Model Order Reduction

For the distillation columns, linear model-order reduction will be used. The linear model is obtained in Aspen Dynamics. Some modifications to the previous study have been done to the linear models, in order to have the reboiler duty and the reflux ratio as input or output variables of the linear models. This is needed to have access to those variables in the reduced model, for the purpose of the dynamic optimization. A balanced realization of the linear models is performed in Matlab. The obtained balanced models are then redueed. The redueed models of the distillation columns are further implemented in gProms. When all the reduced models of the individual units are available, these models are further connected in order to obtain the full reduced model of the alkylation plant. The outeome of the model reduction procedure is presented in Table 1, together with some performances of the reduced model. 

COLl Model order-reduction 188 states 25 states... 

COL2 Model order-reduction 194 states 29 states... 

COL3 Model order-reduction 169 states 17 states... 

While the advantages of parametric controllers are well established, a key challenge for their wider applicability is the ability to derive parametric controllers from arbitrary large scale and complex mathematical models. In this context. Model Order Reduction [5] can be a useful tool, since it could lead to an approximate model of reduced size, and complexity and of sufficient accuracy. 

Amoldi-based algorithm is a classical Krylov-subspace-based Model Order Reduction technique. It reduces the dimension of the spatially semi-discretized form of the original governing PDEs using moment-matching of transfer functions. 

Model order reduction (MOR) is a set of theories and techniques that reduce the order of a complex dynamic system while preserving its essential properties and input-output behavior for efficient and accurate simulation and design. 

Strictly speaking, model order reduction (MOR) refers to compact model generation procedures that lump the spatial dependency of device behavior, extract the most typical characteristics of the governing equations, and, hence, reduce the order of the problem. MOR originally derives from control theory and is widely used in electronic and MEMS design. Many of the... 

Model Order Reduction (MOR), Fig. 1 Schematic representations of three dual networks for droplet traffic modeling (a) a loop, (b) a Y-junction with bypass channel, and (c) a ladder... 

The projection-based model order reduction algorithm begins with a spatial discretization of the governing PDEs to attain the dynamic system equations as Eq. 11. Specifically, here, X(t) is the state vector of unknowns (a function of time) on the discrete nodes, n is the total number of nodes A is formulated by the numerical discretization Z defines the functions of boundary conditions and source terms and B relates the input function to each state X. Equation 11 can be recast into the frequency domain in terms of transfer function T(s). T(s) then is expanded as a Taylor series at s = 0 yielding... 

Model Order Reduction (MOR), Fig. 2 Flow chart for Amoldi-based MOR... 

The detailed implementation steps for Amoldi-based model order reduction are illustrated and summarized in Fig. 2. 

Model Order Reduction (MOR), Fig. 4 (a) An example of a general feedforward network with multiple hidden layers and a single output layer, (b) Output of a single neuron k with incoming neural activations (zi) and connection weights (wi)... 

The first model reduction algorithm based on the activity metric is shown in Fig. 2.2 and is called Model Order Reduction Algorithm (MORA). Given the full model, the goal of MORA is to order the importance of the energy elements in that model as given by their activity and reduce the size of the model based on a user-supplied threshold of the percent of the total activity to be retained in the reduced model. 

Note that if all bonds are subject to the analysis, this algorithm gives a unified approach to the reduction problem in the sense that not only the order but also the structure of the model can be reduced. This will be hereafter referred to as a global application of the ECI. It is also possible to perform the analysis locally, e.g., only for the bonds connected to the components representing the states for the purposes of model order reduction or only for the bonds connected to a junction element for the purposes of model partitioning. 

Model Order Reduction for Multi-Dimensional Population Balances Biggs et al. (7) have developed the concept of binder size distribution (BSD) to correlate moisture content with particle size. Based on BSD, the mass of binder in the size range (v, v + dv) is quantified as dM=M(v) dv and ... 

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