# The Optimization of Marine Diesel Engine Rotational Speed Control Process by Fuzzy Logic Control Based on Particle Swarm Optimization Algorithm

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Fuzzy Logic Control Theory

#### 2.1.1. Fuzzification

#### 2.1.2. Rule Base

#### 2.1.3. Inference Engine

#### 2.1.4. Defuzzification

#### 2.2. Particle Swarm Optimization Algorithm

_{best}. The fitness function value will correspond to the best location (L

_{best}). Especially, a particle takes all of the topological neighbors. In this case, the best value will be a global best value and it is known as G

_{best}(Figure 3) [13].

_{best}; and,

_{best}.

_{best}) and the global best (G

_{best}). On the other hand, the velocity change is weighted by random terms with separate random numbers being generated for acceleration toward the two best solutions (P

_{best}and G

_{best}). The procedures of PSO algorithm have been showed in Figure 4.

- ➢
- Initialization process: Generate a population of particles and allocate a velocity to each particle randomly.
- ➢
- Ø Evaluation process: Update the best locations of particles and calculate the optimization fitness function.
- ➢
- Velocity and location update: Change the location of each particle by means of updating its own velocity as well as the particle will be adjusted dramatically.
- ➢
- The updating process of velocity and location at each particle can be realized through Equations (1) and (2).

_{best}is the previous best;

_{best}is the global best;

_{1}, c

_{2}are the acceleration coefficients; and,

_{1}, r

_{2}are the random numbers between 0 and 1.

_{best}) and the position in the d-dimensional space. Furthermore, the velocity of each particle is adjusted according to its own flying experience and the other particle’s flying experience. It is assumed that the j-th particle is represented as x

_{i}= (x

_{i}

_{1}, x

_{i}

_{2}, ..., x

_{id}) in the d-dimensional space then the best previous position of the i-th particle will be recorded and is described like this:

_{best i}= (P

_{best i1}, P

_{best i2}, ..., P

_{best in})

_{best}

_{d}. The velocity of i-th particle is specified as v

_{i}= (v

_{i}

_{1}, v

_{i}

_{2}, ..., v

_{id}). Additionally, the modified velocity and the position of each particle are computed following Equation (1) and (2).

## 3. Case Study

#### Modeling of Main Diesel Engine Rotational Speed Control by Fuzzy Logic Control Theory

_{best}of each particle and G

_{best}of population (the best movement of all particles). In a result, the update of velocity, position, P

_{best}, and G

_{best}of particles will approach a new best position (best chromosome in our proposition) (Figure 10).

_{e}and K

_{de}coefficients. Secondly, the shape of membership functions includes following coefficients e

_{1}~e

_{7}, de

_{1}~de

_{7}, and n

_{1}~n

_{7}. Thirdly, the fuzzy inference rules include r

_{1}~r

_{49}. On the other hand, the diesel engine speed output is thereby such that the steady state error of response is zero.

_{1}~r

_{49}are corresponded to number 1 (Negative Big—NB), 2 (Negative Medium—NM), 3 (Negative Small—NS), 4 (Zero—Z), 5 (Positive Small—PS), 6 (Positive Medium—PM), and 7 (Positive Big—PB).

## 4. Results

## 5. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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

**Figure 4.**Procedures of the Particle Swarm Optimization [24].

**Figure 8.**Surface of diesel engine speed control.3.2. Optimization of Main Diesel Engine Rotational Speed Control Process by Particle Swarm Optimization Algorithm.

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

e | NB | NM | NS | ZO | PS | PM | PB | |
---|---|---|---|---|---|---|---|---|

de | ||||||||

NB | PB | PB | PM | PM | PS | ZO | ZO | |

NM | PB | PB | PM | PM | PS | ZO | ZO | |

NS | PB | PB | PM | PS | ZO | NM | NM | |

ZO | PB | PB | PM | ZO | NM | NB | NB | |

PS | PM | PM | ZO | NS | NM | NB | NB | |

PM | ZO | ZO | NS | NM | NM | NB | NB | |

PB | ZO | ZO | NS | NM | NM | NB | NB |

e | NB | NM | NS | ZO | PS | PM | PB | |
---|---|---|---|---|---|---|---|---|

de | ||||||||

NB | r_{1} | r_{8} | r_{15} | r_{22} | r_{29} | r_{36} | r_{43} | |

NM | r_{2} | r_{9} | r_{16} | r_{23} | r_{30} | r_{37} | r_{44} | |

NS | r_{3} | r_{10} | r_{17} | r_{24} | r_{31} | r_{38} | r_{45} | |

ZO | r_{4} | r_{11} | r_{18} | r_{25} | r_{32} | r_{39} | r_{46} | |

PS | r_{5} | r_{12} | r_{19} | r_{26} | r_{33} | r_{40} | r_{47} | |

PM | r_{6} | r_{13} | r_{20} | r_{27} | r_{34} | r_{41} | r_{48} | |

PB | r_{7} | r_{14} | r_{21} | r_{28} | r_{35} | r_{42} | r_{49} |

Population Size | 50 | e_{1}, de_{1} and n_{1} | [−1, −1, −0.4] |

Number of Iteration | 100 | e_{2}, de_{2} and n_{2} | [−1, −0.4, −0.2] |

w_{max} | 0.6 | e_{3}, de_{3} and n_{3} | [−0.4, −0.2, 0] |

w_{min} | 0.1 | e_{4}, de_{4} and n_{4} | [−0.2, 0, 0.2] |

c_{1} = c_{2} | 1.5 | e_{5}, de_{5} and n_{5} | [0, 0.2, 0.4] |

Min-offset | 200 | e_{6}, de_{6} and n_{6} | [0.2, 0.4, 1] |

K_{e} and K_{de} | [0.001, 0.005] | e_{7}, de_{7} and n_{7} | [0.4, 1, 1] |

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Tran, T.A.
The Optimization of Marine Diesel Engine Rotational Speed Control Process by Fuzzy Logic Control Based on Particle Swarm Optimization Algorithm. *Future Internet* **2018**, *10*, 99.
https://doi.org/10.3390/fi10100099

**AMA Style**

Tran TA.
The Optimization of Marine Diesel Engine Rotational Speed Control Process by Fuzzy Logic Control Based on Particle Swarm Optimization Algorithm. *Future Internet*. 2018; 10(10):99.
https://doi.org/10.3390/fi10100099

**Chicago/Turabian Style**

Tran, Tien Anh.
2018. "The Optimization of Marine Diesel Engine Rotational Speed Control Process by Fuzzy Logic Control Based on Particle Swarm Optimization Algorithm" *Future Internet* 10, no. 10: 99.
https://doi.org/10.3390/fi10100099