World Academy of Science, Engineering and Technology 47 2008
Auto Tuning PID Controller based on Improved
Genetic Algorithm for Reverse Osmosis Plant
Jin-Sung Kim, Jin-Hwan Kim, Ji-Mo Park, Sung-Man Park, Won-Yong Choe
and Hoon Heo
of water that passes through the membrane reducing strongly
Abstract— An optimal control of Reverse Osmosis (RO) plant is the solute concentration is called permeate. The remaining
studied in this paper utilizing the auto tuning concept in conjunction water (brine) is discharged with a high salt concentration.
with PID controller. A control scheme composing an auto tuning In the last years, significant advances in the membrane
stochastic technique based on an improved Genetic Algorithm (GA) is
technology have allowed an essential improvement in the
proposed. For better evaluation of the process in GA, objective
function defined newly in sense of root mean square error has been filtering quality and simultaneously a general reduction of costs.
used. Also in order to achieve better performance of GA, more Hence, RO plants have today lower energy consumption,
pureness and longer period of random number generation in operation investment cost, space requirements and maintenance than
are sought. The main improvement is made by replacing the uniform other desalination processes [2].
distribution random number generator in conventional GA technique On the other hand, RO desalination plants are energy
to newly designed hybrid random generator composed of Cauchy
intensive and require fine tuned components. Therefore, a good
distribution and linear congruential generator, which provides
independent and different random numbers at each individual steps in control design is necessary to maintain water production costs
Genetic operation. The performance of newly proposed GA tuned at acceptable level and to elevate the plant availability,
controller is compared with those of conventional ones via simulation. particularly in regions with high water scarcity. Therefore, an
advanced control technique is required for more efficient
operation of RO plant. In this paper new GA technique is
Keywords—Genetic Algorithm, Auto tuning, Hybrid random implemented on RO system. [3].
number generator, Reverse Osmosis, PID controller Many PID tuning methods are introduced. The Ziegler
Nichols method is an experimental one that is widely used,
I. INTRODUCTION despite the requirement of a step input application with stopped
A ccording to a report from UNESCO, by the middle of this
century, at worst 7 billion people in sixty countries will be
water scarce, at best 2 billion people in forty eight countries.
process [4]. One of disadvantage on this method is the
necessary of the prior knowledge regarding plant model. Once
tuned the controller by Ziegler Nichols method a good but not
This expectation makes necessary for humanity to look for new optimum system response will be reached. The transient
alternative ways of ensuring a dependable supply of drinking response can be even worse if the plant dynamics change. It
water. The significance of this problem is increasing in the must be noticed that a great amount of plants has time-varying
underdeveloped countries as well as in industrialized regions. dynamics due to external/environmental causes, e.g.
Desalination of seawater and brackish water is one of the temperature and pressure. To assure an environmentally
alternatives for ensuring a dependable supply of drinking water. independent good performance, the controller must be able to
In recent years the process of reverse osmosis (RO) has become adapt the changes of plant dynamic characteristics [5].
a significant technical option to solve this problem through the For these reasons, it is highly desirable to increase the
desalination of seawater [1]. capabilities of PID controllers by adding new features. Many
RO is a process used to clean brackish water or to desalt random search methods, such as genetic algorithm (GA) have
seawater. The process consists in recovering water from a recently received much interest for achieving high efficiency
saline solution pressurized by pumping it into a closed vessel to and searching global optimal solution in problem space [6].
a point grater than the osmotic pressure of the solution. Thus, Due to its high potential for global optimization, GA has
the solution is pressed against a membrane so that it is received great attention in control systems such as the search of
separated from the solutes (the dissolved material). The portion optimal PID controller parameters. Although GA has widely
been applied to many control systems, its natural genetic
operations would still result in enormous computational efforts
Jin-Sung Kim, Jin-Hwan Kim, Ji-Mo Park, Sung-Man Park, Won-Yong
Choe., and Hoon Heo are with Department of Control and Instrumentation [7].
Engineering, Korea University, Seoul 137-701 South. Korea (e-mail: {yawaya,
2000240636, lockhart, yamjun99, untamed, heo257}@korea.ac.kr}.
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World Academy of Science, Engineering and Technology 47 2008
II. PID CONTROLLER KD s 2 KP s KI
The PID controller is well known and widely used to CPID(s) (4)
s
improve the dynamic response as well as to reduce or eliminate
the steady state error. The derivative controller adds a finite
zero to the open loop plant transfer function and improves the III. GENETIC ALGORITHM
transient response. The integral controller adds a pole at the
origin, thus increasing system type by one and reducing the The basic principles of GA were first proposed by Holland.
steady state error due to a step function to zero. This technique was inspired by the mechanism of natural
PID control consists of three types of control, Proportional, selection, a biological process in which stronger individual is
Integral, and Derivative control. likely to be the winners in a competing environment. GA uses a
direct analogy of such natural evolution to do global
optimization in order to solve highly complex problems [14]. It
presumes that the potential solution of a problem is an
individual and can be represented by a set of parameters. These
parameters are regarded as the genes of a chromosome and can
be structured by a string of concatenated values. The form of
variables representation is defined by the encoding scheme.
The variables can be represented by binary, real numbers, or
other forms, depending on the application data. Its range, the
Fig.1 schematic of conventional PID controller search space, is usually defined by the problem.
A. Proportional Control
The proportional controller output uses a ‘proportion’ of the
system error to control the system. However, this introduces an
offset error into the system.
Pterm KP u ERROR (1)
B. Integral control
The integral controller output is proportional to the amount
of time there is an error present in the system. The integral
action removes the offset introduced by the proportional
control but introduces a phase lag into the system.
I term K I u ³ ERRORdt (2)
C. Derivative control
The derivative controller output is proportional to the rate of
change of the error. Derivative control is used to Fig. 2 flow chart of the general genetic algorithm
reduce/eliminate overshoot and introduces a phase lead action
that removes the phase lag introduced by the integral action. GA has been successfully applied to many different
problems, such as: traveling salesman, graph partitioning
d (ERROR.) problem, filters design, power electronics, etc. It has also been
Dterm KI u (3) applied to machine learning, dynamic control system using
dt learning rules and adaptive control. The combination of GA
with other Artificial Intelligence techniques, like Fuzzy Sets
D. Continuous PID control and Artificial Neural Network, in hybrid system has been the
The three types of control are combined together to form a solution for a great amount of problems. Success of GA solving
PID controller with the transfer function [8]. high dimensional problem has been reported in the literature
too. An illustrative flowchart of the GA algorithm
implementation is presented in Figure 2. In the beginning an
initial chromosome population is randomly generated. The
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World Academy of Science, Engineering and Technology 47 2008
chromosomes are candidate solutions to the problem. Than, the there exist some crossover types. The so called arithmetic
fitness values of all chromosomes are evaluated by calculating crossover generates an offspring as a component wise linear
the objective function in a decoded form. So, based on the combination of the parents in later phases of evolution it is
fitness of each individual, a group of the best chromosomes is more desirable to keep individuals intact, so it is a good idea to
selected through the selection process. The genetic operators, use an adaptively changing crossover rate: higher rates in early
crossover and mutation, are applied to this “surviving” phases and a lower rate at the end of the GA. Sometimes it is
population in order to improve the next generation solution. also helpful to use several different types of crossover at
Crossover is a recombination operator that combines subparts different stages of evolution
of two parent chromosomes to produce offspring. This operator
C. Mutation
extracts common features from different chromosomes in order
to achieve even better solutions. Mutation is an operator that A new individual is created by making modifications to one
introduces variations into the chromosome. This operation selected individual. The modifications can consist of changing
occurs occasionally with a small probability. It randomly alters one or more values in the representation or adding/deleting
the value of a bit, in case of binary coding. In real coding it parts of the representation. In GA, mutation is a source of
changes the entire value of a chromosome. Through the variability and too great a mutation rate results in less efficient
mutation operator the search space is explored by looking for evolution, except in the case of particularly simple problems.
better points. The process continues until the population Hence, mutation should be used sparingly because it is a
converges to the global maximum or another stop criterion is random search operator; otherwise, with high mutation rates,
reached [9]. the algorithm will become little more than a random search.
Moreover, at different stages, one may use different mutation
operators. At the beginning, mutation operators resulting in
IV. GENETIC OPERATOR bigger jumps in the search space might be preferred. Later on,
when the solution is close by a mutation operator leading to
In each generation, the genetic operators are applied to
slighter shifts in the search space could be favored [10][18].
selected individuals from the current population in order to
create a new population. Generally, the three main genetic
operators of reproduction, crossover and mutation are V. EVALUATE THE PROCESS USING FITNESS
employed. By using different probabilities for applying these FUNCTION
operators, the speed of convergence can be controlled.
Crossover and mutation operators must be carefully designed, A. Objective function
since their choice highly contributes to the performance of the The most crucial step in applying GA is to choose the
whole genetic algorithm. objective functions that are used to evaluate fitness of each
A. Reproduction chromosome. Some works use performance indices as the
A part of the new population can be created by simply objective functions. The objective functions are Mean of the
copying without change selected individuals from the present Squared Error (MSE), Integral of Time multiplied by Absolute
population. Also new population has the possibility of selection Error (ITAE), Integral of Absolute Magnitude of the Error
by already developed solutions. (IAE), and Integral of the Squared Error (ISE)[8][11].
There are a number of other selection methods available and
W W
it is up to the user to select the appropriate one for each process. 1
(e(t))2dt ITAE
t ³0 ³ t e(t)dt
MSE
All selection methods are based on the same principal i.e. 0 (5)
giving fitter chromosomes a larger probability of selection. W W
2 2
Four common methods for selection are: ISE ³ e(t) dt
0
ITSE ³ te(t) dt
0
1. Roulette Wheel selection
2. Stochastic Universal sampling B. The fitness values
3. Normalized geometric selection The PID controller is used to minimize the error signals, or
4. Tournament selection we can define more rigorously, in the term of error criteria: to
And author uses Roulette Wheel selection. minimize the value of performance indices mentioned above.
B. Crossover And because the smaller the value of performance indices of
New individuals are generally created as offspring of two the corresponding chromosomes the fitter the chromosomes
parents (i.e., crossover being a binary operator). One or more so will be, and vice versa, we define the fitness of the
called crossover points are selected (usually at random) within chromosomes as (6) [11][18].
the chromosome of each parent, at the same place in each. The
parts delimited by the crossover points are then interchanged 1 (6)
Fitness value
between the parents. The individuals resulting in this way are Performanc
e index
the offspring. Beyond one point and multiple point crossover,
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World Academy of Science, Engineering and Technology 47 2008
VI. PROPOSED NEW METHODS input of linear congruential generator.
This paper presents an advanced auto tuning PID controller (ฌ) The mechanism of linear congruential generator is
represented as (8).
for RO plant to search the optimal control gain parameters kP ,
kI , kD with improved GA. The searching steps of the Xi ( aX i 1 c ) mod m ;i 1, 2 ,3 L (8)
proposed optimal PID controller are shown as below. The 0 m, a m, c m, X0 m
improved GA has new random generator and objective
Where X 0 the initial value that selected at random. Random
value is that X 1 divided by m [16] [17]. This method can
kP
expand the period of random function effectively if the
kI
kD
condition satisfies. As a result, the output value is improved
random number.
(ญ) Return the final value to GA.
The newly designed random number generator gives more
Fig. 3 schematic of auto tuning PID controller based on improved GA reliable random generator than normally using conventionally
one.
function.
B. New objective function
A. New random generation In control engineering, Mean of the Squared Error (MSE),
Integral of Time multiplied by Absolute Error (ITAE), Integral
of Absolute Magnitude of the Error (IAE), and Integral of the
Squared Error (ISE) are used as objective function of GA
universally. However in the study use of new objective
function is attempted for RO plant, which is Root Mean Square
Error (RMSE) represented as in (9).
W
1
(e(t ))2 dt
t ³0
R MSE (9)
Fig. 4 schematic of proposed hybrid random generator
Fig 4 is the structure of new hybrid random generator.
Fig. 5 shows the schematic diagram of application of new
Generally, GA is constructed on the basis of probability
hybrid random number generating method and objective
using random function. Conventional GA has used random
function in the MATLAB or C language library. However more
reliable random functions are required for better performance
of GA.
This study proposes more pureness and longer period of
random number generation for GA. The steps are listed below.
(ช) Call the random generator function to make random
values during GA processing.
(ซ) Get a first random number from Cauchy distribution
function method, which is represented as (7).
F ( p, x0 , J ) x 0 J tan[ S ( p 0 . 5 )] (7)
p is random value between 0 and 1, x 0 is the location
parameter, specifying the location of the peak of the
distribution and J is the scale parameter which specifies the
half width at half maximum. Set as x 0 =0, J =1 generally and it
is called ‘standard Cauchy distribution’ [15]. In this paper set
these values as random from 0 to 1. So probability density
function always changes when GA program is called for
random generator function. The output from Cauchy
Fig. 5 flow chart of the improved Genetic Algorithm
distribution is the expanded value between 0 and 1 and the
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World Academy of Science, Engineering and Technology 47 2008
function for GA.
The improved GA work in this paper as follows. Step Response
1.6
(ช) The initial population tribes are filled with Ziegler Nichols tuned controller
Conventional GA tuned controller
1.4
individuals that are generally created at random. Sometimes, Improved GA tuned controller
the individuals in the initial population are the solutions found 1.2
by some method determined by the problem domain. In this 1
paper, we gave random values to these initial populations. But
Amplitude
0.8
their ranges limited around the values. The ranges of PID 0.6
values are rationally chosen by arbitrary and it is true that the
0.4
limitation will influence the results of the GA search; it is
intended to obtain more stable, efficient and accurate solutions. 0.2
(ซ) Every generation is applied RO plant, which was 0
0 5 10 15 20 25 30
described by PID parameters and produced a group of errors Time (sec)
that calculated the RMSE value from transient to steady state. Fig. 7 step response of improved GA tuned controller vs. Ziegler
(ฌ) Each individual in the current population is evaluated Nichols tuned controller
using the objective function.
GAs converged to final values
(ญ) If the termination standard [i.e., the generation 15
Improved GA
Conventional GA
number > preset number] is met, the best solution (i.e., PID
Kp
10
gain parameters) is returned.
(ฎ) From the current population, individuals are selected 5
0 50 100 150 200 250
based on the previously computed fitness values. A new 6
population is formed by applying the genetic operators (i.e., Ki 4
reproduction, crossover, mutation using random generator) to 2
these individuals. 0
0 50 100 150 200 250
(ฏ) Actions starting from step (ซ) are repeated until the 25
termination standard is satisfied, which is called a 20
Kd
generation.[18] 15
10
0 50 100 150 200 250
Generations
VII. SIMULATION RESULTS
Recently the most widely used RO plant has its control Fig. 8 response trends upon improved GA converging through generation
system utilizing empirically determined parameters. The
simulation concept is shown in Fig. 4, where the GA and PID confirm the effectiveness of the proposed method. Parameters
are set for GAs in the study is as in Table1.
It can be seen that improved GA tuned PID controller
reveals shorter settling time. Moreover the overshoot is
considerably lower than the those obtained via the conventional
GA tuned controller and Ziegler Nichols tuned controller. The
comparison of the performances using improved GA based PID
tuned controller, conventional GA based PID tuned controller
TABLE 2
Fig. 6 simulink of auto tuning PID controller based on improved GA PERFORMANCE COMPARISION
control action are implemented in the MATLAB Item Improved GA GA Ziegler Nichols
environment[12][13]. Peak amplitude 1.19 1.5 1.58
In this section, numerical simulation is conducted to Overshoot (%) 19 49.9 58.1
TABLE I Rising time (sec) 0.966 0.755 1.29
GAS PARAMETER SETTING
Settling time (sec) 5.12 6.92 14.9
Parameter Value Final value 1 1 1
Selection method Roulette wheel P gain 6.71275 10.73984 6
Population size 80
I gain 0.0172 3.2230 1.91
Generation size 220
Crossover probability 65% D gain 11.48921 14.36576 4.74
Mutation probability 0.1%
Ranges of PID gain -1000~1000
values and Ziegler Nichols method are made as shown in Table 2.
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World Academy of Science, Engineering and Technology 47 2008
[16] Stephen K. Park and Keith W. Miller. Random number generators: Good
ones are hard to find. CACM, 31(10):1192–1201, 1988.
[17] Donald E. Knuth. “Deciphering a linear congruential encryption,”. IEEE
VIII. CONCLUSION Transactions on Information Theory, IT-31(1):49–52, January 1985.
[18] T. K. Teng, J. S. Shieh and C. S. Chen, “Genetic algorithms applied in
This paper demonstrated how an improved GA can be used
online autotuning PID parameters of a liquid-level control system,”
for the optimal control of RO plant via computer simulation. A Transaction of the Institute of Measurement and control 25, 5 (2003),
new GA method based on hybrid concept of Cauchy pp.433~450
distribution, linear congruential generator and simultaneous
using of RMSE type objective function to design a controller
for RO plant is presented. Much more improved performance
of proposed GA tuned controller than the conventional ones
has been revealed in terms of overshoot and settling time etc.
Real time implementation of the proposed method is under way.
Also at the same time implementation of micro controller based
on the new method in commercially low cost is being sought.
Although GA needs lot of computation, its real time realization
of the idea will be performed via physical experiment.
ACKNOWLEDGMENT
This research was supported by a grant (C106A152000106A
085700200) from Plant Technology Advancement Program
funded by Ministry of Construction & Transportation of
Korean government
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