of input-to-hidden connection are updated as
(18)
(19)
Now, eq. (19) can be rewritten as [35]
(20)
(21)
Where we can define
(22)
(23)
Now we use updated weights, and from eq. (16) and eq. (21) for finding new
weights for hidden-to-output and input-to-hidden connections.
(24)
(25)
The new weights are adjusted by updated weights as per eq. (24) and eq. (25) with iterations till
we get the minimum mean square error in terms of temperature. Now these updated weights are
employed for the experiment discussed below.
The schematic diagram of the experimental setup of the water bath temperature controller is
shown in Fig. 3.
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
platinum resistance thermometer (PRT). When the PRT is excited with a constant current source
of 1mA current, it gives the output in voltage form. This voltage is then fed to the 4½ digit analog
to digital converter (ADC). This digitized voltage is then sent to the personal computer (PC) by
microcontroller 89C51through RS232C interface. The program in PC does the calculations using
the NNPID algorithm. After doing the entire calculations microcontroller controls the TRIAC firing
circuit and the firing angle for the required energy, through heater, to be given to the water bath.
The NNPID 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 NNPID program in PC has been written in Visual

BASIC-5.0 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.
FIGURE 3: Block Diagram of the Experimental Setup
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.
3. EXPERIMENTAL AND SIMULATION RESULTS
In this paper two sets of experiments were conducted in the water bath. In the first set of
experiments, the tracking performance of the two controllers i.e. NNPID controller and
conventional PID controller with respect to setpoint changes are studied. In this system, further
three set of experiments were conducted at three different flow of water i.e. at 100ml/min,
250ml/min and 500ml/min as shown in Figs. 4, 5 and 6 respectively. In these experiments the
setpoint temperature of the water bath was increased in steps of 10o
C from 50o
C to 70o
C to
investigate the effect of flow of water on temperature control at the different setpoint.

0 1000 2000 3000 4000 5000 6000 7000
20
30
40
50
60
70
80
Temperature(
o
C)
Time(sec)
PID
NNPID
FIGURE 4: Showing the comparison of NNPID controller with the conventional PID controller of a water
bath for 100 ml/min flow rate of water with respect to setpoint changes.
The simulation results subjected to the changes in setpoint for different flow rate of water are
shown in Figs. (4-6). The three systems are categorized in terms of change in flow rate of water
are shown in Table I. The settling time taken by NNPID and PID controllers to achieve target
temperatures of 50
o
C, 60
o
C and 70
o
C for different flow rates of water are given in Table II.
According to this table, when we refer Figs. (4-6), we infer that NNPID controller gives better
performance in respect of less settling time as compared to the conventional PID controller in
achieving change in setpoint temperature. Hence the experimental and simulation results of these
systems show the simplicity, reliability and robustness of NNPID over conventional PID.
To compare the results of the NNPID controller with the results of the conventional PID controller,
the parameters of the PID controller were tuned for initial gain setting of NNPID controller by its
best fit values as proportional gain, Kp=2.5, integral gain, Ki=100 and derivative gain, Kd=10. The
neural network fine tunes the system iteratively based on the performance of the closed loop
0 1000 2000 3000 4000 5000 6000 7000
20
30
40
50
60
70
80
Temperature(
o
C)
Time (sec)
PID
NNPID
FIGURE 5: Showing the comparison of NNPID controller with the conventional PID controller of a water bath
for 250 ml/min flow rate of water with respect to setpoint changes.

0 1000 2000 3000 4000 5000 6000 7000
20
30
40
50
60
70
80
Temperature(
o
C)
Time (sec)
NNPID
PID
for 500 ml/min flow rate of water with respect to setpoint changes
Kp 2.5
Ki 100
Kd 10
Power of Heater 1500 Watt
Volume of water 15 liter
Voltage 5volts
Initial and Final Set point
temperature
50o
C and 70o
C
Temperature change +10
o
C
Flow rate of water 100ml/min, 250 ml/min,
500 ml/min
Load disturbance 100ml/min water
TABLE 1: Different Values of System Parameters
system. The temperature response of a water bath having 15 liter volume and heated with a
power of 1.5KW for 100ml/min flow rate of water using NNPID and conventional PID are shown
simultaneously for comparison in Fig.5. Similarly NNPID and conventional PID results for
250ml/min and 500ml/min flow rate of water are shown in Fig.5 and Fig.6 respectively. It is clear
from these figures that there is always overshoot for conventional PID at initial settling time for
each set temperature as 50o
C, 60o
C and 70o
C of the system. This is shown in Table III. This table
also indicates that NNPID controller gives error less than 0.11o
C, 0.12o
C and 0.12o
C without
overshoot for 50
o
C, 60
o
C and 70
o
C respectively for all the three flow rate of water. These errors
are comparatively less than conventional PID controller. In addition, the neural network achieves
setpoint fast as compared to the conventional PID controller as shown in Figs. (4-6). One can
possibly say that the neural network controller tracked well all the three setpoint and has good
generalization capability even with a small number of training patterns.

NNPID Controller PID Controller
Settling Time Settling Time
Temperature
range
50o
C-60o
C 60o
C-70o
C 50o
C-60o
C 60o
C-70o
C
100 ml/min 7min 9min 30sec 23min 23min 30sec
250 ml/min 11min 18min 30sec 31min 31min
500 ml/min 17min 27min 35min 35min
TABLE 2: Settling Time of NNPID and PID Controllers For Three Flow Of Water
NNPID Controller Conventional PID Controller
Error without Overshoot Error with Overshoot
Set
Temperature
50
o
C 60
o
C 70
o
C 50
o
C 60
o
C 70
o
C
Error Over
shoot
Error Over
shoot
Error Over
shoot
100 ml/min
flow
0.09
o
C 0.10
o
C 0.10
o
C 1.38
o
C 4.49
o
C 1.0
o
C 3.03
o
C 1.0
o
C 2.01
o
C
250 ml/min
flow
0.10
o
C 0.11
o
C 0.12
o
C 2.32
o
C 4.35
o
C 1.87
o
C 4.9
o
C 2.73
o
C 4.47
o
C
500 ml/min
flow
0.11
o
C 0.12
o
C 0.11
o
C 2.54
o
C 4.93
o
C 1.90
o
C 4.77
o
C 2.88
o
C 5.48
o
C
TABLE 3: Error and Overshoot of NNPID and Conventional PID controller for three rate of flow of water
0 1000 2000 3000 4000 5000 6000
25
30
35
40
45
50
55
60
Temperature(
o
C)
Time (sec)
PID
NNPID
under the effect of load disturbances.
In second set of experiments, the load disturbances in terms of addition of 100ml/min water were
introduced in the process of system for studying the ability of the two controllers when the

external disturbance was imposed. These external disturbances were made in three steps at
different interval of time. These three disturbances were added to the output at 43min, 59min and
84min respectively for PID controller and for NNPID controller at 25min, 49min and 72min as
shown in Fig. 7. It could be observed from this figure that when we introduce external disturbance
of 100ml/min of water during three steps in the system for set temperature of 50o
C, the NNPID
controller takes much less settling time and overshoot as compared to conventional PID
controller. So it is appropriate to say that neural network controller recovered fast with error less
than 0.08 o
C with less overshoot under the effect of these load disturbances. So we are able to
say that NNPID controller has ability to adapt quickly to changes at its input. On the other hand
the conventional PID controller has poor rate of recovery which deteriorate the system.
Additionally, it has error greater than 0.2o
C. Our experimental setup gives better settling time,
less overshoot and minimum deviation in setpoint.
4. CONCLUSION
In conclusion, the present work shows the new approach of controlling the temperature of the
dynamic system. This particular system designed and developed around Atmel’s 89C51
microcontroller employed on a water bath. The temperature control of the system has been
analyzed by conducting two experiments in respect of setpoint changes and load disturbances.
The first experiment considers change in setpoint temperature in step of 10
o
C from 50
o
C to 70
o
C
for three different rate of flow of water. It is observed that NNPID controller gives error less than
0.11
o
C, 0.12
o
C and 0.12
o
C without overshoot for 50
o
C, 60
o
C and 70
o
C respectively for all three
flow rate of water. In second experiment, the load disturbance in terms of addition of 100ml/min
water at three different intervals of time is introduced. It gives error less than 0.08
o
C with less
overshoot under the effect of the load disturbance. In both the cases NN weights corresponding
to PID parameters, are trained, to achieve better control than existing conventional PID. This
paper has shown that inexpensive neural hardware may become an important technology for
many modern industrial control applications.
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