The application of solvent‐aided crystallization (SAC) is based on the addition of a solvent, here 1‐butanol, to crude biodiesel to catalyze the purification process by separating biodiesel from contaminants via crystallization process. Response surface methodology was applied to optimize the process parameters of SAC, represented by biodiesel purity. The purified biodiesel was analyzed by means of gas chromatography‐mass spectrometry for the composition of the present fatty acid methyl ester (FAME). Under the predicted optimum process conditions within the experimental ranges for the highest biodiesel purity, the predicted biodiesel purity was 99.375 %.
Modern chemical process plants are typically very complex in nature due to the various material and energy recycling streams, including the implementation of process intensification in order to improve the sustainability factor. Looking at each individual unit operation, there are inherent nonlinear properties that may often involve physical and chemical phenomena occurring on different time scales. In addition, there exist chemical processes that also inherently have dynamics that are multi time-scale in nature. However, designing the control system for those integrated and intensified processes poses significant difficulties because they naturally lead to the dynamics of the network having multiple timescale behaviors and a reduced number of degrees of freedom. The status quo approach to handle multiple time scales would be to separate the plant-wide dynamics into their fast and slow components and implement a hierarchical control structure, but the current practices would lead to computational issues when being applied to model-based controllers due to the inversion of ill-conditioned and stiff differential algebraic equation models under large time-scale separation. To address this issue, this study proposes an alternative approach to modeling multi time-scale processes based on the use of multiple time-scale recurrent neural networks (MTRNNs). The analysis is demonstrated via a benchmark multi time-scale continuous stirred tank reactor (CSTR) case study, using input−output data generated via simulation of nonlinear dynamical equations of the CSTR with large parameters (reciprocal of the singular perturbation small parameter) in the form of 1/ε as the large heat transfer coefficient. The MTRNN model is constructed with groups of neuronal nodes grouped together based on their assigned time constant (also known as decay rate), which leads to an improved prediction performance when compared to other common modeling methods. The prediction performance of the proposed MTRNN model when applied to the multi time-scale CSTR results in an R 2 value of 0.9997, in addition to an average of 75 times lower root mean square error when compared to that of the nonlinear autoregressive network with exogenous inputs (NARX) and transfer function methods, implying its higher potential efficacy in modeling complex multi timescale processes.
This study attempts to offer an alternative to the problem of implementing model predictive controllers (MPC) in conditions where the timescale multiplicity of the process model is not accounted for when incorporated into the MPC. Modeling methods that do not account for the timescale multiplicity in system’s dynamics tend to become ill-conditioned and stiff when inversed in model-based controllers, thus requiring high computational loads to solve the equations. Therefore, this study proposes an alternative approach to the control of multi-timescale processes based on the use of multiple timescale recurrent neural network (MTRNN)-based neural network predictive controllers (NNPC). The effectiveness in handling setpoint tracking scenarios by the proposed method is evaluated using a benchmark nonexplicit two-timescale continuous stirred tank reactor (CSTR). After undergoing controller parameter optimization, the optimum configuration is found to be at 110, 37, and 0.2 for the cost horizon, control horizon, and control weighting factor, respectively. Results show that the MTRNN-based NNPC is able to track the reference trajectory with stable response and minimal error with a root mean square error of 0.0642. The optimized MTRNN-based controller is tested for its robustness under plant-model mismatch and is compared for its setpoint tracking abilities with a nonlinear autoregressive exogeneous (NARX)-based NNPC which showed that the proposed controller can satisfy the desired setpoint, resulting in an error that is 1.8 times lower than NARX-based NNPC.
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