Combustion Control of Ship’s Oil-Fired Boilers Based on Prediction of Flame Images

Abstract

This study proposes and validates a novel combustion control system for oil-fired boilers aimed at reducing air pollutant emissions through flame image prediction. The proposed system is easily applicable to existing ships. Traditional proportional combustion control systems supply fuel and air at fixed ratios according to the set steam load, without considering the emission of air pollutants. To address this, a stable and immediate control system is proposed, which adjusts the air supply to modify the combustion state. The combustion control system utilizes oxygen concentration predictions from flame images via SEF+SVM as control inputs and applies internal model control (IMC)-based proportional-integral (PI) control for real-time combustion control. Due to the complexity of modeling the image-based system, IMC filter constant tuning through experimentation is essential for achieving effective control performance. Experimental results showed that optimal control performance was achieved when the filter constant $\lambda$ was set to 1.5. In this scenario, the peak overshoot $M_p$ was reduced to 0.19245, and the Integral of Squared Error (ISE) was minimized to 10.1159, ensuring a stable response with minimal oscillation and maintaining a fast response speed. The results demonstrate the potential of the proposed system to improve combustion efficiency and reduce emissions of air pollutants. This study provides a feasible and effective solution for enhancing the environmental performance of marine oil-fired boilers. Given its ease of application to existing ships, it is expected to contribute to sustainable air pollution reduction across the maritime environment.

1. Introduction

Combustion boilers are widely used for steam generation in marine industries, power plants, and various utilities requiring substantial thermal energy [1,2]. In the marine sector, although the trend of producing steam-powered ships has significantly declined [3], boilers burning diesel fuel are still extensively used on ships employing diesel engines as the primary propulsion system. However, fossil fuels like diesel contribute to global warming by emitting greenhouse gases such as ${\mathrm{N}\mathrm{O}}_{\mathrm{x}}$, ${\mathrm{S}\mathrm{O}}_{\mathrm{x}}$, and ${\mathrm{C}\mathrm{O}}_2$ during combustion [4,5]. Compared to main propulsion systems such as internal combustion engines, there is relatively less regulation and concern regarding pollutants emitted from combustion boilers [6,7]. Thus, reducing air pollutants from ship boiler exhaust gases is imperative.

The boiler system generates exhaust gases with thermal energy through the atomization and combustion of pressurized air and fuel. These exhaust gases convert water into steam via heat transfer surfaces such as water tubes or fire tubes. The amount of air pollutants emitted varies depending on the equivalence ratio, which is the ratio of fuel to air during the combustion process [8].

To reduce air pollutants, it is necessary to properly control the air and fuel supplied for combustion [9]. However, traditional boiler combustion systems use a proportional combustion control, where a load of steam is the control target, and predetermined fuel and airflow rates are supplied for combustion. This method ensures system stability but does not take air pollutant emissions into account [10]. Consequently, research has been continuously conducted to directly control the fuel oil and air flow rates supplied to the combustion system in order to reduce air pollutants [11,12].

While effective, these solutions require design integration at the manufacturing stage, increasing costs and risking combustion instability and flame extinction due to transient responses in dynamic environments [13]. These challenges continue to favor the traditional proportional control approach. Therefore, this study proposes a system that reduces emissions by adding a combustion optimization control system to existing oil-fired boilers (OFBs), ensuring stability.

Previous research used direct measurement or indirect estimation of air pollutants and oxygen concentration based on operational data [14,15,16]. Direct measurement is unsuitable for real-time control due to delays, while indirect methods are economically burdensome and vulnerable to sensor failures [15]. Therefore, control systems using soft measurement have been explored. This study employs a soft measurement method by analyzing quasi-instantaneous flame images to predict air pollutants for real-time control.

Dynamic modeling of a boiler combustion system using flame images as control inputs is complex, often requiring machine learning-based modeling methods [17]. Selecting appropriate control techniques and parameters is crucial [18,19]. This study uses an IMC-based PI controller to maintain a constant oxygen concentration from flame images. PI control is well-established in the industry, and incorporating IMC enhances reliability, making it easy to apply to ships and capable of excellent performance [20,21].

Experiments on a 3000 kg/h heavy oil boiler validate the SEF+SVM method for predicting oxygen concentration, indirectly measuring emissions and combustion efficiency. Prior research validated this method on the same plant, where flame images under six combustion conditions trained a model for oxygen concentration estimation as the control input. The closed-loop transfer function was estimated using experimental input-output data, leading to an IMC-based PI controller design. Parameters were optimized to balance robustness and control performance, demonstrating effectiveness through control verification.

The problem addressed in this study is the reduction of air pollutant emissions from marine oil-fired boilers. Traditional systems do not consider emissions in their control strategies, leading to environmental concerns. The purpose of this research is to develop a combustion control system using real-time predictions from flame images to optimize the combustion process and reduce emissions. This approach is important as it offers a feasible solution that can be easily applied to existing ships, thus contributing significantly to reducing marine air pollution in a cost-effective manner while maintaining system stability.

The objectives of this study can be summarized as follows:

• Propose a combustion control system to reduce air pollutant emissions from marine oil-fired boilers.
• Develop a real-time combustion control system using predicted oxygen concentration from flame images as control inputs.
• Tune an IMC-based PI controller through experiments to compensate for system discrepancies.

2. Combustion Control System for Marine Oil-Fired Boilers

Figure 1 shows a schematic diagram of the experimental setup. $\mathcal{P}1$ represents the steam pressure control process, which is a closed-loop control process that ensures the steam pressure generated by the ship’s OFB reaches the setpoint. This process adjusted the fuel valve and the damper opening of the turbocharger fan at a fixed ratio according to the internal logic programmed into the PLC to achieve the set control target. Since the fuel and air supply cannot be independently controlled in this process, it was difficult to adjust the combustion state independently in response to disturbances such as fuel oil properties or system variations. Therefore, to address this issue in the existing OFB system and improve the combustion state, a new control process, $\mathcal{P}2$, was used, which included an additional servo motor for adjusting the damper controlled by $\mathcal{P}1$, as shown in Figure 1.

The proposed $\mathcal{P}2$ control process where the oxygen concentration control process, directly adjusted the amount of air supplied based on input signals. It predicted the combustion state from flame images and adjusted the servo motor to regulate the air supply based on this feedback.

Combustion parameters such as ${\mathrm{S}\mathrm{O}}_{\mathrm{x}}$, ${\mathrm{N}\mathrm{O}}_{\mathrm{x}}$, ${\mathrm{C}\mathrm{O}}_2$, and $\mathrm{C}\mathrm{O}$ as well as oxygen, included in the exhaust gases could be easily measured using gas analyzers. However, this method has a delay time due to the process of the exhaust gases flowing from the combustion point to the measurement point. This delay tended to cause the feedback control loop, which regulated oxygen concentration, to overcompensate for errors, resulting in slower control responses and larger transient responses. In contrast, using flame images, which are indicators of quasi-instantaneous combustion states, as inputs for oxygen measurement allowed for immediate reflection of the current combustion state, enabling real-time continuous flame control.

The flame images were collected as high-resolution images using a 1920 $\times$ 1080-pixel CMOS webcam. The camera was positioned at the flame observation port on the side of the boiler in accordance with The International Convention for the Safety of Life at Sea (SOLAS) regulations. The collected flame images were transmitted to a computer via a USB 3.0 interface, and the predicted values of oxygen concentration, obtained from a pre-trained model, were used as feedback signals in the control system.

The error in the oxygen concentration setpoint was converted into a control signal for the air regulation damper through the designed controller. In the $\mathcal{P}1$ control system, fuel, and air were controlled simultaneously at a fixed ratio according to the steam load. In contrast, the proposed $\mathcal{P}2$ control system adjusted the damper opening, which regulated the air supply, independently, thereby allowing control over the combustion state. To achieve individual damper control, an A/D converter drive was used to convert the analog control output to an angle ranging from 0 to 90 degrees, and a servo motor was installed at the end of the damper to control it in real-time.

To train the prediction model of oxygen concentration for the experimental OFB and to compare and verify the effectiveness of the control system, information on air pollutants was automatically recorded in the computing system via an exhaust gas analyzer from the funnel during the process. Specifically, the oxygen concentration, which is an indirect measure of energy consumption and combustion state as well as the control target, was recorded as time-series data along with the flame images.

3. Oxygen Concentration Estimation Model Using Saturation Extraction Filter

To estimate control inputs, particularly oxygen concentration, in real-time, flame images representing quasi-instantaneous combustion states are processed through the saturation extraction filter + support vector machine (SEF+SVM) model.

Figure 2 illustrates the schematic of the SEF-SVM model.

The SEF converted the flame images captured in RGB format via a webcam through the flame observation port into HSV format, extracting the saturation (S) component for histogram analysis. This reduced data was then used by the SVM, a machine learning model capable of effective classification and regression even in high-dimensional spaces, to identify and learn linear features [22]. Leveraging these characteristics, the SEF+SVM model enabled real-time prediction of air pollutants and oxygen concentration in exhaust gases.

The validity of the SEF+SVM model was confirmed through experiments conducted on the same ship’s OFB plant, demonstrating an R² value of 0.97 in oxygen concentration measurement. Additionally, the measurement delay time was reduced to an average of 2.1 s, making it suitable for use as a real-time control input [23].

Flame image acquisition used the existing flame observation port, which limited capturing the full size and shape of the flame. To mitigate this, the webcam was positioned 5 cm from the flame observation port’s lens, and the image size was adjusted to 800 × 820 pixels to capture reflective light from the port hole walls. This pixel size was determined through experimentation to ensure the histogram accurately represented the data without exceeding 2 bytes per bin (216 bytes).

The collected flame images were initially captured in RGB format and then converted to HSV format, from which only the saturation component, representing linear characteristics corresponding to different combustion states, was extracted. By representing this information using a histogram, the original 800 (H) × 820 (W) × 3 × 2 byte data was reduced to a 256 × 2 byte feature-extracted dataset. This reduced dataset was then combined with corresponding time-series exhaust gas data and used for regression training in the SVM model.

3.1. Data Collection

Figure 3 presents the data collection process used in the experiment.

During the data collection process, the combustion environment was divided into six distinct stages. For each stage, 200 data points were collected, resulting in a total of 1200 time-series data points. By maintaining a constant ratio of fuel to air, the OFB operated to manually control the combustion environment, ensuring a stable combustion environment regardless of the steam pressure in the $\mathcal{P}1$ control system. To acquire data for model training under various combustion conditions, the amount of air supplied was independently adjusted in six stages by regulating the control holes installed at the linkage of the air damper, as shown in Figure 3, while keeping the air and fuel constant.

Adjustments in the air supply influence the oxygen concentration ${\delta }_o$, which can be expressed by the following Equation (1):

$$\phi ={\displaystyle \frac{{\rho }_e}{{\rho }_a}}=18.5{\left({\displaystyle \frac{13{\delta }_o+37}{2-9.52{\delta }_o}}\right)}^{-1}$$

(1)

This represents the fuel-lean equation. $\phi$ represents the combustion equivalence ratio (CER), which was influenced by the oxygen concentration ${\delta }_o$. Altering the air supply changed ${\delta }_o$, thus affecting the CER, and consequently impacting the exhaust gas composition due to variations in the reactions of carbon $(\mathrm{C})$, hydrogen $(\mathrm{H})$, and nitrogen $(\mathrm{N})$ in the fuel. Changes in the CER also affected the peak value of saturation in the flame image. Data on air pollutants and oxygen concentration in the exhaust gas were stored as time-series data synchronized with the SEF-processed data, forming the dataset for training the SVM model.

During the data collection process, the combustion environment was divided into six distinct stages. For each stage, 200 data points were collected, resulting in a total of 1200 time-series data points.

3.2. Training of the Prediction Model of Oxygen Concentration

The flame images and oxygen concentration data, stored from the process, were used to train a linear regression model for predicting oxygen concentration. The training model employed SEF+SVM, identical to model E1 trained with 300 samples in previous research, and used a training dataset of 1200 data points, with 200 samples for each environmental variation. While increasing the dataset size improved the model’s performance by increasing the learning rate and reliability, it also raised the risk of overfitting, so the dataset size must be appropriately selected through experimentation. The training results for the new prediction model E2 are shown in

Table 1. Learning Results of Predictive Models, E1 and E2.

Prediction Model	Training Dataset	R2	RMSE	MAE
E1	300	0.97	0.1698	0.1213
E2	1200	0.984	0.1159	0.1159

. The evaluation metrics indicate the R² of 0.976, RMSE of 0.1159, and MAE of 0.1159. Compared to the proven performance of SEF+SVM, the R² increased by 0.62%, while the RMSE and MAE decreased by 31.74% and 4.45%, respectively, confirming the effectiveness of the E2 prediction model.

The accuracy of the learning model needed to be verified through periodic calibration and verification using a gas analyzer [24]. While there was no fixed standard for the accuracy of prediction models, processes where accuracy was critical typically require a prediction accuracy of over 95%. Since the input process for flame images can change over time, periodic retraining is necessary to maintain a consistently high level of accuracy.

4. Development of an IMC-PID Based Oxygen Concentration Control System Using Flame Images

By utilizing flame images as input for oxygen concentration, the input delay issues associated with oxygen concentration meters could be resolved, allowing for the establishment of a real-time control system to regulate the oxygen concentration in the exhaust gases of the OFB. The schematic diagram of the control system $S2$ for $\mathcal{P}1$ proposed in this study is shown in Figure 4.

$S1$ is the original control system used for boiler combustion. This system is a proportional combustion control system that simultaneously controls the airflow and fuel quantity to maintain constant steam pressure. Since this ratio was set by the manufacturer during the commissioning part with a primary focus on combustion stability, the flame remained stable despite changes in the environmental conditions of the supplied air and the characteristics of the fuel. However, the emissions of air pollutants varied as a result. Consequently, by adjusting the amount of supplied air while maintaining a constant fuel quantity, it was possible to control the emissions of air pollutants while ensuring combustion stability during the stable combustion process of the flame.

Therefore, this study proposes an oxygen concentration control system, $S2$, that can additionally control the air damper opening, which is proportionally controlled in the existing $S1$ system. The control system uses flame images as real-time input to predict oxygen concentration through the SEF+SVM predictor. The predicted oxygen concentration is then used to adjust a servo motor for the damper via a controller, compensating for any deviation from the target value. This controlled damper alters the amount of air supplied to the combustor, thereby controlling the air pollutants generated during the combustion process.

4.1. Setting Control Objectives

The air pollutants emitted from the OFB were inversely proportional to the amount of air supplied because the amount of oxygen reacting with the fuel components increased during lean combustion when the equivalence ratio was less than 1. Maintaining the oxygen concentration in the exhaust gases was crucial to minimize soot particles and black smoke while effectively controlling cooling losses due to heat release and nitrogen oxide (${\mathrm{N}\mathrm{O}}_{\mathrm{x}}$) emissions. Therefore, setting and maintaining an optimal oxygen concentration was essential for the effective control of air pollutants.

Additionally, previous studies using the same type of boiler as the OFB employed in this research showed that the air pollutants ${\mathrm{C}\mathrm{O}}_2$, ${\mathrm{N}\mathrm{O}}_{\mathrm{x}}$, and ${\mathrm{S}\mathrm{O}}_2$ tend to be inversely proportional to the oxygen concentration in the exhaust gases. Moreover, excessive supercharging, which means supplying an excessively large amount of air to the boiler, should be avoided, as it can reduce combustion efficiency due to heat loss in the exhaust gases. Therefore, it was crucial not to maintain the oxygen concentration excessively low [25].

The previous studies analyzing the exhaust gas characteristics of boiler systems based on oxygen concentration demonstrated similar tendencies and highlighted the importance of maintaining an appropriate oxygen concentration.

In the study by J. Chen et al., the exhaust gas oxygen concentration of a coal-fired boiler was adjusted between 2% and 5%, revealing a correlation between oxygen concentration and ${\mathrm{N}\mathrm{O}}_{\mathrm{x}}$ emissions. Additionally, the study examined the impact of soot and graphite on flame image measurements with varying oxygen concentrations. It was found that at an oxygen concentration of 4.02%, the occurrence of soot and graphite was minimized, resulting in the least noise in flame image recognition [26].

The study conducted by G. Xiao et al. on gas-fired boiler combustion examined the correlation between heat release and ${\mathrm{N}\mathrm{O}}_{\mathrm{x}}$ production in boilers. The study established weightings for heat release and ${\mathrm{N}\mathrm{O}}_{\mathrm{x}}$ production, finding that to double the weighting for reducing ${\mathrm{N}\mathrm{O}}_{\mathrm{x}}$ emissions, the oxygen concentration needs to be increased by approximately 1.14 times under various load conditions. In this research, an oxygen concentration of 3.5% achieved a 1:1 balance between heat release and ${\mathrm{N}\mathrm{O}}_{\mathrm{x}}$ production at 80% load. When adjusting the weighting to reduce ${\mathrm{N}\mathrm{O}}_{\mathrm{x}}$ production, the optimal oxygen concentration was found to be around 4.0% [27].

Based on a comprehensive review of the exhaust gas characteristics of the target ship’s OFB and related research, this study concludes that setting the control target value for the oxygen concentration in the exhaust gas to 4% is appropriate for real-time combustion control of the boiler.

4.2. Estimation of Transfer Function Based on Step Response

To set the controller, the transfer function of the control system must first be determined. Although classical methods such as calculating differential equations can be used to find the transfer function, this approach is not straightforward for the given system due to the numerous variables, including changes in the supplied air, fuel characteristics, and heat transfer efficiency variations with load. Therefore, this study employed a method that identified the system by providing constant input and analyzing the resulting response. This method is well-suited for irregular and non-linear systems, and it offers the advantage of being able to adapt to the desired model structure despite the presence of many system variables by using actual data [17,28].

To identify the system, the combustion control system $S1$ was maintained at a load of 78%, ensuring that the oxygen concentration in the exhaust gas remained at 4% while fuel was supplied at a constant rate. During this process, a step input of +5 degrees in the open direction was applied to the servo motor of $S2$, and the oxygen concentration, as inputted through flame images, was recorded. Figure 5 shows the oxygen concentration output of the system in response to the step input.

The collected data was then used to estimate the transfer function using MATLAB’s System Identification Toolbox, version R2024a. This method utilized machine learning algorithms to estimate the transfer function through the learning of input and output data. The order of the system is specified from first to third order, and the transfer functions are estimated as shown in

Table 2. Transfer Function Estimation through Training of Machine Learning Algorithms.

System Order	Estimated Numerator	Estimated Denominator	Fit Rate to Data	MSE
1	0.2187	1, 2648.14	81.47	0.124
2	0.2187, 0.5960	1, 2847.82, 1508.78	99.28%	0.0001833
3	2.867, 0.05036	1, 44.45, 97.21, 0.0841	90.51%	0.03482

.

The accuracy presented in Table 2 confirms that a second-order system is most suitable. This indicates that the fuel is consistently supplied, and disturbances other than changes in the air supply do not significantly affect the system. Therefore, the system transfer function is designated as ${\overline{\mathcal{G}}}_{\mathrm{S}2}$ in Equation (2), and a controller is designed accordingly.

$${\overline{\mathcal{G}}}_{\mathrm{S}2}={\displaystyle \frac{0.2187s+0.5960}{s^2+2847.82s+1508.78}}={\displaystyle \frac{0.2187(s+2.728)}{(s+0.523)(s+2847.29)}}$$

(2)

Examining the poles and zeros of the transfer function ${\overline{\mathcal{G}}}_{\mathrm{S}2}$, the poles are located at $\mathrm{s}1\approx -0.523,\mathrm{s}2\approx -2847.29$. Since the real parts of both poles are negative, they are positioned on the left half of the complex plane, indicating that the system is stable and controllable. The zeros are also real and negative, which confirms that they do not affect the system’s stability [29].

4.3. Tuning of the IMC-Based PI Controller

To effectively control the image-based combustion system of the $S2$ system, it was essential to employ an appropriate controller. This experiment utilized an IMC-based PI controller for system regulation. Given that the $S2$ system used flame images as input signals, high-frequency noise may arise from intermittent prediction errors. In such cases, the derivative component of a PID controller could amplify the noise, making a PI controller more suitable [30]. Furthermore, for the sake of computational simplicity in tuning the IMC controller, a PI controller was used.

Figure 6 shows the closed-loop structure of the IMC applied to the actual system transfer function ${\mathcal{G}}_{\mathrm{S}2}$.

${\overline{\mathcal{G}}}_{\mathrm{S}2}$ is the internal model transfer function estimated from the data, $\mathcal{q}(\mathrm{s})$ is the IMC controller, and ${\mathcal{K}}_{\mathrm{S}2}(\mathrm{s})$ is the controller integrated with the internal model. As determined in Section 4.2, ${\overline{\mathcal{G}}}_{\mathrm{S}2}$ is a second-order function and can be expressed as shown in Equation (3).

$${\overline{\mathcal{G}}}_{\mathrm{S}2}(s)={\displaystyle \frac{k_p(\beta s+1)}{\left({\tau }_{a}s+1\right)({\tau }_{b}s+1)}}({\tau }_a<{\tau }_b)$$

(3)

The ${\tau }_a{\mathrm{a}\mathrm{n}\mathrm{d}\tau }_b$ are the time constants of the system, $k_p$ is the proportional gain, and $\beta$is the constant associated with the zero. Consequently, the IMC controller can be expressed as shown in Equation (4a), where $f(s)$ represents the IMC filter. The filter function $f(s)$ is set as a second-order system, corresponding to the order of the internal model. In Equation (4b), $\lambda$ is the filter constant that defines the trade-off between control performance and robustness.

$$\mathcal{q}\left(\mathrm{s}\right)={\overline{\mathcal{G}}}_{\mathrm{S}2}^{-1}f(s)$$

(4a)

$$f(s)={\displaystyle \frac{s+1}{{\left(\lambda s+1\right)}^2}}$$

(4b)

By standardizing the closed-loop structure using this approach, the IMC controller $\mathcal{q}(\mathrm{s})$ and the internal model ${\overline{\mathcal{G}}}_{\mathrm{S}2}$ can be integrated to form the classic controller ${\mathcal{K}}_{\mathrm{S}2}(\mathrm{s})$. This can be expanded using Equations (4a) and (4b) to be expressed in the form shown in Equation (5a).

$${\mathcal{K}}_{\mathrm{S}2}(\mathrm{s})={\displaystyle \frac{\mathcal{q}\left(\mathrm{s}\right)}{1-{\overline{\mathcal{G}}}_{\mathrm{S}2}\mathcal{q}\left(\mathrm{s}\right)}}={\displaystyle \frac{{\overline{\mathcal{G}}}_{\mathrm{S}2}^{-1}f(s)}{1-{\overline{\mathcal{G}}}_{\mathrm{S}2}{\overline{\mathcal{G}}}_{\mathrm{S}2}^{-1}f(s)}}$$

(5a)

$${\mathcal{K}}_{\mathrm{S}2}\left(\mathrm{s}\right)={\displaystyle \frac{{\tau }_b}{k_p\lambda }}\left(1+{\displaystyle \frac{1}{{\tau }_{b}s}}\right){\displaystyle \frac{\left({\tau }_{a}s+1\right)}{\left(\beta s+1\right)}}={\displaystyle \frac{{\tau }_b}{k_p\lambda }}\left(1+{\displaystyle \frac{1}{{\tau }_{b}s}}\right)f_l(s)$$

(5b)

The expanded Equation (5b) shows that ${\mathcal{K}}_{\mathrm{S}2}(\mathrm{s})$ takes the form of a PI controller. The term ${\displaystyle \frac{({\tau }_{a}s+1)}{(\beta s+1)}}$ can be considered as a lead-lag filter and is denoted $f_l(s)$ [31]. The classic controller is expressed as ${\mathcal{K}}_{\mathrm{S}2}^{\prime }\left(\mathrm{s}\right)$ in Equation (6), using the proportional gain $K_p$ and the integral gain$K_i$.

$${\mathcal{K}}_{\mathrm{S}2}^{\prime }\left(\mathrm{s}\right)={\displaystyle \frac{{\tau }_b}{k_p\lambda }}\left(1+{\displaystyle \frac{1}{{\tau }_{b}s}}\right)=K_p\left(1+{\displaystyle \frac{K_i}{s}}\right)$$

(6)

Figure 7 shows the final form of the closed-loop control system for $S2$.

Therefore, the IMC-based PI controller ${\mathcal{K}}_{\mathrm{S}2}^{\prime }\left(\mathrm{s}\right)$ can be expressed as a function of the proportional gain $K_p$ and the integral gain $K_i$ with respect to $\lambda$, as shown in Equation (7).

$$K_p={\displaystyle \frac{{\tau }_b}{k_p\lambda }},K_i={\displaystyle \frac{1}{k_p\lambda }}$$

(7)

The control elements for system $S2$ are summarized in

Table 3. Control Elements of the System.

${\overline{\mathcal{G}}}_{\mathbf{S}2}(\mathit{s})$	$\mathit{f}(\mathit{s})$	${\mathcal{K}}_{\mathbf{S}2}^{\prime }\left(\mathbf{s}\right)$	${\mathit{K}}_{\mathit{p}}$	${\mathit{K}}_{\mathit{i}}$
${\displaystyle \frac{k_p(\beta s+1)}{\left({\tau }_{a}s+1\right)({\tau }_{b}s+1)}}$	${\displaystyle \frac{s+1}{{\left(\lambda s+1\right)}^2}}$	$K_p\left(1+{\displaystyle \frac{K_i}{s}}\right)$	${\displaystyle \frac{{\tau }_b}{k_p\lambda }}$	${\displaystyle \frac{1}{k_p\lambda }}$
${\mathit{k}}_{\mathit{p}}$ = 2.1865704, $\mathit{\beta }$ = 2.728423 × 103, ${\mathit{\tau }}_{\mathit{a}}$ = 3.51 × 10−4, ${\mathit{\tau }}_{\mathit{b}}$ = 1.887649

.

Therefore, by adjusting the IMC filter constant $\lambda$, the values of $K_p$ and $K_i$ can be modified to tune the control performance.

5. Case Study

5.1. Example Case

By installing an IMC-based PI controller in the $S2$ combustion control system and specifying an appropriate filter constant, effective control can be achieved. However, it is essential to determine the optimal filter constant value by considering the trade-off between response performance and robustness to noise.

Generally, a higher filter constant $\lambda$, results in slower response times but increases stability due to robustness against model mismatches. Conversely, a lower $\lambda$ leads to faster response times but may cause overshoot due to noise from model inaccuracies [21].

The steady-state control output for an oxygen concentration of 4% is analyzed for the five specified controllers, along with the response performance when a step input changes the oxygen concentration from 4% to 5%. By examining the stability of the steady state at 4% oxygen concentration and the response performance to the step input across the five cases, the optimal filter constant $\lambda$ can be determined.

The internal model ${\overline{\mathcal{G}}}_{\mathrm{S}2}\left(s\right)$estimated from experimental data may experience discrepancies from the actual plant due to disturbances and changes in environmental variables. Therefore, it is necessary to determine a stable filter constant $\lambda$ through experimentation to ensure effective control performance in the actual plant. The values of $\lambda$ for $K_p$ and $K_i$ in Equation (7) can be set between 0.5 and 2.5, as shown in

Table 4. Control Gain according to IMC Constant λ of $S2$ System Controller.

Controller	$\mathit{\lambda }$	${\mathit{K}}_{\mathit{p}}$	${\mathit{K}}_{\mathit{i}}$
$C_{br1}$	0.5	17.265	9.147
$C_{br2}$	1.0	8.633	4.573
$C_{br3}$	1.5	5.755	3.049
$C_{br4}$	2.0	4.316	2.287
$C_{br5}$	2.5	3.453	1.829

. Accordingly, five controllers are specified with filter constant values increasing by 0.5 increments, starting from 0.5.

5.2. Evaluation Methods

To analyze the steady-state response for the target oxygen concentration of 4% across the five cases, the normal distribution of the measured response data was determined, and the mean and variance are calculated. Additionally, to evaluate the response performance for a step input change from 4% to 5% oxygen concentration in each case, the stability index $M_p$ was analyzed using the Integral of Squared Error [32].

The $M_p$ represents the maximum peak error in the step response, as represented by Equation (8). This generally indicates the maximum overshoot before the system reaches a steady state. This metric allows for the comparison of the maximum magnitude of overshoot across different controllers.

$$M_p=max\left|e(t)\right|$$

(8)

The Integral of Squared Error (ISE) is calculated by integrating the square of the error over time, as represented by Equation (9). This approach amplifies the impact of larger errors by squaring them, allowing for a more significant reflection of their effects. This metric enabled the comparative evaluation of overall stability during the transient response period.

$$ISE={\int }_{t_s}^{t_f}\left|e(t)\right|dt$$

(9)

5.3. Steady-State Response

To apply the optimal IMC-PI control parameters to the proposed OFB combustion improvement system $S2$, experimental characteristics were compared. The experiments were conducted with a constant fuel supply of 131 kg/h to the OFB, and the $S1$ process was halted to measure the standalone performance of $S2$.

Figure 8 presents the experimental results of controlling the oxygen concentration of the OFB system, $\mathcal{P}2$, at 4% for each case. The combustion system $S2$ was controlled for each case, and data was collected for a total of 1200 s in the steady state. With a sampling period of 0.25 s, the estimation was based on a total of 4800 image data points.

Through this analysis, the mean values for the IMC filter constant $\lambda$ ranging from 0.5 to 2.5 were found to be 4.1571, 4.0509, 3.9823, 4.0156, and 4.0076, respectively, with variances of 0.0397, 0.0181, 0.0182, 0.0068, and 0.0052.

Figure 8A demonstrates that the control system accurately tracks the target value of 4% for all values of $\lambda$. However, it also indicates that as the filter constant $\lambda$ decreases, the variability around the target value of 4% in the steady state increases.

Figure 8B visualizes the normal distribution of the data collected in the steady state. When $\lambda$ is 0.5, the steady-state values show a significant error from the target value of 4%, greatly reducing control stability. Conversely, as the value of $\lambda$ increases, both the steady-state error and variance decrease, indicating improved stability of the control system. These results suggest that increasing the filter constant $\lambda$ was advantageous for accurate tracking of the target value and maintaining control stability.

5.4. Transient Response Comparison for Step Input

To verify the response performance of the controller, a step change was applied to the control setpoint, and the corresponding step response was observed. The experimental results are shown in Figure 9, and

Table 5. Response by case to oxygen concentration target value step change.

Controller	4% > 5% Transient Response Comparison
	$\mathit{\lambda }$	${\mathit{M}}_{\mathit{p}}$	$\mathit{I}\mathit{S}\mathit{E}$
$C_{br1}$	0.5	0.377	10.9183
$C_{br2}$	1.0	0.3579	10.1689
$C_{br3}$	1.5	0.19245	10.1159
$C_{br4}$	2.0	0.15869	13.6268
$C_{br5}$	2.5	0.13824	14.2537

presents the performance evaluation based on the filter constant $\lambda$.

Examining the transient response period from 50 to 56 s allows us to assess the control response performance to the step input. In Case 1, with a filter constant $\lambda$ of 0.5, the transient response is significant, resulting in an $M_p$ of 0.377, and the system exhibits oscillations. In Case 2, with an increased $\lambda$, the value of $M_p$is 0.3579; although the system’s oscillations are dampened, the transient response remains unimproved. However, from Case 3 onwards, the $M_p$significantly improves to 0.19245, and the system no longer oscillates. The ISE represents the error between the target value of 5% and the actual response from 50 to 56 s. In Cases 1 to 3, as shown in the graph in Figure 9, the response speeds are similar, resulting in comparable ISE values. However, from Case 4 onwards, the response speed drastically decreases, causing the ISE to spike to 13.6268. This indicates that starting from a $\lambda$ of 2.0, the system exhibits discrepancies with the internal model, rendering it unsuitable as a controller for step responses.

Overall, when the values of $\lambda$ are 0.5 and 1.0, the response speed is faster, but the system experiences oscillations and significant transient responses. At $\lambda$ is 1.5, although the $M_p$is slightly higher than in cases 4 and 5, it ensures adequate control response speed without causing oscillations. Additionally, it shows the lowest error in ISE. Therefore, for efficient control of the OFB combustion system, the optimal parameter is achieved by selecting the values of $\lambda$ as 1.5, as indicated in Case 3.

6. Conclusions

This study proposes and validates a new control system to optimize the combustion process of marine oil-fired boilers, aiming to reduce emissions and increase efficiency. The proposed system uses a SEF and a SVM model to predict oxygen concentration, which is then utilized as an input for an IMC-based PI controller. The major findings and contributions of this study can be summarized as follows.

• By analyzing flame images in real time, the proposed system overcomes the measurement delays associated with traditional gas measurement methods, enabling faster and more accurate control of the combustion process.
• To address the combustion instability caused by transient responses during control, the study proposed and validated system $S2$, which allows for additional adjustments to the air supply while ensuring the combustion stability of the existing proportional combustion control system $S1$.
• The machine learning-based model estimation method plays a crucial role in accurately estimating internal models, achieving a prediction accuracy of 99.28%, and ensuring high reliability in control system design.
• Through experimental tuning, the study found that an IMC filter constant ($\lambda$) of 1.5 optimizes the balance between responsiveness and stability, achieving an overshoot ($M_p$) of 0.192 and an integral of squared error (ISE) of 10.116.

In conclusion, the implementation of the proposed system, combined with real-time IMC-based PI control using flame images, offers a feasible and effective solution for enhancing the environmental performance of OFB. This approach improves combustion efficiency, reduces emissions of harmful air pollutants, and can be easily applied to existing ships, contributing to more sustainable marine air pollution reduction. When the proportional combustion control system $S1$ operates independently, it maintains an average oxygen concentration of 2.81%. By incorporating the proposed combustion control system $S2$ to maintain the oxygen concentration at 4%, it is anticipated through interpolation that the emissions of ${\mathrm{C}\mathrm{O}}_2$, $\mathrm{N}\mathrm{O}\mathrm{x}$, and ${\mathrm{S}\mathrm{O}}_2$ will decrease by 30.63 kg, 0.0196 kg, and 0.0051 kg per hour, respectively. Notably, the proposed system has the potential to be applied to approximately 56,500 vessels in the global merchant fleet over 1,000 GT (Gross Tonnage), significantly impacting environmental performance on a global scale. Furthermore, the ease of installation can encourage adoption by shipping companies.

The focus of future research will be designing an intelligent control system for the proposed system that uses flame images as input, with high adaptability to environmental changes and effective control of nonlinear systems. The goal is to enhance combustion efficiency and minimize emissions of air pollutants. In particular, efforts will be made to further strengthen the current system’s ability to overcome the nonlinearities caused by prediction errors and to develop adaptive control methods that continuously improve over time.

By advancing the proposed system and integrating it into the combustion system, $S2$, as described in this paper, future studies will aim to evaluate its applicability in real marine environments and achieve optimal performance.