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International Journal of Fuzzy Logic and Intelligent Systems 2024; 24(3): 306-316

Published online September 25, 2024

https://doi.org/10.5391/IJFIS.2024.24.3.306

© The Korean Institute of Intelligent Systems

Design and Noise Reduction for Fuzzy Proportional-Integral-Derivative Logic Controller Using Kalman Filter

Tien Anh Tran1,2

1Faculty of Marine Engineering, Vietnam Maritime University, Haiphong, Vietnam
2Marine Research Institute, Vietnam Maritime University, Haiphong, Vietnam

Correspondence to :
Tien Anh Tran (trantienanhvimaru@gmail.com)

Received: June 9, 2020; Accepted: September 16, 2024

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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Controlling diesel engine speed is essential for stable and efficient ship operation. The diesel engine speed directly affects the fuel consumption of marine diesel engines. The choice of optimal engine speed is guided by extensive research in ship energy efficiency and diesel engine speed control theory. This study investigates the above issues by proposing a novel approach. The proposed method is more effective than traditional control methods. First, the traditional proportional-integral-derivative (PID) controller of marine diesel engine speed is established. Secondly, this controller adopts online tuning through fuzzy logic control theory using the Kalman filter method. Thereafter, a fuzzy logic controller and genetic algorithm are applied to tune the traditional PID controller. This study aims to obtain the optimal diesel engine speed controller with better dynamic and static performance than the traditional control methods. The results have been compared and verified with the equivalence fuzzy PID controller. The proposed controller is useful and significant in marine engineering, as it increases the stable and responded characteristics of marine diesel engine speed controllers.

Keywords: Marine diesel engine, Modern control theory, Genetic algorithm, Fuel oil consumption, Fuzzy PID control

1. Introduction

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Diesel engines are crucial in marine engineering applications and are widely used as power-generating devices to rotate screw propellers in ships. In some studies, diesel engines have been driven by propulsion systems, including automobiles, ships, and backup power units [1]. Marine propulsion plants require high-power engines for component rotation. A large diesel engine rotates its moving parts, including the camshaft, fuel oil injector, and governor. The camshaft adjusts the appropriate timing to inject fuel oil into the combustion chamber of the diesel engine. The governor is an important device for maintaining diesel engine speed when external loads affect diesel engine rotation.

Furthermore, controlling the diesel engine speed is an important factor to consider when improving the energy efficiency management of ships by selecting the optimal diesel engine speed during operation. Selecting the optimal diesel engine speed reduces the fuel oil consumption of the main diesel engine. Extensive research has been conducted on ship energy-efficiency management. They indicated that the best solution for ship energy efficiency management methods is selecting an appropriate diesel engine speed corresponding to the sea environmental conditions.

Previous studies have shown that modern control theory has some advantages over traditional control theory; these include high stability and flexibility. Moreover, the traditional control theory has been widely used as a proportional-integral-derivative (PID) conventional control theory. The device is used to regulate the diesel engine speed and is called the governor. Normally, the governor can be designed as either proportional (P) or proportional plus integral (P + I) plus derivative (P + I + D). These types are designed according to the control strategies for diesel engines. A marine diesel engine speed controller was assigned as a governor to control the speed of the diesel engine. The model system is shown in Figure 1 with the devices and sensors used in this system.

The rotational speed of the marine diesel engine was measured using a magnetic pickup set on the ring gear of the fly-wheel of the diesel engine. The diesel engine speed signal was then transmitted to the comparative component through a frequency/voltage (F/V) converter (Figure 1).

However, some previous studies compared classical PID controllers and fuzzy PID logic controllers. Normally, a conventional PID controller presents the disadvantages of insufficient information to control the control process, including time delay, significant oscillatory behavior, parameter variations, nonlinearities, and multi-input and multi-output (MIMO) [2, 3]. Additionally, there are some practical implications of the conventional structure of a PID controller because of its proportional and derivative applications with the external error signal. This is caused by the change in the initial set-point value of the controller. Normally, this control signal can be driven by an actuator such as a motor and/or valve, which is a significant problem in electronic circuitry. This is the primary reason for modifying the classical PID controller to an integral-minus-proportional-minus-derivative (P-I-D) [4–13] Fuzzy logic control theory was applied to establish a marine diesel engine speed controller [14]. Therefore, an advanced research direction has been addressed by combining the traditional PID controller and the fuzzy logic controller. This combination enhances traditional PID controllers.

Recently, a novel idea was generated by providing a more robust and optimal PID controller through other techniques such as the Ziegler-Nichols, Cohen–Coon, Chien-Hrones-Reswick methods [15]. Fuzzy logic theory and fuzzy PID controllers were applied to establish a marine diesel engine speed controller. Extensive research has been conducted on diesel engine speed control. Tran et al. [16] designed a marine diesel engine speed controller based on fuzzy PID control theory. Wang et al. [17] developed a novel control method based on multiple model predictive functional controls (MMPFCs) for marine diesel engine speed control. Recently, research on novel methods has been conducted. In particular, evolutionary algorithms (EAs) offer some advantages in modern control theory. An EA is a novel algorithm used to search for the optimal point to control the output objects. EA consists of particle swarm optimization (PSO) and a genetic algorithm (GA). The EA is an effective tool for optimizing PID control theory turning [18]. A study of diesel engine speed controllers was conducted using the fuzzy logic control theory method based on the PSO method [19]. Normally, the EA is selected as an optimal algorithm that can address the definition problem domain, including multimodality, discontinuity, time variance, randomness, and noise [20]. However, the parameters of the diesel engine speed controller are important because they determine the appropriate degree of control. Consequently, the optimization of these parameters has been investigated using various methods. Here, the EA was studied to optimize these parameters. Bio-inspired algorithms, particularly PI controllers, have been considered for optimizing the parameters of marine diesel engines [21]. On another side, the GA is a stochastic search algorithm [22]. The actions of a population of possible solutions can be determined [22]. A GA can be a useful tool for dealing with numerous problems in control theory. The priority of GA is not necessarily to require information regarding the continuity and differentiability of the search space. Finding convergence without information is easier compared to other methods. Therefore, a GA is used to optimize the parameters of the fuzzy PID logic controller.

Some researchers have addressed these proposed methods in control theory; notably, Xie et al. [23] investigated the backstepping method, excluding modern control theories like the state-compensated extended state observer. Hence, studies have been conducted on the control strategies for marine diesel engine speed controllers. In general, the control strategy benefits the ship operational activities by reducing fuel oil consumption of the main diesel engine and limiting exhaust gas emissions. Hu et al. [24] studied a control strategy for a medium-speed marine diesel engine using a control algorithm.

Overall, some previous studies offered optimization of the marine diesel engine speed controller, including conventional PID control theory [25, 26], adaptive control method [27, 28], and sliding mode control [29–32]. However, these studies also have drawbacks in designing the control rule and the external factors influencing the diesel engine speed. Therefore, it is necessary to develop a novel control method to propose an appropriate control strategy for marine diesel engines. Here, we propose a novel method using a combination of modern and conventional control theories. Subsequently, the Kalman filter method was applied to extract the external factors influencing the marine diesel engine speed controller. The framework of this study is illustrated in Figure 2.

This study aims to determine the appropriate diesel engine speed for a marine diesel engine to increase the reliability of the diesel engine speed controller. Research on modern control theories is necessary in marine engineering. The proposed methods were studied to establish the appropriate diesel engine speed through modern control theory, as well as the use of filters to eliminate noise during the control process.

The rest of this paper is organized as follows. Section 2 outlines the materials and methods. Section 3 details the marine diesel engine speed controller, Section 4 highlights the results along with a discussion, and Section 5 provided the conclusions.

2. Materials and Methods

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2.1 Mathematical Model of Marine Diesel Engine

A marine diesel engine speed controller is called a governor and is based on standard control engineering principles. Its principles can be based on either a proportional (P) or proportional plus integral (P + I) plus derivative (P + I + D). This combination was based on the actual application of a diesel engine speed controller in ships.

Establishing a mathematical model is important for marine diesel engines when designing a diesel engine speed controller [33, 34].

Ta·dϕdt+Tg·ϕ=-ξ-αN,

where Ta is the diesel acceleration–time coefficient, ϕ represents the relative variation in diesel speed, Tg stands for the diesel speed recovery coefficient, ξ represents the pump plunger angle variation, and αN represents the relative variation in the diesel load.

The mathematical model of the diesel engine speed sensitization element is given in Eq. (2).

Tr2·d2ηdt2+Tk·dηdt+δn·η=ϕ,

where Tr is the speed sensitization element time coefficient, η is the relative displacement of the sliding valve, Tk is the liquid friction time coefficient, and δn is the degree of the governor instability.

2.2 Mathematical Model of Rigid Feedback Servo Mechanism

A rigid feedback servo mechanism is an automated control system that can adjust the output signal based on feedback received from the designed controller. This device is an intermediate device that interconnects the output signal of the controlled object with the initial setting signal of the controller. The rigid feedback servo mechanism is an independent device compared with a marine diesel engine (Figure 1). Therefore, a mathematical model for the rigid feedback servo mechanism is described in this section. The mathematical model of the rigid feedback servo mechanism has been extensively studied in the past [33, 34].

Ts·dξdt+B·ξ=η,

where Ts is the servo mechanism time coefficient, and B is the rigid feedback coefficient.

2.3 Mathematical Model of Constant-Speed Feedback Servo Mechanism

The mathematical model of the constant-speed feedback servo mechanism is based on previous research [33, 34].

Ts·dξdt+B·ɛ=η,Ti·dɛdt+ɛ=β0·Ti·dξdt,

where Ti represents the constant-speed servo time coefficient, ɛ represents the constant-speed servo-compensation piston relative displacement, and βo stands for the proportion coefficient.

2.4 Kalman Filter Method for Tuning Fuzzy PID Controller

Previous research has been conducted to determine the appropriate membership functions of fuzzy logic controllers. The derivative kick problem was developed by Muniandy et al. [35]. The phenomenon is caused by the nature of the PID controller and the conventional fuzzy PID control theory combined with an anti-roll-roll bar (AARB) [35]. They proposed two types of controllers: a self-tuning fuzzy proportional–integral–proportional–derivative (STF-PI-PD) and a PI-PD-type fuzzy controller [35].

The Kalman filter is an effective tool for estimating the state-of-the-art performance of a system from noisy measurements. A zero-mean white noise process was used to determine the appropriate Kalman filter for the innovation sequence process. The priority of the Kalman filter method is applied through its adaptation to temporal changes. The accomplishments of nonlinear filters, parallel Kalman filters, and covariance-matching techniques have been addressed previously. These methods yield good results at the expense of a large amount of considerable computational time (Figure 3). In addition, an adaptable algorithm employs fuzzy logic control theory through its rule base. Subsequently, the Kalman filter algorithm was adopted to accommodate the changes in the system parameters. The Kalman filter algorithm examines the innovative sequence process of the system and makes appropriate changes to the system model.

The Kalman filter algorithm is crucial in removing noise from external factors that influence the marine diesel engine speed controller during the control process (Figure 4).

3. Marine Diesel Engine Speed Controller

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The study of marine diesel engine speed controllers is important in marine engineering. The revolution of marine diesel engines has consistently varied owing to the navigation environment conditions. In addition, this variation occurs at different levels depending on the ocean area. Therefore, the navigation environment condition was determined to be an uncertain external factor affecting diesel engine speed. Determining the optimal diesel engine speed can be a difficult task. This research addresses this issue by establishing a marine diesel engine speed controller.

The general scheme of the marine diesel engine controller is shown in Figure 5. A diesel engine is used as the reference speed signal. Typically, this signal is set by the engine officer, particularly the 1st engineer. The control signal is sent to a diesel engine speed controller. Using the initial coefficients, the acting signal of the diesel engine speed controller is released to adjust the fuel oil rack position of the marine diesel engine. This study changes the diesel engine speed by varying the mass of fuel oil consumed by the diesel engine. The comparison component was equipped with a marine diesel engine speed controller to compare reference and actual speeds.

A combination of a PID controller and a fuzzy logic controller was established in this research. The priority of this controller was investigated and analyzed in Section 4. The advantages of this controller were identified and compared with those of a conventional PID controller. The control logic is described and analyzed using mathematical equations. The achievement of high performance under specific operating conditions and the desired possession of other features were investigated in this study. These features include stability, robustness, and two basic structures.

The fuzzy PID controller designed in this study corresponds to a conventional PID controller, which is derived from its equivalence equations. First, a conventional PID controller with an output signal u(t) in the time domain is presented as follows:

u(t)=Kp·e(t)+KI·∫e(t)dt+KD·de(t)dt.

The error signal e(t) is given by Eq. (7):

e(t)=f(Sset)-f(Sact),

where u(t) is the control signal of a marine diesel engine speed controller (governor), e(t) is the error signal between the set and measured values, and Sset and Sact represent the set and actual diesel engine speeds, respectively.

Kp, KI, and KD represent the proportional, integral, and derivative gains, respectively. This controller provides proportional integration and a derivative platform. The reaction of the current error was specified for the proportional gain Kp. The reaction of the sum of the recent error or reset action is specified for the integral gain KI, and the reaction of the error rate is specified for KD. Additionally, the output u(t) with three inputs, e(t), ∫ e(t), and e(t) could be thought of as a fuzzy variable in the FLC design.

The combination of a fuzzy logic controller and a PID controller was investigated in this research. This implies that the use of intelligent control theory with a conventional PID will benefit the diesel engine speed controller. The fuzzy PID logic controller reduces the number of inputs from three to two compared with the conventional PID logic controller. In addition, nine possible combinations of linguistic rules exist [36]. The output of the fuzzy PID logic controller would be expressed under Eq. (8).

uFs(t)=∑n=19un(t)/∑n=1μn(t),

where

un(t)={Kp.e(t)+KD.de(t)dt}·μ(|es|)+KI·μI·(|∫e(t)dt|)·∫e(t)dt,un(t)=min{μi(|es|),μj(∫e(t)dt)},∫e(t)dt=∫e(t-1)dt+0.5Ts(e(t-1)+e(t)),de(t)dt=(e(t)-e(t-a))/Ts,n=i+3(j-1).

Here, Ts represents the sample period, and μi and μj are the membership functions.

A mathematical model is used to design and simulate a marine diesel engine speed controller. The Simulink/MATLAB platform is a useful tool for supporting and simulating the operation of marine diesel engine speed controllers. A model of the marine diesel engine speed controller was presented in the Simulink/MATLAB platform. Each functional block of the speed-control system is illustrated using the Simulink platform.

4. Results and Discussion

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4.1 Simulation of the Marine Diesel Engine Speed Controller

The appropriate value of the marine diesel engine speed is important for ship propulsion characteristics and power generation [37]. Research on marine diesel engine speed controllers is important in marine engineering. An appropriate diesel engine speed controller is crucial to ship owners and ship operators both in terms of ship energy efficiency management and controlling theory. Therefore, the proposed method is necessary for speed controllers in marine diesel engines. In this study, the author addressed and researched a novel method for improving the control quality of a marine diesel engine speed controller. This study is conducted to simulate and analyze the results of the proposed controller.

4.1.1 Fuzzy PID logic controller

The fuzzy logic controller is applied from modern control theory to linear and nonlinear control theories. A combination of modern and conventional control theories is addressed in this study. PID theory is combined with modern control theories, such as fuzzy logic control theory. The proposed controller was designed using a fuzzy simulation platform. The input signals are the speed error (e) and variable-speed error (ec). The output signals are represented as coefficients of the proposed controller. These coefficients include the proportional, integral, and derivative gains. The simulation results are presented in this research.

A rule view is shown in Figure 6. Both input and output signals were obtained by simulating the fuzzy platform in MATLAB.

Surface inferences of the control parameters are presented in this study. The relationship between the inputs and outputs was identified using a 3D simulation platform. The values of speed error and derivative error are in the range of [−1, 1] (Figure 7). The output signals are simulated using proportional, integral, and derivative gains (Figure 8). These coefficients vary based on the uncertain environment affecting the speed controller. The proposed controller with these coefficients can then obtain the optimal diesel engine speed with minimum error.

The establishment of marine diesel engine speed controllers is crucial in marine engineering. The proposed methods have been investigated previously, and the objective of this study is a main target to understand marine diesel engine speed controllers.

As shown in Figure 9, a fuzzy PID logic controller was established on the Simulink platform. This controller combines fuzzy logic control theory and conventional PID control theory to achieve high-quality control performance. The fuzzy logic controller regulates the control coefficients (KP, KD, KI ) to obtain an appropriate control signal. This was based on a mathematical model of a marine diesel engine speed controller. Each functional block contributes to the control characteristics of a marine diesel engine speed controller. In this study, the characteristics of a marine diesel engine speed controller were investigated and validated by installing the controller in a specific marine diesel engine.

4.1.2 Elimination of external noise using the Kalman filter method

The Kalman filter method is used in this study. The physical characteristics of a Kalman filter are linear, discrete-time, and finite-dimensional systems [38]. The Kalman algorithm was associated with a fuzzy PID logic controller to automatically adjust the proposed controller parameters during the working process. This adjustment makes it adaptable to the parameters of the proposed controller to decrease noisy factors. The Kalman filter is an important tool for separating noisy variable factors influencing the marine diesel engine speed controller. Normally, these noisy variables appear in the navigational environment of ships.

The navigational environment of ships is an external factor that affects the rotational engine speed of marine diesel engines. The navigational environment conditions include the weather conditions of the sea (atmospheric pressure, temperature, humidity, salty content, etc.), mechanical vibration of engines, and technical assembly clearance.

4.2 Comparison of the Proposed Methods with an Equivalence Fuzzy PID Controller

Research on marine diesel engine speed controllers has been conducted using different methods in modern control theories. The validation of the research results is important for evaluating the working ability of marine diesel engines under the impact of external factors. Additionally, different researchers worldwide have studied novel marine diesel engine speed controllers. This is because the fuzzy PID logic controller equipped with the Kalman filter is compared with the equivalence fuzzy PID controller.

The proposed controller was validated using an equivalent fuzzy PID logic controller. Initially, an equivalent fuzzy PID logic controller was established based on an experimental model of a marine diesel engine speed controller. The establishment of functional blocks was designed on the Simulink platform and is detailed in Figure 10.

In Figure 10, the equivalent PID logic controller is established with the traditional KD, KI, and KP for the marine diesel engine speed controller. These coefficients vary during the control process of the equivalent controller, supporting the fuzzy logic control theory. Therefore, the control signal of the traditional controller varies under uncertain environmental conditions. The error derivative signal approaches one, and this value exhibits a reduction trend through this equivalent controller with the fuzzy PID logic control theory. This study aims to reduce external factors and environmental conditions by proposing a combined fuzzy PID logic control theory and Kalman filter to address the noisy signals affecting the diesel engine speed controller.

The results of the equivalent fuzzy PID logic controller are shown in Figures 11–14. In the proposed controller, the trajectory between the input and output signals of the marine diesel engine speed controller was provided and flexibly controlled under external environmental conditions. This study also addressed the expression of the controlling characteristic curves. The coefficients of the proportional, integral, and derivative gains were simulated and validated using the Simulink platform. The results are presented in Figure 15.

As shown in Figure 15, the quality of this controller was better than that of the equivalent PID controller using the Kalman filter algorithm. This controller is smooth and variable with a large range to increase its adaptability to external factors impacting the proposed controller. These coefficients (KD, KP, KI ) are regulated automatically according to environmental conditions. Therefore, the control performance is better when using a combination of fuzzy logic control theory and the Kalman filter by automatically regulating these controlling coefficients. The trajectories of the proposed speed controller were presented in this study. The values of the coefficients are presented in the results of this study. The fuzzy PID logic controller with the Kalman filter has a better control quality than the equivalent fuzzy PID logic controller. The trajectories of the proposed controller for the control process and the relationship between the inputs and output (diesel engine speed) are presented.

5. Conclusion

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Marine diesel-engine speed controllers are crucial in marine engineering. A study on the optimal diesel engine speed controller is necessary for the operation process and working of a marine diesel engine. The control quality of a marine diesel engine is first considered by ship operators to control and maintain the diesel engine speed similar to the desired reference speed. The novelty of the proposed method is that it addresses the problem of control theory. The following conclusions were drawn from this research:

  • - The relationship between the input and output signals should be considered because they determine the quality control process of marine diesel engines. The input and output signals were directly supervised and controlled by operators.

  • - The application of a filter in a marine diesel engine speed controller is significant for increasing control quality and eliminating the impact of external factors on the marine diesel engine speed controller. The characteristic curves of a marine diesel engine are smoother when the speed controller is equipped with a Kalman filter algorithm.

Acknowledgments

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The author appreciates the colleagues at the Marine Research Institute, Vietnam Maritime University, Haiphong City, Vietnam, for their support.

Figures

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Fig. 1.

Marine diesel engine speed control system.


Fig. 2.

Framework of marine diesel engine speed controller.


Fig. 3.

General scheme of a control system using state estimation.


Fig. 4.

Marine diesel engine speed controller using Kalman filter.


Fig. 5.

Control model of marine diesel engine speed.


Fig. 6.

Inference of the fuzzy logic controller.


Fig. 7.

Fuzzy logic control rule.


Fig. 8.

Surface simulation of output signals: (a) proportional gain (Kp), (b) integral gain (Ki), and (c) derivative gain (Kd).


Fig. 9.

Model of marine diesel engine speed controller in Simulink/MATLAB.


Fig. 10.

Equivalent PID logic controller on the Simulink platform.


Fig. 11.

Control signal .


Fig. 12.

Output signal.


Fig. 13.

Unit step signal.


Fig. 14.

Error derivative signal.


Fig. 15.

Trajectory between output gains and input. (a) Trajectory of Kp and input. (b) Trajectory of Ki and input. (c) Trajectory of Kd and input.


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Biography

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Tien Anh Tran is a Researcher at the Department of Electrical Engineering, University of Malta, Malta. He was a Postdoctoral researcher at the Department of Naval Architecture and Ocean Engineering, Seoul National University (SNU), Seoul, South Korea (October 2022–October 2023). Currently, he is an Assistant Professor (Lecturer) at the Department of Marine Engineering, Vietnam Maritime University, Haiphong City, Vietnam, an Honorary Professor at School of Computing Science and Engineering, Galgotias University, India, and an Honorary Adjunct Professor at School of Computer Science and Engineering, Lovely Professional University (LPU), India. Additionally, he is an adjunct faculty member at SIMATS Engineering, Saveetha Institute of Medical and Technical Sciences, Tamil Nadu, India. He received his B.Eng. and M.Sc. from Vietnam Maritime University, Vietnam in 2011 and 2014, respectively. He got his Ph.D. Degree at Wuhan University of Technology, Wuhan, China in 2018. He is an Editor/Guest Editor for reputed journals indexed in SCI/SCIE, such as Environment, Development and Sustainability, IET Intelligent Transport System, International Journal of Distributed Sensor Networks, Sustainable Computing: Informatics and Systems, International Journal of Renewable Energy Technology, International Journal of Energy Optimization and Engineering, IEEE Internet of Things Magazine, and Mathematics. In 2015, he was awarded the Chinese Government Scholarship (CSC) for a full funding of the Doctor of Philosophy (Ph.D.) program in China. In 2019, he was awarded the NEPTUNE prize for outstanding researchers by Vietnam Maritime University. In 2022, he was one of the five outstanding scientists in Vietnam to be nominated for the Ta Quang Buu prize by the National Foundation for Science & Technology Development (NAFOSTED). Additionally, he had been selected and awarded a full scholarship for the Postdoctoral Fellowship Program of the National Research Foundation (NRF) for Foreign Researchers by the Government of South Korea.

Article

Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2024; 24(3): 306-316

Published online September 25, 2024 https://doi.org/10.5391/IJFIS.2024.24.3.306

Copyright © The Korean Institute of Intelligent Systems.

Design and Noise Reduction for Fuzzy Proportional-Integral-Derivative Logic Controller Using Kalman Filter

Tien Anh Tran1,2

1Faculty of Marine Engineering, Vietnam Maritime University, Haiphong, Vietnam
2Marine Research Institute, Vietnam Maritime University, Haiphong, Vietnam

Correspondence to:Tien Anh Tran (trantienanhvimaru@gmail.com)

Received: June 9, 2020; Accepted: September 16, 2024

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Controlling diesel engine speed is essential for stable and efficient ship operation. The diesel engine speed directly affects the fuel consumption of marine diesel engines. The choice of optimal engine speed is guided by extensive research in ship energy efficiency and diesel engine speed control theory. This study investigates the above issues by proposing a novel approach. The proposed method is more effective than traditional control methods. First, the traditional proportional-integral-derivative (PID) controller of marine diesel engine speed is established. Secondly, this controller adopts online tuning through fuzzy logic control theory using the Kalman filter method. Thereafter, a fuzzy logic controller and genetic algorithm are applied to tune the traditional PID controller. This study aims to obtain the optimal diesel engine speed controller with better dynamic and static performance than the traditional control methods. The results have been compared and verified with the equivalence fuzzy PID controller. The proposed controller is useful and significant in marine engineering, as it increases the stable and responded characteristics of marine diesel engine speed controllers.

Keywords: Marine diesel engine, Modern control theory, Genetic algorithm, Fuel oil consumption, Fuzzy PID control

1. Introduction

Diesel engines are crucial in marine engineering applications and are widely used as power-generating devices to rotate screw propellers in ships. In some studies, diesel engines have been driven by propulsion systems, including automobiles, ships, and backup power units [1]. Marine propulsion plants require high-power engines for component rotation. A large diesel engine rotates its moving parts, including the camshaft, fuel oil injector, and governor. The camshaft adjusts the appropriate timing to inject fuel oil into the combustion chamber of the diesel engine. The governor is an important device for maintaining diesel engine speed when external loads affect diesel engine rotation.

Furthermore, controlling the diesel engine speed is an important factor to consider when improving the energy efficiency management of ships by selecting the optimal diesel engine speed during operation. Selecting the optimal diesel engine speed reduces the fuel oil consumption of the main diesel engine. Extensive research has been conducted on ship energy-efficiency management. They indicated that the best solution for ship energy efficiency management methods is selecting an appropriate diesel engine speed corresponding to the sea environmental conditions.

Previous studies have shown that modern control theory has some advantages over traditional control theory; these include high stability and flexibility. Moreover, the traditional control theory has been widely used as a proportional-integral-derivative (PID) conventional control theory. The device is used to regulate the diesel engine speed and is called the governor. Normally, the governor can be designed as either proportional (P) or proportional plus integral (P + I) plus derivative (P + I + D). These types are designed according to the control strategies for diesel engines. A marine diesel engine speed controller was assigned as a governor to control the speed of the diesel engine. The model system is shown in Figure 1 with the devices and sensors used in this system.

The rotational speed of the marine diesel engine was measured using a magnetic pickup set on the ring gear of the fly-wheel of the diesel engine. The diesel engine speed signal was then transmitted to the comparative component through a frequency/voltage (F/V) converter (Figure 1).

However, some previous studies compared classical PID controllers and fuzzy PID logic controllers. Normally, a conventional PID controller presents the disadvantages of insufficient information to control the control process, including time delay, significant oscillatory behavior, parameter variations, nonlinearities, and multi-input and multi-output (MIMO) [2, 3]. Additionally, there are some practical implications of the conventional structure of a PID controller because of its proportional and derivative applications with the external error signal. This is caused by the change in the initial set-point value of the controller. Normally, this control signal can be driven by an actuator such as a motor and/or valve, which is a significant problem in electronic circuitry. This is the primary reason for modifying the classical PID controller to an integral-minus-proportional-minus-derivative (P-I-D) [4–13] Fuzzy logic control theory was applied to establish a marine diesel engine speed controller [14]. Therefore, an advanced research direction has been addressed by combining the traditional PID controller and the fuzzy logic controller. This combination enhances traditional PID controllers.

Recently, a novel idea was generated by providing a more robust and optimal PID controller through other techniques such as the Ziegler-Nichols, Cohen–Coon, Chien-Hrones-Reswick methods [15]. Fuzzy logic theory and fuzzy PID controllers were applied to establish a marine diesel engine speed controller. Extensive research has been conducted on diesel engine speed control. Tran et al. [16] designed a marine diesel engine speed controller based on fuzzy PID control theory. Wang et al. [17] developed a novel control method based on multiple model predictive functional controls (MMPFCs) for marine diesel engine speed control. Recently, research on novel methods has been conducted. In particular, evolutionary algorithms (EAs) offer some advantages in modern control theory. An EA is a novel algorithm used to search for the optimal point to control the output objects. EA consists of particle swarm optimization (PSO) and a genetic algorithm (GA). The EA is an effective tool for optimizing PID control theory turning [18]. A study of diesel engine speed controllers was conducted using the fuzzy logic control theory method based on the PSO method [19]. Normally, the EA is selected as an optimal algorithm that can address the definition problem domain, including multimodality, discontinuity, time variance, randomness, and noise [20]. However, the parameters of the diesel engine speed controller are important because they determine the appropriate degree of control. Consequently, the optimization of these parameters has been investigated using various methods. Here, the EA was studied to optimize these parameters. Bio-inspired algorithms, particularly PI controllers, have been considered for optimizing the parameters of marine diesel engines [21]. On another side, the GA is a stochastic search algorithm [22]. The actions of a population of possible solutions can be determined [22]. A GA can be a useful tool for dealing with numerous problems in control theory. The priority of GA is not necessarily to require information regarding the continuity and differentiability of the search space. Finding convergence without information is easier compared to other methods. Therefore, a GA is used to optimize the parameters of the fuzzy PID logic controller.

Some researchers have addressed these proposed methods in control theory; notably, Xie et al. [23] investigated the backstepping method, excluding modern control theories like the state-compensated extended state observer. Hence, studies have been conducted on the control strategies for marine diesel engine speed controllers. In general, the control strategy benefits the ship operational activities by reducing fuel oil consumption of the main diesel engine and limiting exhaust gas emissions. Hu et al. [24] studied a control strategy for a medium-speed marine diesel engine using a control algorithm.

Overall, some previous studies offered optimization of the marine diesel engine speed controller, including conventional PID control theory [25, 26], adaptive control method [27, 28], and sliding mode control [29–32]. However, these studies also have drawbacks in designing the control rule and the external factors influencing the diesel engine speed. Therefore, it is necessary to develop a novel control method to propose an appropriate control strategy for marine diesel engines. Here, we propose a novel method using a combination of modern and conventional control theories. Subsequently, the Kalman filter method was applied to extract the external factors influencing the marine diesel engine speed controller. The framework of this study is illustrated in Figure 2.

This study aims to determine the appropriate diesel engine speed for a marine diesel engine to increase the reliability of the diesel engine speed controller. Research on modern control theories is necessary in marine engineering. The proposed methods were studied to establish the appropriate diesel engine speed through modern control theory, as well as the use of filters to eliminate noise during the control process.

The rest of this paper is organized as follows. Section 2 outlines the materials and methods. Section 3 details the marine diesel engine speed controller, Section 4 highlights the results along with a discussion, and Section 5 provided the conclusions.

2. Materials and Methods

2.1 Mathematical Model of Marine Diesel Engine

A marine diesel engine speed controller is called a governor and is based on standard control engineering principles. Its principles can be based on either a proportional (P) or proportional plus integral (P + I) plus derivative (P + I + D). This combination was based on the actual application of a diesel engine speed controller in ships.

Establishing a mathematical model is important for marine diesel engines when designing a diesel engine speed controller [33, 34].

Ta·dϕdt+Tg·ϕ=-ξ-αN,

where Ta is the diesel acceleration–time coefficient, ϕ represents the relative variation in diesel speed, Tg stands for the diesel speed recovery coefficient, ξ represents the pump plunger angle variation, and αN represents the relative variation in the diesel load.

The mathematical model of the diesel engine speed sensitization element is given in Eq. (2).

Tr2·d2ηdt2+Tk·dηdt+δn·η=ϕ,

where Tr is the speed sensitization element time coefficient, η is the relative displacement of the sliding valve, Tk is the liquid friction time coefficient, and δn is the degree of the governor instability.

2.2 Mathematical Model of Rigid Feedback Servo Mechanism

A rigid feedback servo mechanism is an automated control system that can adjust the output signal based on feedback received from the designed controller. This device is an intermediate device that interconnects the output signal of the controlled object with the initial setting signal of the controller. The rigid feedback servo mechanism is an independent device compared with a marine diesel engine (Figure 1). Therefore, a mathematical model for the rigid feedback servo mechanism is described in this section. The mathematical model of the rigid feedback servo mechanism has been extensively studied in the past [33, 34].

Ts·dξdt+B·ξ=η,

where Ts is the servo mechanism time coefficient, and B is the rigid feedback coefficient.

2.3 Mathematical Model of Constant-Speed Feedback Servo Mechanism

The mathematical model of the constant-speed feedback servo mechanism is based on previous research [33, 34].

Ts·dξdt+B·ɛ=η,Ti·dɛdt+ɛ=β0·Ti·dξdt,

where Ti represents the constant-speed servo time coefficient, ɛ represents the constant-speed servo-compensation piston relative displacement, and βo stands for the proportion coefficient.

2.4 Kalman Filter Method for Tuning Fuzzy PID Controller

Previous research has been conducted to determine the appropriate membership functions of fuzzy logic controllers. The derivative kick problem was developed by Muniandy et al. [35]. The phenomenon is caused by the nature of the PID controller and the conventional fuzzy PID control theory combined with an anti-roll-roll bar (AARB) [35]. They proposed two types of controllers: a self-tuning fuzzy proportional–integral–proportional–derivative (STF-PI-PD) and a PI-PD-type fuzzy controller [35].

The Kalman filter is an effective tool for estimating the state-of-the-art performance of a system from noisy measurements. A zero-mean white noise process was used to determine the appropriate Kalman filter for the innovation sequence process. The priority of the Kalman filter method is applied through its adaptation to temporal changes. The accomplishments of nonlinear filters, parallel Kalman filters, and covariance-matching techniques have been addressed previously. These methods yield good results at the expense of a large amount of considerable computational time (Figure 3). In addition, an adaptable algorithm employs fuzzy logic control theory through its rule base. Subsequently, the Kalman filter algorithm was adopted to accommodate the changes in the system parameters. The Kalman filter algorithm examines the innovative sequence process of the system and makes appropriate changes to the system model.

The Kalman filter algorithm is crucial in removing noise from external factors that influence the marine diesel engine speed controller during the control process (Figure 4).

3. Marine Diesel Engine Speed Controller

The study of marine diesel engine speed controllers is important in marine engineering. The revolution of marine diesel engines has consistently varied owing to the navigation environment conditions. In addition, this variation occurs at different levels depending on the ocean area. Therefore, the navigation environment condition was determined to be an uncertain external factor affecting diesel engine speed. Determining the optimal diesel engine speed can be a difficult task. This research addresses this issue by establishing a marine diesel engine speed controller.

The general scheme of the marine diesel engine controller is shown in Figure 5. A diesel engine is used as the reference speed signal. Typically, this signal is set by the engine officer, particularly the 1st engineer. The control signal is sent to a diesel engine speed controller. Using the initial coefficients, the acting signal of the diesel engine speed controller is released to adjust the fuel oil rack position of the marine diesel engine. This study changes the diesel engine speed by varying the mass of fuel oil consumed by the diesel engine. The comparison component was equipped with a marine diesel engine speed controller to compare reference and actual speeds.

A combination of a PID controller and a fuzzy logic controller was established in this research. The priority of this controller was investigated and analyzed in Section 4. The advantages of this controller were identified and compared with those of a conventional PID controller. The control logic is described and analyzed using mathematical equations. The achievement of high performance under specific operating conditions and the desired possession of other features were investigated in this study. These features include stability, robustness, and two basic structures.

The fuzzy PID controller designed in this study corresponds to a conventional PID controller, which is derived from its equivalence equations. First, a conventional PID controller with an output signal u(t) in the time domain is presented as follows:

u(t)=Kp·e(t)+KI·∫e(t)dt+KD·de(t)dt.

The error signal e(t) is given by Eq. (7):

e(t)=f(Sset)-f(Sact),

where u(t) is the control signal of a marine diesel engine speed controller (governor), e(t) is the error signal between the set and measured values, and Sset and Sact represent the set and actual diesel engine speeds, respectively.

Kp, KI, and KD represent the proportional, integral, and derivative gains, respectively. This controller provides proportional integration and a derivative platform. The reaction of the current error was specified for the proportional gain Kp. The reaction of the sum of the recent error or reset action is specified for the integral gain KI, and the reaction of the error rate is specified for KD. Additionally, the output u(t) with three inputs, e(t), ∫ e(t), and e(t) could be thought of as a fuzzy variable in the FLC design.

The combination of a fuzzy logic controller and a PID controller was investigated in this research. This implies that the use of intelligent control theory with a conventional PID will benefit the diesel engine speed controller. The fuzzy PID logic controller reduces the number of inputs from three to two compared with the conventional PID logic controller. In addition, nine possible combinations of linguistic rules exist [36]. The output of the fuzzy PID logic controller would be expressed under Eq. (8).

uFs(t)=∑n=19un(t)/∑n=1μn(t),

where

un(t)={Kp.e(t)+KD.de(t)dt}·μ(|es|)+KI·μI·(|∫e(t)dt|)·∫e(t)dt,un(t)=min{μi(|es|),μj(∫e(t)dt)},∫e(t)dt=∫e(t-1)dt+0.5Ts(e(t-1)+e(t)),de(t)dt=(e(t)-e(t-a))/Ts,n=i+3(j-1).

Here, Ts represents the sample period, and μi and μj are the membership functions.

A mathematical model is used to design and simulate a marine diesel engine speed controller. The Simulink/MATLAB platform is a useful tool for supporting and simulating the operation of marine diesel engine speed controllers. A model of the marine diesel engine speed controller was presented in the Simulink/MATLAB platform. Each functional block of the speed-control system is illustrated using the Simulink platform.

4. Results and Discussion

4.1 Simulation of the Marine Diesel Engine Speed Controller

The appropriate value of the marine diesel engine speed is important for ship propulsion characteristics and power generation [37]. Research on marine diesel engine speed controllers is important in marine engineering. An appropriate diesel engine speed controller is crucial to ship owners and ship operators both in terms of ship energy efficiency management and controlling theory. Therefore, the proposed method is necessary for speed controllers in marine diesel engines. In this study, the author addressed and researched a novel method for improving the control quality of a marine diesel engine speed controller. This study is conducted to simulate and analyze the results of the proposed controller.

4.1.1 Fuzzy PID logic controller

The fuzzy logic controller is applied from modern control theory to linear and nonlinear control theories. A combination of modern and conventional control theories is addressed in this study. PID theory is combined with modern control theories, such as fuzzy logic control theory. The proposed controller was designed using a fuzzy simulation platform. The input signals are the speed error (e) and variable-speed error (ec). The output signals are represented as coefficients of the proposed controller. These coefficients include the proportional, integral, and derivative gains. The simulation results are presented in this research.

A rule view is shown in Figure 6. Both input and output signals were obtained by simulating the fuzzy platform in MATLAB.

Surface inferences of the control parameters are presented in this study. The relationship between the inputs and outputs was identified using a 3D simulation platform. The values of speed error and derivative error are in the range of [−1, 1] (Figure 7). The output signals are simulated using proportional, integral, and derivative gains (Figure 8). These coefficients vary based on the uncertain environment affecting the speed controller. The proposed controller with these coefficients can then obtain the optimal diesel engine speed with minimum error.

The establishment of marine diesel engine speed controllers is crucial in marine engineering. The proposed methods have been investigated previously, and the objective of this study is a main target to understand marine diesel engine speed controllers.

As shown in Figure 9, a fuzzy PID logic controller was established on the Simulink platform. This controller combines fuzzy logic control theory and conventional PID control theory to achieve high-quality control performance. The fuzzy logic controller regulates the control coefficients (KP, KD, KI ) to obtain an appropriate control signal. This was based on a mathematical model of a marine diesel engine speed controller. Each functional block contributes to the control characteristics of a marine diesel engine speed controller. In this study, the characteristics of a marine diesel engine speed controller were investigated and validated by installing the controller in a specific marine diesel engine.

4.1.2 Elimination of external noise using the Kalman filter method

The Kalman filter method is used in this study. The physical characteristics of a Kalman filter are linear, discrete-time, and finite-dimensional systems [38]. The Kalman algorithm was associated with a fuzzy PID logic controller to automatically adjust the proposed controller parameters during the working process. This adjustment makes it adaptable to the parameters of the proposed controller to decrease noisy factors. The Kalman filter is an important tool for separating noisy variable factors influencing the marine diesel engine speed controller. Normally, these noisy variables appear in the navigational environment of ships.

The navigational environment of ships is an external factor that affects the rotational engine speed of marine diesel engines. The navigational environment conditions include the weather conditions of the sea (atmospheric pressure, temperature, humidity, salty content, etc.), mechanical vibration of engines, and technical assembly clearance.

4.2 Comparison of the Proposed Methods with an Equivalence Fuzzy PID Controller

Research on marine diesel engine speed controllers has been conducted using different methods in modern control theories. The validation of the research results is important for evaluating the working ability of marine diesel engines under the impact of external factors. Additionally, different researchers worldwide have studied novel marine diesel engine speed controllers. This is because the fuzzy PID logic controller equipped with the Kalman filter is compared with the equivalence fuzzy PID controller.

The proposed controller was validated using an equivalent fuzzy PID logic controller. Initially, an equivalent fuzzy PID logic controller was established based on an experimental model of a marine diesel engine speed controller. The establishment of functional blocks was designed on the Simulink platform and is detailed in Figure 10.

In Figure 10, the equivalent PID logic controller is established with the traditional KD, KI, and KP for the marine diesel engine speed controller. These coefficients vary during the control process of the equivalent controller, supporting the fuzzy logic control theory. Therefore, the control signal of the traditional controller varies under uncertain environmental conditions. The error derivative signal approaches one, and this value exhibits a reduction trend through this equivalent controller with the fuzzy PID logic control theory. This study aims to reduce external factors and environmental conditions by proposing a combined fuzzy PID logic control theory and Kalman filter to address the noisy signals affecting the diesel engine speed controller.

The results of the equivalent fuzzy PID logic controller are shown in Figures 11–14. In the proposed controller, the trajectory between the input and output signals of the marine diesel engine speed controller was provided and flexibly controlled under external environmental conditions. This study also addressed the expression of the controlling characteristic curves. The coefficients of the proportional, integral, and derivative gains were simulated and validated using the Simulink platform. The results are presented in Figure 15.

As shown in Figure 15, the quality of this controller was better than that of the equivalent PID controller using the Kalman filter algorithm. This controller is smooth and variable with a large range to increase its adaptability to external factors impacting the proposed controller. These coefficients (KD, KP, KI ) are regulated automatically according to environmental conditions. Therefore, the control performance is better when using a combination of fuzzy logic control theory and the Kalman filter by automatically regulating these controlling coefficients. The trajectories of the proposed speed controller were presented in this study. The values of the coefficients are presented in the results of this study. The fuzzy PID logic controller with the Kalman filter has a better control quality than the equivalent fuzzy PID logic controller. The trajectories of the proposed controller for the control process and the relationship between the inputs and output (diesel engine speed) are presented.

5. Conclusion

Marine diesel-engine speed controllers are crucial in marine engineering. A study on the optimal diesel engine speed controller is necessary for the operation process and working of a marine diesel engine. The control quality of a marine diesel engine is first considered by ship operators to control and maintain the diesel engine speed similar to the desired reference speed. The novelty of the proposed method is that it addresses the problem of control theory. The following conclusions were drawn from this research:

  • - The relationship between the input and output signals should be considered because they determine the quality control process of marine diesel engines. The input and output signals were directly supervised and controlled by operators.

  • - The application of a filter in a marine diesel engine speed controller is significant for increasing control quality and eliminating the impact of external factors on the marine diesel engine speed controller. The characteristic curves of a marine diesel engine are smoother when the speed controller is equipped with a Kalman filter algorithm.

Fig 1.

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Figure 1.

Marine diesel engine speed control system.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 2.

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Figure 2.

Framework of marine diesel engine speed controller.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 3.

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Figure 3.

General scheme of a control system using state estimation.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 4.

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Figure 4.

Marine diesel engine speed controller using Kalman filter.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 5.

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Figure 5.

Control model of marine diesel engine speed.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 6.

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Figure 6.

Inference of the fuzzy logic controller.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 7.

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Figure 7.

Fuzzy logic control rule.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 8.

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Figure 8.

Surface simulation of output signals: (a) proportional gain (Kp), (b) integral gain (Ki), and (c) derivative gain (Kd).

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 9.

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Figure 9.

Model of marine diesel engine speed controller in Simulink/MATLAB.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 10.

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Figure 10.

Equivalent PID logic controller on the Simulink platform.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 11.

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Figure 11.

Control signal .

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 12.

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Figure 12.

Output signal.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 13.

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Figure 13.

Unit step signal.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 14.

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Figure 14.

Error derivative signal.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

Fig 15.

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Figure 15.

Trajectory between output gains and input. (a) Trajectory of Kp and input. (b) Trajectory of Ki and input. (c) Trajectory of Kd and input.

The International Journal of Fuzzy Logic and Intelligent Systems 2024; 24: 306-316https://doi.org/10.5391/IJFIS.2024.24.3.306

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