ABSTRACT
Optimization has always been the goal in engineering applications but the traditional optimization techniques are incapable of solving many of the problems because they often depend on the quality of the objective functions and they need a vast amount of computation� In this chapter, the artificial fish swarm algorithm (AFSA) is proposed to solve the PID controller tuning problem for several process plants� Although the Ziegler-Nichols (ZN) tuning method and other related methods are the workhorse of the industrial applications, this chapter shows that the AFSA is able to produce better performance compared to ZN method and other swarm intelligence techniques such as particle swarm optimization (PSO) method�
The three-term proportional-integral-derivative (PID) controller is playing a vital role in the field of automation and control, and has been looked upon as a reliable component of industry because of its simplicity and satisfactory performance with a vast range of processes� Because of its modest structure, it has the ability to be easily understood and implemented in real-world environment� Thus, its presence is highly appreciated in practical applications� Conventionally, the PID parameters are tuned by the most commonly used ZN method� But these conventional tuning methods have several limitations (Astrom & Hang, 1991; Visioli, 2006)�
Therefore, recently, many intelligent approaches are used� Of these, swarm approaches are gaining popularity� In engineering studies, the terminology of “swarm” is defined as a group of agents having independent individual dynamics but exhibiting closely coupled behaviors and performing any specific task as a group (Gazi & Passino, 2011)� Another terminology that relates to such a system is termed as “multiagent dynamics system” (Luo, Zhang, & Li, 2007)� From a biological perspective, the term swarm relates to some species when they are in certain behavioral modes� Similar to swarm there are also some biological synonyms such as colonies of ants, flocks of birds, schools of fish, and so on� For many years, scientists and researchers in biology and engineering have been attracted to these coordinated behaviors of such clusters of species� A type of artificial intelligence (AI), swarm intelligence is the study of collective behavior of a reorganized system, usually a set of species that communicate locally among themselves as well as with the environment� There are many algorithms that use swarm techniques such as AFSA, ant colony optimization (ACO), PSO, honeybees optimization (HBO), and others (Li, Shao, & Qian, 2002; Luo, Wei, & Wang, 2010)�
The AFSA is a recent and easy-to-implement artificial life-computing algorithm that simulates fish swarm behaviors and has been successfully used in some engineering applications� A variety of techniques have been proposed to handle the equality and inequality constraints of the problem� In this context, parameter estimation in engineering systems (Li, Xue, Lu, & Tian, 2004), determination of cluster number using average information entropy and density function based on fuzzy C-means cluster analysis and FSA (Zhu, Jiang, Song, & Bao, 2011), feed-forward neural networks (Wang, Zhou, & Ma, 2005), infinite impulse response (IIR) digital filter design (Yin & Tian, 2006), combinatorial optimization problem (Cai, 2010), forecasting stock indices using radial basis function neural networks (Shen, Guo, Wu, & Wu, 2011), Augmented Lagrangian fish swarm-based method for global optimization (Rocha, Martins, & Fernandes, 2011), hybridization of the FSA with the particle swarm algorithm to solve engineering systems (Tsai & Lin, 2011), combinatorial problems (Zheng & Lin, 2012), parameter estimation in control problems (Lobato, Souza, & Gedraite, 2012), and other applications (Wang, Gao, Cai, & Huang, 2006; Jiang, Wang, Pfletschinger, Lagunas, & Yuan, 2007)�
In this chapter, the details on principles of AFSA and their implementation details for PID tuning are discussed� In addition, its application in four different process plants is explored� A comparative analysis of the performance of AFSA with ZN tuning and PSO methods was carried out�
In the underwater world, fish can find areas with more food based on their individual or swarm search� Inspired by this characteristic, the AFSA model is represented by searching, swarming, and following behaviors� The artificial fish (AF) model searches the problem space by those behaviors� The environment where the AF lives in is the problem space� The objective function of AFSA is to find maximum food density (Reza, 2014)� Figure 5�1 shows that the AF model observes external concepts with its visual perception�
5.2.1.1 Structure of AFSA The current position of AF is shown by vector,
( )=X x x x, ,..., n1 2 (5�1) where xi (i = 1,…, n)�
The Visual is equal to visibility domain of AF and Xv is an intended position in Visual where the AF selects to move toward� If Xv has better food density than current position, AF moves one step toward Xv, which results in displacement of the AF from X to Xnext� Otherwise, if the current position of the AF is better than Xv, it selects another position in its Visual� Food density in position X is the fitness value of the position and is shown with Food Concentration (FC)�
The state of AFSA individual can be represented as a vector; the variable Xi is for searching optimum value�
FC = f(X), represents the present position of AF food consistence where the objective function is FC�
The total distance between two AF individuals is represented by:
= −d X Xi j i j, (5�2)
where Vision is distance of visibility, Step is step length (maximum), and Delta (δ) is crowded factor�
AFSA model has got the most significance in the overall optimization process of PID parameters using AFSA� In the study the parameters that need to be optimized are Kp, Ki, and Kd� The AF vector can be expressed as
( )=X K T T, ,p i d (5�3) And the total distance between two AF individuals can be represented as
( ) ( ) ( )= − + − + −d K K T T T Ti j i j i j i j, p p 2 i i 2 d d 2
(5�4)
At the initial position, the consistence of AF food can be represented by the steps outlined in following section�
5.2.1.2 Behavior Description A. Searching Action
Xi = AF at initial position Xj = AF in the visibility range
If FCi < FCj, proceed with a step within the same direction or else select Xj again�
= +
−
−
>x x x x
X X Random(Step) , FC FCik jk ik
(5�5)
= + ≤x x Random(Step), FC FCik j iinextk (5�6) where K = 1, 2, 3, …, n; Xjk, Xik, and Xinextk represent the k element of state vector Xj, Xi�
B. Swarming Action Xc = AF state at center, FCc = food availability at center�
nf = number of fishes nearby (dij ≤ Visual), if nf ≥ 1, the center position of its fellow is discovered by Xj�
= x
x
n k
(5�7)
= +
−
−
x x x x
X X Random(Step)ik k ik
c (5�8)
C. Following Action Xi = AF at initial position Xmax = Max state FCmax = largest amount of fellow fishes in nearby field (dij ≤ Visual)
If
> δ
n
(5�9)
Fellow Xi has highest consistence of food and if the surrounding is not packed, then proceed with a step to Max�
= +
−
−
x x x x
X X Random(Step)ik k ik
max (5�10)
If nf = 0, AF individual performs the action of searching food� The algorithm establishes a bulletin board and its purpose it to save the optimal
position of AFSA and food consistence of the AFSA at corresponding position�
D. Effect of Parameters While Convergence 1. Visual and Step Searching and moving behavior is more prominent when the vision scope is smaller but in case of larger scope of vision the behavior of following is prominent� So for the better convergence larger scope of vision would be preferable, while the larger step is good for the convergence�
2. Crowd Factor (δ) For maximum desired value, the area of crowded factor is 0 < δ < 1� And, for minimal value, δ < 1�
3. The Total of Fish Individual (N) If the number of fish is high the size of local extreme would be strong, leading to a faster convergence speed but the amount of iterations will be more�
The essence of AFSA optimization searching is the estimation of fitness function� And its design is directly proportional to the performance of AFSA� This study is aimed at the parameters Kp, Ki, and Kd� To establish the objective function is a must to do for evaluation of performance index for searching and optimizing in a certain rule� The essence for designing PID controller is making minimum the system performance of index function J� In this study, the ITAE is used as performance index�
∫= ∞J w t t dt(ITAE) e( ) 0
(5�11)
The representation of objective function for this study is as follows:
J k k(ITAE) DT e( ) k
(5�12)
where DT is the calculation of step, and LP is the number of calculation� In this study the searching is aimed to be maximum; so the fitness functions are
fixed accordingly� Hence, the reciprocal of system performance index is used as fitness function�
= JFC 1/ (ITAE) (5�13)
AFSA creates a group of initialization of parameters as the fish colony to narrow down the area of PID parameters that are being optimized� These three parameters ( )K T T, ,p* i* d* are first tuned by ZN approach and the center is expanded to both directions of polarities as follows:
− λ ≤ ≤ + λ
− λ ≤ ≤ + λ
− λ ≤ ≤ + λ
K K K
T T T
T T T
(1 ) (1 )
(1 ) (1 )
(1 ) (1 )
(5�14)
where λ is the value in [1,0]� In AFSA the convergence is considered to terminate the algorithm when there is
no higher value of fitness function after a number of iterations of searching�
The plant parameters (Kp, Ki, and Kd) are tuned using AFSA as shown in Figures 5�2 and 5�3� The MATLAB Simulink Model was used to carry out the simulation�
In industrial environments, typically, there are several plants that widely use PID tuning to optimize the output� In this study, five plants were studied� Pressure is one of the important conditions to ensure chemical reactions occur at a desired rate� It is also closely related to process temperature and both are closely monitored by plant operators to ensure safety in operation and maintaining product quality� As an example, the vapor-phase flow, pressure, and temperature plant’s piping and instrumentation diagram (P&ID) diagram is shown in Figure 5�4, and is illustrated in Figure 5�5�
The scaled-down vapor-phase flow, pressure, and temperature process pilot plant is a self-contained unit designed to simulate real flow, pressure, and temperature processes of a compressible fluid found in industrial plants Azhar (2010)� Compressed air is used as the medium� This plant consists of two buffer tanks, VE-210 and VE-220, which supply regulated, compressed air to the cooling vessel, VE-240� As more and more air enters VE-240, the inside pressure builds up� However, the compressed air is vented out at a certain rate through the solenoid valve MV-244 to ensure a safe pressure limit inside VE-240�
In order to get the transfer function of the plant, the process reaction curve is needed� The process reaction curve is shown in Figure 5�6 as indicated by the light gray line�
Table 5�1 shows the results obtained from process reaction curve� The general transfer function of the plant is given as
=
τ +
−θ G s
s ( ) e
(5�15)
TABLE 5.1 Readings from the Plant
The derived transfer function of the plant based on the parameters of Table 5�1 is given as
=
+
G s s
( ) e 140 1
(5�16)
The PID parameters that were obtained using the ZN method are shown in Table 5�2� Initially, the PID controller is tuned by ZN method based on the parameter shown
in Table 5�2� The simulated effect of the PID controller is shown in Figure 5�7�
The result of the AFSA simulation is shown in Figure 5�8� Based on Figure 5�8, the new optimized parameters are shown in Table 5�3�
TABLE 5.2 PID Parameters
It can be seen from Figures 5�7 and 5�8 that the system response using AFSA method was better than that using ZN method� The study was compared with other optimization methods such as PSO to validate and observe the mutual response of different optimization approaches� Figure 5�9 shows the responses of different optimization methods�
Based on Figure 5�9, the new optimized parameters are shown in Table 5�4�
TABLE 5.3 AFSA Optimized Parameters
Observing the optimization of PID parameters using different approaches in Table 5�4 we find that the intelligent methods present very acceptable results over the conventional methods of PID tuning� The traditional ZN method gives 63% of overshoot and requires some settling time, while PSO provides acceptably better results than ZN method with the overshoot of only 15% and less settling time� It can be seen that the PID parameter optimization using AFSA provides better results than both ZN and PSO methods where the overshoot is almost equal to 0% and the settling time is really less�
For the further validation of the study, an additional three plants were optimized using AFSA and compared with other optimization approaches as follows:
=
+ +
G s s s
( ) 0.5e 1.24 3.5 1
(5�17)
=
+ + G s
s s ( ) 1
0.1 12 (5�18)
=
+
G s s
( ) e( 1) s0.5
(5�19)
The optimization results of the three plants are shown in Figures 5�10 through 5�12 and Tables 5�5 and 5�6�
The results from Figures 5�10 through 5�12 and Tables 5�5 through 5�7 show that for all the three plants, AFSA produces comparatively lower overshoots then other approaches, and the settling time is also reduced as compared to the other methods� Overall, the results show that the plant tuned with AFSA is superior in performance in terms of tuned parameters and percent overshoot�
This chapter has shown that AFSA is an optimization technique that works effectively for the PID controller tuning problems� AFSA that was applied to four different plants in this study has shown superior performance compared to the traditional ZN and the PSO methods� It can be deduced that the AFSA has a major advantage, that is, it enables automatic tuning of PID parameters to produce system response of process plants� This would be a boon for engineers if it is implemented in the real-world environment�
TABLE 5.4 Performance Based on Different Optimization Approaches
TABLE 5.7 Performance Based on Different Optimization Approaches for Plant III
TABLE 5.6 Performance Based on Different Optimization Approaches for Plant II
TABLE 5.5 Performance Based on Different Optimization Approaches for Plant I
