# Low Temperature Combustion Modeling and Predictive Control of Marine Engines
## 2 Materials and Methods
### Experimental Setup  
The current study is based on the same engine platform as in [25]. Thus, this provides the possibility to use UVATZ to explore the design space. As outlined in [27], multizone models possess the capability to attain the accuracy and predictivity of computational fluid dynamics (CFD) models. This is achieved with computational times in the order of seconds, maintaining a 5% error margin compared to experimental data. The experimental data, which are used for calibrating and validating the UVATZ, are generated from a Wartsila \"Mono\" single-cylinder research engine (SCRE). This engine is a variant of the commercial multi-cylinder, dual-fuel, two-staged turbocharged W31 engine [39]. The SCRE operates in RCCI mode using natural gas (NG) as LRF and light fuel oil (LFO) as HRF. NG is controlled via a multipoint upstream of the intake valve and LFO is directly injected via a twin-needle injector [40]. The specifications of the engine are presented in Table 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Systems** & **Configuration** \\ \hline Displacement & 32.45 L \\ Nominal speed & 720 RPM \\ Stroke/bore & 1.39 \\ Air system & External compressor with air \\  & temperature and pressure control (up to 10 bar) \\ Valvetrain & four valves with swirl + tumble ports \\  & variable intake valve closure (VIC) \\  & fixed exhaust valve opening (EVO) \\ Engine control & Rapid prototyping platform \\ Test fuels & ISO 8217 compliant LFO/LNG (MN = 8) [41] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specifications of the Wartsila single-cylinder research engine (SCRE). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Prediction Horizon** & **Control Horizon** & **Y Weighting** & **U Weighting** & **Sampling Time** \\
**[cycles]** & **[cycles]** & **[–]** & **[–]** & **[s]** \\ \hline
30 & 3 & \
\begin{tabular}{c} [160 0 \\ 0 1000 \\ \end{tabular} &
\begin{tabular}{c} [1 \times 10^{-10}\) 0 \\ 0 1.1 \(\times 10^{5}\) \\ \end{tabular} & 0.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Adaptive MPC parameter values. Figure 2: Schematics of the designed system. The measurements obtained from the SCRE contain six steady state operating conditions, which are used as baseline conditions for the research. These operating conditions are indicated as A to F in Table 3. The data is presented with respect to \"Ref\", which corresponds to an IMO TIER III 25% load calibration point of the W31 DF engine. The blend ratio of LRF and HRF is defined using NG on an energy basis as described in Equation (18). The remaining parameters in the table are air-to-fuel ratio (\(\lambda\)) and the injection timing of the HRF (\(\theta_{\text{SO,ILFO}}\)). Due its accuracy and predictive nature in multiple operating conditions, the UVATZ model is used to generate calibration and validation data for the nonlinear RCCI model. This approach allows for the generation of quasi-transient data, which are based on the assumption that inputs to UVATZ vary linearly between the steady state measurement points. It must be emphasized that the original experimental data of the W31 DF engine presented in Table 3 lack transient conditions. The reference data are synthetically generated utilizing mixed-factorial design. Unlike full factorial design, mixed-factorial does not incorporate all of the factor interaction, which reduces the size of the dataset and costs, especially with high number of factors [43]. In this work, the levels in the design represents the operating conditions and factors are the inputs that have been altered for each test run. The factors and their respective levels are highlighted in Table 4. In this work, operating conditions indicated by A, B and E in Table 3 are chosen for mixed-factorial design. The factors chosen for the data generation are \(\lambda\), \(T_{\text{IVC}}\), \(m_{\text{EGR}}\), BR and \(\theta_{\text{SOI}}\), which are considered to be most influential to the COM.