Abstract
The dynamic optimization of promising forced periodic processes has always been limited by time-consuming and expensive numerical calculations. The Nonlinear Frequency Response (NFR) method removes these limitations by providing excellent estimates of any process performance criteria of interest. Recently, the NFR method evolved to the computer-aided NFR method (cNFR) through a user-friendly software application for the automatic derivation of the functions necessary to estimate process improvement. By combining the cNFR method with standard multi-objective optimization (MOO) techniques, we developed a unique cNFR–MOO methodology for the optimization of periodic operations in the frequency domain. Since the objective functions are defined with entirely algebraic expressions, the dynamic optimization of forced periodic operations is extraordinarily fast. All optimization parameters, i.e., the steady-state point and the forcing parameters (frequency, amplitudes, and phase difference), are determined rapidly in one step. This gives the ability to find an optimal periodic operation around a sub-optimal steady-state point. The cNFR–MOO methodology was applied to two examples and is shown as an efficient and powerful tool for finding the best forced periodic operation. In both examples, the cNFR–MOO methodology gave conditions that could greatly enhance a process that is normally operated in a steady state.
Highlights
Zone I is shown with a dashed rectangle. Both SS and forced periodic (FP) operations showed the same trend of achieving the highest product yields YP, at the lowest continuous stirred tank reactor (CSTR) volumetric capacities, κ (Figure 4a)
We introduced a completely new approach to optimizing the forced periodic operations of processes that are classically operated in a steady-state regime
Thanks to the Nonlinear Frequency Response (NFR) method, the objective functions could be defined as algebraic expressions
Summary
The idea of intensifying a process by switching from a steady-state (SS) to a forced periodic (FP). The NFR method can only be applied to stable, by using only the asymmetrical second‐order FRF G , ω, ω relating the output y and input x: weakly nonlinear systems that can be represented with convergent Volterra series Another limitation is that the analyzed systems must not have multiple steady states. The recently developed computer-aided Nonlinear Frequency Response (cNFR) method [36] is an upgrade of the NFR method using a software application for the automatic derivation of the FRFs of interest It has an easy-to-use interface where the user can define the dynamic model equations of the system and automatically generate MATLAB files for the desired FRFs and DC components [36]. That can be used for the determination of system stability (Figure 2)
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