Abstract
Chemical processes often exhibit nonlinear dynamics and tend to generate complex state trajectories, which present challenging operational problems due to complexities such as output multiplicity, oscillation, and even chaos. For this reason, a complete knowledge of the static and dynamic nature of these behaviors is required to understand, to operate, to control, and to optimize continuous stirred tank reactors (CSTRs). Through nonlinear analysis, the possibility of output multiplicity, self-sustained oscillation, and torus dynamics are studied in this paper. Specifically, output multiplicity is investigated in a case-by-case basis, and related operation and control strategies are discussed. Bifurcation analysis to identify different dynamic behaviors of a CSTR is also implemented, where operational parameters are identified to obtain self-oscillatory dynamics and possible unsteady-state operation strategy through designing the CSTR as self-sustained periodic. Finally, a discussion on codimension-1 bifurcations of limits cycles is also provided for the exploration of periodic forcing on self-oscillators. Through this synergistic study on the CSTRs, possible output multiplicity, oscillatory, and chaotic dynamics facilitates the implementation of novel operation/control strategies for the process industry.
Highlights
It is well recognized that the natural world is complex, presenting an environment with chemical and ecological networks that interact on a global scale
Since an optimal scenario can be obtained by optimal periodic control (OPC) in terms of an oscillatory input profile, the problem of OPC is realized by using economic- model predictive control [14], differential flatness [15], or extreme seeking [16]
To investigate the dynamics of the lumped system, we introduce a simple first-order, irreversible reaction A→B occurring at a jacket continuous stirred tank reactors (CSTRs); the governing equations for mass and energy balance are provided as follows: dC
Summary
It is well recognized that the natural world is complex, presenting an environment with chemical and ecological networks that interact on a global scale Elements of many such systems always exhibit nonlinear dynamics, and continuous stirred tank reactors (CSTRs) are typical process units that exhibit nonlinear dynamics, presenting challenging operational problems due to complex behavior such as output multiplicities, oscillations, and even chaos [1]. For the former, a matter of primary concern is whether perturbation on the input parameters deliberately could outperform the steady operation To address this point, nonlinear frequency analysis through π-criterion [9], higher-order corrections of the π-criterion [10], Carleman linearization [11], Volterra series [12], and Laplace–Borel transform [13] has been implemented on the CSTRs. Since an optimal scenario can be obtained by optimal periodic control (OPC) in terms of an oscillatory input profile, the problem of OPC is realized by using economic- model predictive control (eMPC) [14], differential flatness [15], or extreme seeking [16].
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