# Low Temperature Combustion Modeling and Predictive Control of Marine Engines
## 1 Introduction
[17] controlled the combustion phasing, i.e., \(\theta_{50}\) of an RCCI engine with a linear-quadratic-integrator (LQI) controller achieving an overshoot below 1 \({}^{\circ}\)CA, a 0 \({}^{\circ}\)CA steady state error and a settling time of 6 cycles. [PERSON] et al. [18] adopted a model-predictive controller (MPC) for an RCCI engine, where \(\theta_{50}\) and IMEP were controlled by BR and \(\theta_{\text{SGI}}\). A rise time of 2 cycles with relatively low steady state error for \(\theta_{50}\) and IMEP were achieved with a single MPC. Their switched MPCs achieved a steady error of 1.3 \({}^{\circ}\)CA and 23.8 kPa for \(\theta_{50}\) and IMEP, respectively. In [19] a support vector machine (SVM) based data-based model was developed to estimate linear parameter-varying (LPV) models for RCCI combustion enabling real-time control. The model was used in their MPC framework to control \(\theta_{50}\) with \(\theta_{\text{SGI}}\) achieving a steady state error below 1 \({}^{\circ}\)CA and settling time of 3 cycles. [PERSON] et al. have further developed their data-based LPV model to estimate PRR\({}_{\text{max}}\)[20], fuel stratification [21] and identifying RCCI states [22] for their control framework. In [23], an optimal controller was developed to control the in-cylinder pressure and, subsequently, to evaluate the thermal efficiency using total fuel energy, BR and \(\theta_{\text{SGI}}\) as control signals to achieve an optimal fuel path. [PERSON] et al. [24] controlled IMEP, PRR\({}_{\text{max}}\) and combustion centroid (CC) with PI-controllers obtaining a steady state error of 0.13 bar, 0.5 \({}^{\circ}\)CA and 0.52 bar/\({}^{\circ}\)CA for IMEP, CC and PRR\({}_{\text{max}}\), respectively. Unlike most of the aforementioned works, which focus mostly on controlling the fuel path of an RCCI engine, [PERSON] et al. [15] developed a robust multi-input and multiple-output (MIMO) feedback control methodology to control the airpath of an RCCI engine using fuel quantities, \(\theta_{\text{SGI}}\), variable geometry turbocharger (VGT) and exhaust gas recirculation (EGR) valve positions to control emission, \(p_{\text{max}}\) and PRR\({}_{\text{max}}\) for transient engine operating conditions. Their closed-loop system achieved tracking errors of 0.24 bar and 0.45 \({}^{\circ}\)CAfor IMEP and \(\theta_{50}\), respectively, while reducing NO\({}_{x}\) emission by 12.8% and PRR\({}_{\text{max}}\) by 3.8 bar/\({}^{\circ}\)CA with respect to baseline conditions. Marine engines have also traversed towards the RCCI within the field of low-temperature combustion in the recent years. Many novel modeling methodologies have been developed, especially in the form of multizone models (MZM) [5; 25; 26]. However, the model-based control of RCCI combustion is at its initial stage in non-road and marine sector. It is also worth mentioning that the current multizone models could be used as plant models for RCCI control, but they do not enable real-time simulations due to their long calculation times. To the authors' knowledge, this is the first paper that covers model-predictive control of RCCI combustion for marine engines. The work presents a MIMO control system consisting of a phenomenological RCCI combustion model, a state-of-the-art LPV model called the real-time model (RTM) [14] capable of simulation time in order of milliseconds and an adaptive MPC, which updates the aforementioned RTM for each engine operating condition and their transient. The main contributions of this work compared to previous studies are:  
* and cycle-wise. Furthermore, the model has predictive capabilities in both nominal and transient engine operating conditions. * Model-in-loop validation of MPC system based on the RTM model to control combustion phasing and IMEP with the nonlinear RCCI COM as plant model. The validation is done in both nominal and transient engine operating conditions. This paper is organised in the following manner: Section 2 presents the methodology.