The Optimization of Marine Diesel Engine Rotational Speed Control

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The Optimization of Marine Diesel Engine Rotational Speed Control Process by Fuzzy Logic Control Based on Particle Swarm Optimization Algorithm Tien Anh Tran Faculty of Marine Engineering, Vietnam Maritime University, Haiphong 180000, Vietnam; [email protected]; Tel.: +84-973-900-853 Received: 3 September 2018; Accepted: 28 September 2018; Published: 4 October 2018

Abstract: The marine main diesel engine rotational speed automatic control plays a significant role in determining the optimal main diesel engine speed under impacting on navigation environment conditions. In this article, the application of fuzzy logic control theory for main diesel engine speed control has been associated with Particle Swarm Optimization (PSO). Firstly, the controller is designed according to fuzzy logic control theory. Secondly, the fuzzy logic controller will be optimized by Particle Swarm Optimization (PSO) in order to obtain the optimal adjustment of the membership functions only. Finally, the fuzzy logic controller has been completely innovated by Particle Swarm Optimization algorithm. The study results will be represented under digital simulation form, as well as comparison between traditional fuzzy logic controller with fuzzy logic control–particle swarm optimization speed controller being obtained. Keywords: main diesel engine; fuzzy logic control theory; particle swarm optimization algorithm; optimal engine speed; navigation environment

1. Introduction Fuzzy logic control was proposed by Prof. Zadeh in 1965. The Mamdani fuzzy inference system was displayed to conduct a steam engine and boiler control process by linguistic rule [1,2]. On the other hand, fuzzy logic control has been expressed by if-then rules with the human language. Besides that, the mathematical model does not need to establish in design process of a fuzzy logic controller. So, the fuzzy logic control is a good robustness. Its advantage is easy application, because there is no need an intensive information technology programmers and it has been used widely in science and industry. The rules and membership functions of a fuzzy logic controller are definitely based on empirical experience or knowledge database. Fuzzy logic control has been reported to be successfully to use a number of complex and nonlinear processes. Fuzzy logic control is occasionally proved to be more robust and their performances that are less sensitive to parametric variations than conventional controllers [3,4]. Zhou, et al., have analyzed the fuzzy control rules and membership function parameters [2]. H. Wei, et al., 2009 have compared between rigid feedback and constant-speed feedback control system, and construct a fuzzy control system of diesel speed. This comparison will result that the fuzzy control method is a feasible method and better than the other methods [5]. Some other researches of scholars and scientists have been indicated the benefits to apply fuzzy logic control in optimizing service system of diesel engine. S. Simani and M. Bonfe’ have established fuzzy modelling and control system of the air system for diesel engine [6]. David J. McGowan et al. have integrated governor control for a diesel by the detailed implementation of real-time fuzzy logic speed control for a standby diesel-generating set [7]. Tran et al., had established the diesel engine rotational speed automatic controller by using fuzzy-PID logic control theory [8]. On the other

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hand, the study of fuzzy logic theory has also conducted through some articles. Jafari et al., had modeled the uncertain nonlinear systems along with fuzzy differential equations (FDEs) by fuzzy set [9]. Moreover, the determination of uncertainty property through Z-number of fuzzy equation has also been investigated by Jafari et al. [10]. Furthermore, Particle Swarm Optimization (PSO) algorithm has been used to get the optimal values from fuzzy logic control rules. PSO has been based on a metaphor of social interaction. PSO’s function conducts to look up a space by adjusting the trajectories of individual vectors and called ‘Particles’. The movement of points in multidimensional space is conceptualized by Particles. The positions of their own previous best performances and the best previous performance of their neighbors are determined stochastically by individual particles. One another side, two notable improvements have been referred as the initial PSO, which attempt to strike a balance between the two conditions. The first condition is introduced by Shi and Eberhart which has been used like as an extra ‘inertia weight’ term and to scale down the velocity of each particle and this term is typically decreased linearly throughout a run [11]. The left condition has been introduced by Clerc and Kennedy involves a ‘constriction factor’ where the entire right side of the formula is weighted by a coefficient [12]. On the other hand, the combination between fuzzy logic control and PSO has been conducted by some researches at individual field. Fevrier. V, et al. have introduced evolutionary methodology for combining Particle Swarm Optimization (PSO) and Genetic Algorithms (GAs) when using fuzzy logic control for decision making [13]. In this study, the Particle Swarm model allows an infinite number of ways in which the balance between exploration and convergence can be controlled. Particle Swarm Optimization algorithm is studied to choose the membership functions and the fuzzy control rules. In addition, the ranges of membership functions in controller are very important to conduct an accuracy control process due to the expert experiences or knowledge database play an important role in designing the control model. The combination between fuzzy logic control and PSO will help the control process more realizably when considering the control objective is diesel engine speed. This study has been divided into sections, in particular, Section 1, Introduction; Section 2, Methodology with fuzzy logic control theory and Particle Swarm Optimization (PSO); Section 3, Case study with modelling of main diesel engine rotational speed control by fuzzy logic and optimization of diesel engine speed control process by PSO; Section 4, Results; and, Section 5, Conclusions. 2. Methodology 2.1. Fuzzy Logic Control Theory Fuzzy logic control was first proposed by Lotfi A.Zadeh who comes from the University of Carlifornia at Berkeley in his paper in 1965 [14]. In his paper, he has elaborated on his ideas in a 1973 paper in which he proposed the concept of “liguistic variables”. The content of his paper has been equated to a variable defined as a fuzzy set [15]. Fuzzy logic idea is similar to the human being’s feeling and inference process. Unlike the classical control theory that is a point-to-point control but fuzzy logic control has approached a range-to-point or range-to-range control. In Figure 1, the certain fuzzy logic control system will have four functional blocks: Fuzzification, inference engine, rule base, and defuzzification. The initial signal is a crisp input data that will be admitted into the fuzzy logic control system. After that, this signal will be converted into fuzzy input data by the fuzzification block. The inference engine or decision making logic will determine how the fuzzy logic control operations are displayed (Sup-Min inference), and together with the rule base will identify the output parameters of each fuzzy control by If-Then rules. The combination will be converted to crispy values with the defuzzification block. The output crisp value can be computed by the center of gravity or the weighted average. The fuzzy control system is based on the rule system that is on expert knowledge and including fuzzy sets and fuzzy algorithms. In summary, from Figure 1, fuzzy logic control process will be conducted following function blocks. The first block is fuzzification and membership functions that understands and characterizes the system behavior by


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using knowledge and experience. The second block is fuzzy control rule with directly designing the 3 of 18 control algorithm with fuzzy rules in which they describe the principles of the controller’s regulation in terms of the relationship between its inputs and outputs. The block is defuzzification to simulate controller’s regulation in terms of the relationship between itslast inputs and outputs. The last block is and debug the design. defuzzification to simulate and debug the design. Future Internet 2018, 10, x FOR PEER REVIEW

Figure 1. Block Block of of fuzzy fuzzy logic control system.

variables in infuzzy fuzzylogic logicsystem systemcould couldhave havethe thevalues valuesininrange range 0 and Hence, type The variables ofof 0 and 1. 1. Hence, thethe type of of logic system able addressthese thesevalues valuesofofthe thevariables variablestotoset set between between completely completely true true and logic system is is able to to address completely false. areare called as linguistic variables and each linguistic variable isvariable appointed false.The Thevariables variables called as linguistic variables and each linguistic is by a membership function along withalong has awith certain of membership function atfunction a particular appointed by a membership function hasdegree a certain degree of membership at a instance. In practice, functions have multiple suchtypes, as thesuch triangular particular instance. Inmembership practice, membership functions havedifferent multipletypes, different as the waveform, trapezoidal waveform, Gaussian waveform, bell-shaped waveform, sigmoidal waveform, triangular waveform, trapezoidal waveform, Gaussian waveform, bell-shaped waveform, sigmoidal and S-curveand waveform In order accurate of membership functionsfunctions needs to waveform, S-curve [16]. waveform [16].toInchoose order to choosetype accurate type of membership depend on the actual applications. However, in this research case, it needs to have significant needs to depend on the actual applications. However, in this research case, it needs dynamic to have variation indynamic a short time, so a triangular trapezoidal waveform be utilized. significant variation in a shortortime, so a triangular orwould trapezoidal waveform would be Whether the performance is not satisfactory then users only modify some fuzzy rules and utilized. resume. Fuzzythe logic control has is been widely to the control fuzzyrules linguistic Whether performance notapplied satisfactory then users onlyprocess modifythrough some fuzzy and descriptions [17,18]. orderhas to process, in detail, the inputs get the outputs reasoning, there are six resume. Fuzzy logic In control been applied widely to the to control process through fuzzy linguistic works that need to doIninorder applying to fuzzy control theory descriptions [17,18]. to process, in logic detail, the inputs to(Figure get the2). outputs reasoning, there are The first work needs to identify the input factors along with their ranges. six works that need to do in applying to fuzzy logic control theory (Figure 2). This work completely basesThe on first experimental knowledge of the fuzzy logic control theory. second work is work also similar with work needs to identify input factors along withThe their ranges. This completely the first but instead of determining thelogic output factors. The The output factors canisinclude one factor bases onwork experimental knowledge of fuzzy control theory. second work also similar with or more, but in but this instead study, the factor only has onefactors. factor: The diesel enginefactors speed can (n). include one the first work of output determining the output output third work conduct create factor the degree function for each input factorThe or more, but inmust this study, thetooutput only of hasmembership one factor: diesel engine speed (n). factor and output factor. The fourth work is an establishment of the construct of rule base in aims with The third work must conduct to create the degree of membership function for each input factor controlling Thework next is work needs to give the action that willofberule executed byaims assigning and outputsystem factor. operates. The fourth an establishment of the construct base in with strengths to system rule baseoperates. of controlling system. Theneeds final istoa combination the rules of controlling The next work give the action that and willdefuzzification be executed by the output factor. assigning strengths to rule base of controlling system. The final is a combination the rules and defuzzification of the output factor.

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Figure 2. 2. The Thesteps stepsto tocreate create fuzzy fuzzy control control system. system. Figure

2.1.1. Fuzzification Fuzzification 2.1.1. Fuzzification inindesigning a fuzzy logic logic controller is established by the state representing Fuzzification designing a fuzzy controller is established byvariables the state variables the system dynamic performance. The system dynamic performance consists of the input representing the system dynamic performance. The system dynamic performance consistsvariable of the signalvariable to control. Fuzzy logic control uses thetheory linguistic suchvariables, as low, medium, input signal to control. Fuzzytheory logic control usesvariables, the linguistic such as high, low, big, small, positive, negative, zero, etc. instead of using numerical simulation method. The fuzzification medium, high, big, small, positive, negative, zero, etc. instead of using numerical simulation is knownThe as converting a numerical variable (real number or crisp variables) variable method. fuzzification is known as converting a numerical variable into (reala linguistic number or crisp (fuzzy number). The fuzzy sets are characterized by membership functions that cover all universe of variables) into a linguistic variable (fuzzy number). The fuzzy sets are characterized by membership discourse.that Thecover triangular, trapezoidal, Gaussian, are different form of fuzzy sets [16]. functions all universe of discourse. Theetc triangular, trapezoidal, Gaussian, etc are different

form of fuzzy sets [16]. 2.1.2. Rule Base 2.1.2. The Rulerule Basebase is defined as If-Then format and called the conditional control rule. Under the supporting computer program that is able to execute the rules and calculate a control signal. The rule base is defined as If-Then format and called the conditional control rule. Under the The calculation is definitely based on error (e) and change in error (de) of the measured input signals. supporting computer program that is able to execute the rules and calculate a control signal. The calculation is definitely 2.1.3. Inference Engine based on error (e) and change in error (de) of the measured input signals. inference engine or inference operation comprises an information processing system such as 2.1.3. The Inference Engine a computer program. The inference engine is similar to the human brain and evaluates the fuzzy rules. The inference or inference operation comprises an information system types such The output signal isengine generated completely to base on each fuzzy control rule. processing There are different as computer program. The inference engine is similar to the humanetc. brain of ainference engine for example max-min method, max-dot product, [19].and evaluates the fuzzy rules. The output signal is generated completely to base on each fuzzy control rule. There are different types of inference engine for example max-min method, max-dot product, etc. [19]. 2.1.4. Defuzzification The defuzzification is reversible process of fuzzification. In order to use the fuzzy logic controller 2.1.4. Defuzzification needs the output in a linguistic variable (fuzzy number). Depending on real requirements, the linguistic The defuzzification is reversible process of [20,21]. fuzzification. In many order defuzzification to use the fuzzy logic variables must be transformed to the crisp output There are methods, controller needs the output in a linguistic variable (fuzzy number). Depending on real requirements, but the most common use methods are Center of Gravity (COG), Bisector of Area (BOA), and Mean of the linguistic variables must be transformed to the crisp output [20,21]. There are many Maximum (MOM). defuzzification methods, but the most common use methods are Center of Gravity (COG), Bisector of Area (BOA), and Mean of Maximum (MOM).

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2.2. Particle Particle Swarm Swarm Optimization Optimization Algorithm Algorithm 2.2. Eberhart and and Kennedy Kennedy [22] [22] have have foundated foundated the the theory theory of of Particle Particle Swarm Swarm Optimization Optimization (PSO). (PSO). Eberhart This method is based on stochastic optimization and the social behavior of bird flock or fish school. This method is based on stochastic optimization and the social behavior of bird flock or fish school. Each particle particle plays useuse of Particle Swarm Optimization method. The Each plays an animportant importantrole roleininthethe of Particle Swarm Optimization method. particles will associate together after that they look forlook the best fitness or function The The particles will associate together after that they for solution the best or solution fitnessvalue. function fitness function value is called as P best. The fitness function value will correspond to the best location value. The fitness function value is called as Pbest . The fitness function value will correspond to the (Lbest). Especially, takes all of thetakes topological neighbors. In this case, theInbest be a best location (Lbesta).particle Especially, a particle all of the topological neighbors. thisvalue case, will the best globalwill bestbevalue andbest it is value knownand as G (Figure as 3) G [13]. (Figure 3) [13]. value a global it best is known best

Y X ik +1

Vi k

Vi k +1

Gbest (i ) Vi

X ik

Vi Pbest

Gbest

Pbest (i )

X Figure Figure 3. 3. The The modification modification of of aa searching searching points points by by Particle Particle Swarm Swarm Optimization Optimization (PSO) (PSO)[23]. [23].

Where: Where: Xik kis the current position; X is the current position; Xik+i 1 is the modified position; X k +1 is current the modified position; V k iis the velocity; i

Viki k+1isisthe velocity; V thecurrent modified velocity; Pk +1

thevelocity modified VVi i best isisthe of velocity; Pbest ; and, best V isisthe Vi i Pbest thevelocity velocityofofGPbest best.; and,

G

The Swarm of Optimization (PSO), which is known as an evolutionary computation Vi GbestParticle is the velocity Gbest. algorithm, is different from other one such as Genetic Algorithms (GAs). The search space of PSO The Particle Swarm Optimization (PSO), which is known as an evolutionary computation algorithm is carried out by a population. The simulation of bird flock or fish school behavior is known algorithm, is different from other one such as Genetic Algorithms (GAs). The search space of PSO as PSO method. The discovery and previous experience of bird flock behavior in the finding food have algorithm is carried out by a population. The simulation of bird flock or fish school behavior is made an effective evolutionary computation algorithm, like the PSO method. So, particle particle is known as PSO method. The discovery and previous experience of bird flock behavior in the finding called as each companion in the population, which is called swarm swarm. Swarm is assumed to ‘fly’ food have made an effective evolutionary computation algorithm, like the PSO method. So, particle over the search space in order to find promising regions of the landscape. particle is called as each companion in the population, which is called swarm swarm. Swarm is Each particle is allocated with a random velocity initially and its location is adjusted according assumed to ‘fly’ over the search space in order to find promising regions of the landscape. to its own previous best (Pbest ) and the global best (Gbest ). On the other hand, the velocity change is Each particle is allocated with a random velocity initially and its location is adjusted according weighted by random terms with separate random numbers being generated for acceleration toward to its own previous best (Pbest) and the global best (Gbest). On the other hand, the velocity change is the two best solutions (Pbest and Gbest ). The procedures of PSO algorithm have been showed in Figure 4. weighted by random terms with separate random numbers being generated for acceleration toward the two best solutions (Pbest and Gbest). The procedures of PSO algorithm have been showed in Figure 4.


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Figure4.4.Procedures Proceduresofofthe theParticle ParticleSwarm SwarmOptimization Optimization[24]. [24]. Figure

â

Initialization Generatea population a population of particles allocate a velocity each Initialization process: Generate of particles and and allocate a velocity to eachtoparticle particle randomly. randomly. â Ø Evaluation process: Update locations of particles and calculate the optimization Evaluation process: Update the the bestbest locations of particles and calculate the optimization fitness fitness function. function. Velocityand andlocation locationupdate: update:Change Changethe thelocation locationofofeach eachparticle particleby bymeans meansofofupdating updatingits itsown own â Velocity velocityas aswell wellas asthe theparticle particlewill willbe beadjusted adjusteddramatically. dramatically. velocity Theupdating updatingprocess processofofvelocity velocity and location at each particle be realized through Equations â The and location at each particle cancan be realized through Equations (1) (1) and and (2). (2). k +1

k

k

kk kk k +1 k k VimV k= − best,im − =w.V wV .im ++c1c.r.1r.(.(PP − XXim ))++ cc2 .r.r2 ..((GGbest,im −X Ximk )) im

im

1 1

best , im

2

im

k

k +1

k +1 Xim = Xim k+ Vim k +1 k +1

X im = X im + Vim

where:

2

best ,im

im

(1) (1) (2) (2)

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i = 1, 2, ..., n; and m = 1, 2, ..., d; n is the number of particles in the group; where: dimension id=is1,the 2, ..., n; and mof = the 1, 2,group; ..., d; k is the number of iterations thegroup; current particle; n particles inofthe thedimension inertia weight factor; dwisisthe of the group; is the previous best; kPbest is the number of iterations of the current particle; G best is the global best; w is the inertia weight factor; Xbest is the location of the particle; P is the previous best; V is the velocity of the particle; Gbest is the global best; c1,isc2the arelocation the acceleration coefficients; and, X of the particle; r1,isr2the are velocity the random numbers V of the particle;between 0 and 1. is a basiccoefficients; definition ofand, Particle Swarm Optimization (PSO). In PSO algorithm, a cThe are the acceleration 1 , c2assumption flockr1of are put numbers into the between d-dimensional , r2particles are the random 0 and 1.search space with randomly in order to choose velocities and positions that definition are known as theirSwarm best values (Pbest) and theInposition in the The assumption is a basic of Particle Optimization (PSO). PSO algorithm, d-dimensional space. Furthermore, the velocity of each particle is adjusted according to its own a flock of particles are put into the d-dimensional search space with randomly in order to choose flying experience and that the other particle’s flying is assumed thatinthe particle is velocities and positions are known as their best experience. values (Pbest )Itand the position the j-th d-dimensional represented as x i = (x i1 , x i2 , ..., x id ) in the d-dimensional space then the best previous position of the and i-th space. Furthermore, the velocity of each particle is adjusted according to its own flying experience particle be recorded is described like this: that the j-th particle is represented as xi = (xi1 , xi2 , the otherwill particle’s flying and experience. It is assumed ..., xid ) in the d-dimensional space then best previous position of the i-th particle will be recorded Pbestthe i = (Pbest i1, Pbest i2, ..., Pbest in) (3) and is described like this: In where, the index of best particle among the particles is Gbest d. The velocity of i-th particle Pbest i = (Pbest i1all , Pof (3) best i2 , ..., Pbest in ) is specified as vi = (vi1, vi2, ..., vid). Additionally, the modified velocity and the position of each particle In where, following the index of best particle among are computed Equation (1) and (2). all of the particles is Gbest d . The velocity of i-th particle is specified as vi = (vi1 , vi2 , ..., vid ). Additionally, the modified velocity and the position of each particle are computed 3. Case Study following Equation (1) and (2). 3. Case Study Modeling of Main Diesel Engine Rotational Speed Control by Fuzzy Logic Control Theory

Fuzzy controller includes functional blocks (fuzzification, rule base, inference engine, and Modeling of Main Diesel Engine Rotational Speed Control by Fuzzy Logic Control Theory defuzzification), and it has been described in Figure 1. In this research, the objective of controlling Fuzzy includes blocks (fuzzification, rule in base, process is a controller diesel engine speed.functional In fact, marine diesel engine operates hardinference conditionengine, under and defuzzification), and it has been described in Figure 1. In this research, the objective of controlling impacting on navigation environment, like as wind, wave, tidal current, etc. All of the external process is a be diesel engine speed. Inoffact, marine diesel engine operates in speed hard condition under factors will made the instability engine when it works. Diesel engine is an important impacting on navigation environment, like as wind, wave, tidal current, etc. All of the external factor that it will decide the engine working condition when external load is variable. Furthermore, factors will be made instability engine when works. Diesel speed is an important fuel consumption of the engine always of associates with it engine speed. Inengine a result, diesel engine speed factor that is it will the engine condition when external load5,isthe variable. Furthermore, controller verydecide necessary to helpworking engine works effectively. In Figure modelling of diesel fuel consumption of enginecontrol alwayshas associates with engineSpeed speed.error In a result, diesel engine engine speed automatic been presented. and variable speed speed error controller d ( speed )is very necessary to help engine works effectively. In Figure 5, the modelling of diesel engine d(speed) are control the input signals of fuzzy controller. Speed error willerror be compared between speeddtautomatic has been presented. Speed error and variable speed are the input dt signals of fuzzy error will be compared between speed feedback reference speed controller. and speedSpeed feedback signal that took from outputreference source ofspeed dieseland engine (revolution signal that took from output source of diesel engine (revolution on engine speed). on engine speed).

d ( speed ) dt

Figure 5. Modelling of diesel engine speed control by fuzzy logic controller. controller.


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In order to conduct the fuzzy control process, the definition of speed error (e) and variable speed error (de) as the input signals of the fuzzy controller. Besides that, the output signals of fuzzy controller must also be determined as engine is18NB, NM, Future Internet 2018, 10, x FOR PEER REVIEWspeed. The linguistic set of e, de, and the engine speed 8 of NS, ZO, PS, PM, and PB. order to conduct the fuzzy process, the definition speed error (e) and variable InInwhere: NB = Negative Big,control NM = Negative Medium,ofNS = Negative Small, ZO = Zero, speed error (de) as the input signals of the fuzzy controller. Besides that, the output signals of fuzzy PS = Positive Small, PM = Positive Medium, and PB = Positive Big. controller must also be determined as engine speed. The linguistic set of e, de, and the engine speed The discourse universe of input signals and output signal is a range of [0, 1]. In addition, triangular is NB, NM, NS, ZO, PS, PM, and PB. membership function has been adopted as the membership of input In where: NB = Negative Big, NM = Negative Medium, NS =functions Negative Small, ZOsignals = Zero, and PS = output signal of fuzzy controller, respectively. Positive Small, PM = Positive Medium, and PB = Positive Big. Since inputuniverse signal ofoflinguistic set has members NM, ZO, PS, PM, The each discourse input signals andseven output signal isinclusding a range of NB, [0, 1]. In NS, addition, triangular has been adopted ascontroller the membership functions inputand signals and PB, thenmembership the control function rule construction of fuzzy will include 49 of rules, theyand have been output signal of fuzzy described in Table 1. controller, respectively. Since each input signal of linguistic set has seven members inclusding NB, NM, NS, ZO, PS, Table 1. Control rules of dieselofengine by fuzzy logic control. PM, and PB, then the control rule construction fuzzy speed controller will include 49 rules, and they have been described in Table 1. e NB NM PM PB NS ZO PS de Table 1. Control rules of diesel engine speed by fuzzy logic control. NB PB PB PM PM PS ZO ZO e PB NM PB PM PM PS ZO ZO NB NM NS ZO PS PM PB NSde PB PB PM PS ZO NM NM ZO NB PBPB PB PM PM ZO NM ZONB NB PB PM PS ZO PS NM PMPB PM ZO PM NSPS NM ZONB NB PB PM ZO PM NS ZOPB ZO NM NMNB NB PB PMNS PS NM ZO NM PB ZO ZOPB ZO NM NBNB NB PB PMNS ZO NM NM NB PS PM PM ZO NS NM NB NB PM ZO has NStwo NM NM NB then NBthe antecedent of each control On the other hand, the fuzzy ZO controller input signals PB ZO ZO NS NM NM NB NB

rule will have two parts. Equation “And” will be used to combine the two parts of the antecedent to gain a signal number that represents the result of the antecedent for that rule. So, the result will On the other hand, the fuzzy controller has two input signals then the antecedent of each be control appliedrule in the process to achieve fuzzy set oftothe output. willimplication have two parts. Equation “And”the will be used combine theThe twoimplication parts of themethod hasantecedent been used “And”. It number means that minimum valueofwill compared aimsSo, inthe obtaining toas gain a signal that the represents the result the be antecedent for with that rule. theresult desired output value in fuzzy control process. So, the implication process will be implemented will be applied in the implication process to achieve the fuzzy set of the output. The method been rules. used as “And”. It means that the value will be compared forimplication each rule in fuzzyhas control The simulation process ofminimum fuzzy logic controller for diesel engine withhas aims in obtaining thein desired output value in fuzzy control process. So, the implication process speed been identified Figures 6–8 below. 1. 2. 3. 4. 5. .. .

will be implemented for each rule in fuzzy control rules. The simulation process of fuzzy logic If Speedfor error (e)engine is NB speed and Speed error variable is NB Engine speed (n) is PB. controller diesel has been identified in(de) Figures 6–8then below.

If Speed error (e) is NB and Speed error variable (de) is NM then Engine speed (n) is PB.

1. If Speed error (e) is NB and Speed error variable (de) is NB then Engine speed (n) is PB. If Speed error (e) is NB and Speed error variable (de) is NS then Engine speed (n) is PB. 2. If Speed error (e) is NB and Speed error variable (de) is NM then Engine speed (n) is PB. If Speed error (e) is NB and Speed error variable (de) is ZO then Engine speed (n) is PB. 3. If Speed error (e) is NB and Speed error variable (de) is NS then Engine speed (n) is PB. error (e)(e)isisNB errorvariable variable (de) is PS then Engine speed 4.If Speed If Speed error NBand and Speed Speed error (de) is ZO then Engine speed (n) is(n) PB.is PM. 5. If Speed error (e) is NB and Speed error variable (de) is PS then Engine speed (n) is PM. 48.⋮ If Speed error (e) is PB and Speed error variable (de) is PM then Engine speed (n) is NB. 48. If Speed error (e) is PB and Speed error variable (de) is PM then Engine speed (n) is NB. 49. If Speed error (e) is PB and Speed error variable (de) is PB then Engine speed (n) is NB. 49. If Speed error (e) is PB and Speed error variable (de) is PB then Engine speed (n) is NB.

Figure Fuzzy logic control inference. Figure6.6. Fuzzy logic control inference.


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Figure Figure7. 7.Diesel Dieselengine enginespeed speedcontrol controlrules. rules. Figure 7. Diesel engine speed control rules.

Figure 8.8.Surface Surface of diesel engine speed control.3.2. Optimization of Main Diesel Engine Rotational Figure8. Surfaceof ofdiesel dieselengine enginespeed speedcontrol.3.2. control.3.2.Optimization Optimization of ofMain MainDiesel DieselEngine EngineRotational Rotational Figure Speed Control Process by Particle Swarm Optimization Algorithm. SpeedControl ControlProcess Processby byParticle ParticleSwarm SwarmOptimization OptimizationAlgorithm. Algorithm. Speed

The Theapplication application of ofParticle ParticleSwarm SwarmOptimization Optimization(PSO) (PSO)algorithms algorithmsfor forfuzzy fuzzylogic logiccontroller controllerhas has been been described described in in Figure Figure9. 9. The The initial initial populations populations are are the the first firststep stepof ofParticle ParticleSwarm SwarmOptimization Optimization (PSO) (PSO) algorithms. algorithms. Especially, population is Especially, the the population population is composed composed of of the the chromosomes chromosomes that that are are real real codes. codes. Hence, the “fitness function” isis generated the judgment of Hence,the the“fitness “fitness function” generated by the corresponding corresponding judgment of aa population. population. function” is generated by theby corresponding judgment of a population. Moreover, Moreover, “fitness function” isisthe of In Moreover, the “fitnessis function” theperformance performance index ofaapopulation. population. Inparticular, particular, the valueof of the “fitnessthe function” the performance index of aindex population. In particular, the valuethe of value “fitness “fitness function” is bigger and then the performance is better. Equation (4) is represented for “fitness function” is bigger then the is performance is better. Equation (4) represented for function” is bigger and then theand performance better. Equation (4) is represented foris“fitness function”. “fitness “fitnessfunction”. function”. PI = K.∑|e| (4) PI (4) PI == KK.. ee (4) where: where: where: PI is the fitness value; PI is the fitness value; the fitness value; ePI is is the speed error; and, eeisisthe speed error; and, the speed error; and, K is a coefficient. KKisisaacoefficient. coefficient. Afterward, the fitness function has been determined then the fitness value and the number of Afterward, the fitness has been determined then the value the of Afterward, the fitness function function has determined then the fitness fitness value and and the number number of generation will be considered if or not thebeen applicable process stopped (maximum iteration number generation generation will will be be considered considered ifif or or not not the the applicable applicable process process stopped stopped (maximum (maximum iteration iteration number number reached?). reached?). In In addition, addition, the the calculation calculation of of the the PPbest best of of each each particle particle and and GGbest best of of population population (the (the best best

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reached?). In addition, the calculation of the Pbest of each particle and Gbest of population (the best movement of all particles). In a result, the update of velocity, position, Pbest , and Gbest of particles will movement of all particles). In a result, the update of velocity, position, Pbest, and Gbest of particles will approach a new best position (best chromosome in our proposition) (Figure 10). approach a new best position (best chromosome in our proposition) (Figure 10).

Figure9.9.Particle ParticleSwarm SwarmOptimization Optimizationtotoadjust adjustmembership membershipfunctions. functions. Figure



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Figure Figure10. 10.Algorithm Algorithmofofapplying applyingPSO PSOtotooptimize optimizefuzzy fuzzylogic logiccontroller. controller.

On the the other other hand, hand, the the performance performance ofof aa fuzzy fuzzy model model can can be be measured measured by by the the On mean-square-error(mse). (mse).InInthe thecase caseofoftwo twomodel modelestimates, estimates,for forinstance, instance,the theone onewith withthe thesmaller smaller mean-square-error mse with respect to the experimental model has a better match. The mse is defined by Equation (5) that is used as the fitness measure for the PSO algorithm implementation.


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mse with respect to the experimental model has a better match. The mse is defined by Equation (5) that is used as the fitness measure for the PSO algorithm implementation. q

^

 ( yk − y k ) 2 q

=1 ( y k − yˆ k )2 mse = kk∑ q mse = =1 q 2  y2k

(5) (5)

∑ yk

k =1

k =1 ^

In where, yˆ k represents the actual the estimated value at data point respectively; y k represents the value actualand value and the estimated value at k,data point k, where,ykyand k and and, q is the number of data points. respectively; and, q is the number of data points. In this thethe chromosomes of the swarmswarm optimization (PSO) algorithms will consist of In thisstudy, study, chromosomes ofparticle the particle optimization (PSO) algorithms will three elements (Figure 11). Firstly, the range of membership functions includes K and K coefficients. de Ke and Kde consist of three elements (Figure 11). Firstly, the range of membership functionse includes Secondly, the shape of membership functions includes following coefficients e ~e , de ~de 1 7 1 7 , and ne11~n coefficients. Secondly, the shape of membership functions includes following coefficients ~e77,. Thirdly, the fuzzy inference rules include r ~r . On the other hand, the diesel engine speed output is 1 49 rules include r1~r49. On the other hand, the diesel de1~de7, and n1~n7. Thirdly, the fuzzy inference thereby such that the steady state error of response is zero. engine speed output is thereby such that the steady state error of response is zero.

Figure 11. Block diagram of fuzzy logic control with particle swarm optimization. Figure 11. Block diagram of fuzzy logic control with particle swarm optimization.

Moreover, the fuzzy inference rules from r1 ~r49 are corresponded to number Moreover, the fuzzy inference rules from r1~r49 are corresponded to number 1 (Negative 1 (Negative Big—NB), 2 (Negative Medium—NM), 3 (Negative Small—NS), 4 (Zero—Z), Big—NB), 2 (Negative Medium—NM), 3 (Negative Small—NS), 4 (Zero—Z), 5 (Positive Small—PS), 5 (Positive Small—PS), 6 (Positive Medium—PM), and 7 (Positive Big—PB). 6 (Positive Medium—PM), and 7 (Positive Big—PB). Table 2 represents the fuzzy inference rules with PSO algorithms. Table 2 represents the fuzzy inference rules with PSO algorithms. Table 2. Fuzzy inference rules with PSO algorithms. Table 2. Fuzzy inference rules with PSO algorithms. e NBe NM PM NS ZO PS

de NBde NM NS ZO PS PM PB

NB

r1

NB r2 NM r3 NS r4 r5 ZO r 6 PS r7 PM PB

r8

r1r9 rr210 rr311 r12 rr4 13 rr514 r6 r7

NM

r15

r8 r16 r9 r17 r10 r18 r19 r11 r 20 r12 r21 r13 r14

NS r15 r16 r17 r18 r19 r20 r21

ZO

r22 r23r22 r24r23 r25r24 r26 r27r25 r28r26

r27 r28

PS

r29

r29 r30 r31 r30 r32 r31 r33 r32 r34 r33 r35 r34 r35

PM r36 r37 r38 r39 r40 r41 r42

PB

PB

r36 r37 r43 r38 r44 r39 r45 r40 r41 r46 r42 r47

r48 r49

r43 r44 r45 r46 r47 r48 r49


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Future The Internet 2018,diesel 10, 99 engine speed controller has been established throughout the fuzzy logic control 13 of 18 main

theory. This controller completely responses to the targets of main diesel engine speed control when considering the navigation environment conditions. Furthermore, fuzzy logic controller has been The main diesel engine speed controller has been established throughout the fuzzy logic control designed based on experience knowledge from the fact on ships that use the diesel engine speed theory. This controller completely responses to the targets of main diesel engine speed control controller (governor) for main diesel engines with specific types like MAN B&W and SULZER. In when considering the navigation environment conditions. Furthermore, fuzzy logic controller has addition, based on the actual operation situation, the main diesel engine speed controller has been been designed based on experience knowledge from the fact on ships that use the diesel engine acted appropriately for adjusting the fuel rack handle in aim with keeping engine speed constantly. speed controller (governor) for main diesel engines with specific types like MAN B&W and SULZER. Although the conventional controller bases on the accuracy of the system model and In addition, based on the actual operation situation, the main diesel engine speed controller has been parameters, fuzzy logic controller uses the different strategies for adjusting diesel engine speed acted appropriately for adjusting the fuel rack handle in aim with keeping engine speed constantly. under impacting on the external environment factors. Fuzzy logic controller proposes the Although the conventional controller bases on the accuracy of the system model and parameters, experiences and linguistic definitions. Moreover, if there is not enough knowledge about control fuzzy logic controller uses the different strategies for adjusting diesel engine speed under impacting process, the fuzzy logic controller might give satisfactory results. The aim of fuzzy logic controller is on the external environment factors. Fuzzy logic controller proposes the experiences and linguistic to minimize the speed error. Besides that, the change of speed error plays a virtal role to define the definitions. Moreover, if there is not enough knowledge about control process, the fuzzy logic controller controller input. Consequently, fuzzy logic controller uses the speed error and change of speed error might give satisfactory results. The aim of fuzzy logic controller is to minimize the speed error. for linguistic knowledge which are generated from the control rules. Besides that, the change of speed error plays a virtal role to define the controller input. Consequently, The speed error is computed with comparison between reference speed and speed signal fuzzy logic controller uses the speed error and change of speed error for linguistic knowledge which feedback from speed output of main diesel engine. Both speed error and change of speed error are are generated from the control rules. fuzzy controller inputs. From output signal of fuzzy logic controller will act on actuator and then The speed error is computed with comparison between reference speed and speed signal feedback make the movement of fuel control position on main diesel engine. In reality, the fuel rack handle from speed output of main diesel engine. Both speed error and change of speed error are fuzzy will decide the diesel engine speed. If the fuel control position is at an increasing level, then diesel controller inputs. From output signal of fuzzy logic controller will act on actuator and then make the engine speed will increase and vice versa. movement of fuel control position on main diesel engine. In reality, the fuel rack handle will decide In Figure 12, the model of main diesel engine speed controller has been built on the diesel engine speed. If the fuel control position is at an increasing level, then diesel engine speed Simulink/Matlab environment. To establish this model, the input signals and output signal of fuzzy will increase and vice versa. logic controller have been defined. The speed error and change of speed error are input signals of In Figure 12, the model of main diesel engine speed controller has been built on Simulink/Matlab controller. The main diesel engine speed is output signal of controller. The output signal of environment. To establish this model, the input signals and output signal of fuzzy logic controller 1 have been defined. Theactuator speed error and change speed error areform input signals of controller. Theas main controller will act on through transferoffunction under , as well the s +will 0.2 act on actuator diesel engine speed is output signal of controller. The output signal of 0.5979 controller 1 1 through transfer function under form the transfer main diesel engine transfer 0.5979s+0.2 , as well as . The functions of with actuator and main diesel engine with transfer function 1 function 0.01s+0.004 . The transfer functions of actuator main diesel engine have been assumed with 0.01s + and 0.004 testing the main diesel engine controller based the on fuzzy logic control On the other hand, main diesel engine have been speed assumed with testing main diesel enginetheory. speed controller based on the external load hastheory. been added in other order hand, to change the dieselload engine It likesinasorder the navigation fuzzy logic control On the the external has speed. been added to change environment factorspeed. impacts. Fromas thethe model of diesel engine speedfactor controller has been the diesel engine It likes navigation environment impacts. Fromestablished the modelon of Simulink/Matlab environment thathas appropriately verified the logic controller for main diesel diesel engine speed controller been established on fuzzy Simulink/Matlab environment that engine speed control. appropriately verified the fuzzy logic controller for main diesel engine speed control.

Figure Figure 12. 12. Simulation model of marine diesel engine engine speed speed Controller. Controller.

In ofof diesel engine speed controller areare optimized by In this thisstudy, study,the thefuzzy fuzzymembership membershipfunctions functions diesel engine speed controller optimized Particle Swarm Optimization (PSO) algorithms. PSO algorithms will find out the optimal positions, by Particle Swarm Optimization (PSO) algorithms. PSO algorithms will find out the optimal as well as the best ranges each variable in diesel engine speed controller. Based on coefficients of positions, as well as the of best ranges of each variable in diesel engine speed controller. Based on


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Future Internet 2018, 10, x FOR PEER(PSO) REVIEW 14 of 18 particle swarm optimization algorithms in Table 3, the shapes of fuzzy membership functions (e, de, n) are represented in Figures 13–15. coefficients coefficients of of particle particle swarm swarm optimization optimization (PSO) (PSO) algorithms algorithms in in Table Table 3, 3, the the shapes shapes of of fuzzy fuzzy membership functions (e, de, n) are represented in Figures 13–15. membership functions de, n) are represented in Figures 13–15. (PSO) algorithms. Table (e, 3. Coefficients of Particle Swarm Optimization

Table Population Size3. 50Particle e1 , de1 and n1(PSO) [−1, −1, −0.4] Table 3. Coefficients Coefficients of of Particle Swarm Swarm Optimization Optimization (PSO) algorithms. algorithms. Number of Iteration Population Size

50 Population Size 100 50 wmax 0.6 Number of Iteration 100 Number of Iteration 100 max w 0.6 wmin 0.1 wmax max 0.6 w min 0.1 min w min 0.1 c1 = c2 1.5 cc111 == cc222 1.5 1.5 Min-offset 200 Min-offset 200 Min-offset 200 Ke and Kde [0.001, 0.005] K [0.001, Keee and and K Kdede de [0.001, 0.005] 0.005]

ee211,, de de211 and andnn211

e1, de1 and n1 ee de and e3222,, de de3222 and andnn n3222 3 3 e 3 , de 3 and n ee43, de de43 and andnn4333 e 4 , de 4 and de544 and andnn n5444 ee544, de e55, de and de6555 and andnn n6555 ee65,, de ee666,, de 6 and de66 and andnn n666 e7 , de 7 7 ee777,, de de777 and and n n777

[−1,−0.4] −0.4, −0.2] [−1, [−1, −1, −1, −0.4] [−0.4, −0.2, 0] [−1, −0.2] [−1, −0.4, −0.4, −0.2] [−0.4, −0.2, 0] [−0.2,0]0, 0.2] [−0.4, −0.2, [−0.2, [−0.2, 0, 0,[0,0.2] 0.2] 0.2, 0.4] [0, 0.2, 0.4] [0, 0.2,[0.2, 0.4]0.4, 1] [0.2, 1] [0.2, 0.4, 0.4, 1] 1, 1] [0.4, [0.4, 1, 1] [0.4, 1, 1]

Figure 13. Membership function of speed error (e) optimized by PSO. Figure Figure13. 13. Membership Membership function functionof ofspeed speederror error(e) (e)optimized optimizedby byPSO. PSO.

Figure 14. Membership function of speed error variable (de) optimized by PSO. Figure Figure14. 14. Membership Membership function function of ofspeed speederror errorvariable variable(de) (de)optimized optimizedby byPSO. PSO.

Figure 15. Diesel engine speed output (n) optimized by PSO. Figure15. 15. Diesel Dieselengine enginespeed speedoutput output(n) (n)optimized optimizedby byPSO. PSO. Figure

The simulation process of the main diesel engine speed control has been represented in Figure 16 below. In where, the horizontal axis presents the time of adjusting (Unit: second) and the vertical axis presents the change of diesel engine speed in controlling process. Consequently, the simulation process has been indicated that main diesel engine speed will be adjusted after having action signal from actuator under 1 (second). In the case of research, if there is Future Internet 2018, 10, 99 15 of 18 a change of main diesel engine speed when the external load impacts then fuzzy logic controller will give a control signal in order to keep constant for the desired speed of operator. It assumes that if the diesel engine speed increases then fuzzy controller will give a signal to 4. Results reduce diesel engine speed and vice versa. In Figure 16 the diesel engine speed always keeps at The diesel engine speed will be controlled through fuzzy logic controller when the assumptions constant level when comparing with the initial reference speed. When there is a change of diesel have been given out in modelling of diesel engine speed controller on Simulink/Matlab (Figure 12). engine speed then diesel engine speed controller will control speed to gain the constant level like as The simulation process of the main diesel engine speed control has been represented in Figure 16 the initial reference speed. On the other hand, the change level of diesel engine speed in this case is a below. In where, the horizontal axis presents the time of adjusting (Unit: second) and the vertical axis range of [−2, 2] and it can vary if the external load and output signal (gain 4) are set at different levels presents the change of diesel engine speed in controlling process. corresponding to the test case.

Figure16. 16.Simulation Simulationof ofdiesel dieselengine enginespeed speedcontrol controlprocess. process. Figure

In this case, the adjusting range diesel enginethat has main been diesel reduced through Consequently, thespeed simulation process hasof been indicated engine speedreference will be speed in controlling model (Figure 12). Despite engine speed changes, the proposed speed controller adjusted after having action signal from actuator under 1 (second). In the case of research, if there is a also keeps constantly according to the diesel engine speed control then curvefuzzy in Figure So, thiswill one change of main diesel engine speed when the external load impacts logic 17. controller presents accurately proposed model. give a control signal in establishing order to keepthis constant for the desired speed of operator. It assumes that if the diesel engine speed increases then fuzzy controller will give a signal to reduce diesel engine speed and vice versa. In Figure 16 the diesel engine speed always keeps at constant level when comparing with the initial reference speed. When there is a change of diesel engine speed then diesel engine speed controller will control speed to gain the constant level like as the initial reference speed. On the other hand, the change level of diesel engine speed in this case is a range of [−2, 2] and it can vary if the external load and output signal (gain 4) are set at different levels corresponding to the test case. In this case, the speed adjusting range of diesel engine has been reduced through reference speed in controlling model (Figure 12). Despite engine speed changes, the proposed speed controller also keeps constantly according to the diesel engine speed control curve in Figure 17. So, this one presents accurately in establishing this proposed model.

Future Internet 2018, 10, 99 Future Internet 2018, 10, x FOR PEER REVIEW Future Internet 2018, 10, x FOR PEER REVIEW

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Figure 17. Simulation of diesel engine speed controller when decreasing the setting value (Reference Figure 17. 17. Simulation of diesel engine speedspeed controller when decreasing the setting (Reference Speed). Figure Simulation of diesel engine controller when decreasing thevalue setting value Speed). Speed). (Reference

Moreover, diesel engine speed controller based on fuzzy logic control that is optimized by Moreover, diesel engine speed controller based on fuzzy logic control that optimized by Moreover, diesel speed controller based on fuzzy logic control that is optimized by machine machine learning, in engine particular, particle swarm optimization (PSO) algorithms. So,isparticle swarm machine learning, in particular, particle swarm optimization (PSO) algorithms. So, particle swarm learning, in particular, particle swarm optimization (PSO) So, particle swarm optimization optimization (PSO) algorithms have been found the bestalgorithms. ranges of membership functions of diesel optimization (PSO) algorithms have been found the best ranges of membership functions ofspeed diesel (PSO) algorithms have been found the best ranges of membership functions of diesel engine engine speed controller. In Figure 18, the characteristic curves are represented with a comparison engine speed controller. In Figure 18, the characteristic curves are represented with a comparison controller. In Figure 18, the characteristic curves are represented with a comparison between diesel between diesel engine speed controller without using PSO algorithms and controller using PSO between diesel engine without speed controller using PSO algorithms using PSO engine speed controller using PSOwithout algorithms and controller usingand PSOcontroller algorithms. algorithms. algorithms.

Figure Figure 18. 18. Characteristic Characteristic curves curves of of diesel diesel engine engine speed speed control control using using PSO PSO algorithms. algorithms. Figure 18. Characteristic curves of diesel engine speed control using PSO algorithms.

Consequently, the diesel engine speed controller using PSO algorithms have significantly benefits Consequently, the diesel engine speed controller using PSO algorithms have significantly whenConsequently, compared with the traditionally fuzzy logic controller when applying into this research. The range of diesel engine speed controller using PSO algorithms significantly benefits when compared with traditionally fuzzy logic controller when applying have into this research. benefits when compared with traditionally fuzzy logic controller when applying into this research. The range of diesel engine speed control has been enlarged when applying into particle swarm The range of diesel engine speed control has been enlarged when applying into particle swarm


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diesel engine speed control has been enlarged when applying into particle swarm optimization (PSO) algorithms. In Figure 18, the traditional fuzzy logic controller has just limited at speed range 200 rpm (revolution per minute) but this range will be increased in 250 rpm when applying to PSO algorithms. 5. Conclusions The diesel engine speed control plays a vital role in maintaining the desired speed of operators. The application of modern control theory like as fuzzy logic control is necessary in condition of the external loads changing. The fuzzy logic controller for main diesel engine speed has been brought a lot of advantages instead of using traditional PID (Proportional–Integrative–Derivative) controller. Furthermore, this study has associated with particle swarm optimization (PSO) algorithms along with fuzzy logic controller for main diesel engine on ships that achieved benefits. The range of diesel engine speed has been improved, as well as the control process is more stable. Moreover, the fuzzy logic controller combined with PSO algorithm has represented more advantages when comparing with other traditional controllers, such as PID logic controller and fuzzy logic controller. The proposed controller has been designed according to fuzzy rule base of fuzzy logic controller and automatically adjust the membership function. The advantages of the fuzzy logic controller based PSO algorithm are more convenient than fuzzy logic controller since this proposed method is able to adjust automatically the membership function of input signal and output signal. This one is an optimal point comparing with fuzzy logic controller without using the PSO algorithm. However, the use of this proposed method also meets the drawnbacks such as more complex, requiring the high degree of operators. From these research results, the author will continue the development of proposed method not only fuzzy based PSO algorithm, but also fuzzy combined with GA (Genetic Algorithm) or fuzzy combined with neural networks artificial. Acknowledgments: The author wants to kindly thank to Key Laboratory of Marine Power Engineering & Technology (Ministry of Transportation), School of Energy and Power Engineering, Wuhan University of Technology, 1178 Heping Road, Wuhan 430063, Hubei, China supports to complete this research. Conflicts of Interest: The author declares no conflicts of interest

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