# Low Temperature Combustion Modeling and Predictive Control of Marine Engines
## 1 Introduction  
Maritime transport covers the majority of global trade; 77% of external and 35% of internal trade of the European Union (EU) is transported by sea. Despite its economic benefits, marine transportation is a major source of emissions [1]. Maritime transportation is a source of pollutants such as nitrogen oxides (NO\({}_{x}\)), carbon dioxide (CO\({}_{2}\)), sulphur dioxide (SO\({}_{2}\)), unburned hydrocarbons (UHC) and particulate matter (PM). These pollutants have detrimental effects on both environment and human health, impacting regions beyond just coastal areas [2]. The emissions of transportation sector in Europe has rebounded by 8.6% since the COVID-pandemic and has further increased by 2.7% since 2022. The levels especially in aviation and maritime sector are expected to further increase in the upcoming years [3]. The latest mandatory energy efficiency improvement set by the International Maritime Organization (IMO) covers a diverse range of design, operational and economic solutions, such as alternative fuels, hybridization of propulsion systems, as well as voyage and speed optimization [4]. As the regulations of maritime combustion engine emissions have become stricter over the years, new and more advanced combustion processes have been a great area ofinterest within the research communities. Low-temperature combustion (LTC) processes have been utilized in the next generation of combustion engines, not only in maritime sector, but also in off- and on-road sectors due to their high efficiency [5]. LTC techniques include homogeneous charge compression ignition (HCCI), premixed charge compression ignition (PCCI), partially premixed combustion (PPC) and reactivity controlled compression ignition (RCCI), among other techniques. The superiority of RCCI compared to other LTC techniques can be explained by its ability to achieve higher brake thermal efficiency (BTE) while maintaining low NO\({}_{x}\) and PM levels [6]. Additionally, a 25% reduction of CO\({}_{2}\) has been observed with biofuels [7] and contemporary research proceeds towards flexible accommodation of hydrogen as low reactivity fuel [8]. Although the RCCI concept has numerous advantages and benefits, there exist certain challenges regarding its practical adoption. These challenges are:  
* High dependency of auto-ignition on the conditions at inlet valve closing (IVC), making the real-time combustion control a challenging task [9]. * Excessive maximum in-cylinder pressure (\(p_{\text{max}}\)), maximum pressure rise rate (PRR\({}_{\text{max}}\)), knock and noise at high engine loads, which reduce the effective operating range as well as increases the emission of UHC [10]
* Increase of hydrocarbons (HC) and carbon monoxide (CO) emissions at low engine loads [11]
* Combustion stability issues at transient operating conditions
* Overall complex and nonlinear nature of the RCCI process itself  
Model-based control of RCCI combustion has gained popularity over the past decade. Many works have concentrated on light- and heavy-duty engines. [PERSON] et al. [12; 13] developed a physics-based control-oriented model (COM) for RCCI combustion capable of predicting main combustion indicators such as start of combustion (\(\theta_{\text{SOC}}\)), burn duration (\(\theta_{\text{BD}}\)), combustion phasing (\(\theta_{50}\)) and indicated mean effective pressure (IMEP). This model has been widely applied in works covering model-based control of RCCI process. An important characteristic of RCCI fuel blend of low- and high-reactivity fuel (LRF, HRF) [14] is the fact that it is highly correlated with the formation CO and HC [15]. Initial works include controlling \(\theta_{50}\) with a PI-controller using blend ratio (BR) and start of injection (\(\theta_{\text{SGI}}\)) as control signals achieving low steady state error and settling time of 3-4 cycles [16]. [PERSON] et al.