Study on the Nonlinear Dynamics of the Continuous Stirred Tank Reactors

Investigation into a multiple input/output bifurcated biochemical reaction with substrate inhibition in a real CSTR based on Cholette’s model

CSTR operations entailing high nonlinearity and complexity such as multiple input and output steady-states present a real challenge to chemical engineers and process designers. The input multiplicity in chemical reactions leads to control probems such as process instability and low efficiency. Therefore, it is of critical importance to predict and avoid the multiplicity regions during reactor operation. Since the bifurcation analysis of biochemical processes with nonideal mixing has been carried out by the authors in the previous publication (Yang, C. Y., D. C. Tsai, and Y. S. Chien. 2021. “The Strategy Developed for High Conversion and the Multiplicity Problems of Biochemical Reaction in a Real CSTR with Cholette’s Model.” International Journal of Chemical Reactor Engineering 19: 1245–70), the goal of the present work is to use Sturm’s method, Routh stability criteria and the discriminator roots method with the tangent analysis method to derive the input multiplicity conditions in substrate inhibition in a real CSTR based on Chollete’s model. Four kinetic schemes are used in the analysis as examples to show that all three methods can precisely obtain the bifurcation starting point for the input multiplicity. In addition to the multiple input steady-states, the start-up diagram obtained by the discriminator root method is of critical importance to avoid operating in the input multiplicity regions.

Bifurcation Control on the Un-Linearizable Dynamic System via Washout Filters

Information fusion integrates aspects of data and knowledge mostly on the basis that system information is accumulative/distributive, but a subtle case emerges for a system with bifurcations, which is always un-linearizable and exacerbates information acquisition and presents a control problem. In this paper, the problem of an un-linearizable system related to system observation and control is addressed, and Andronov-Hopf bifurcation is taken as a typical example of an un-linearizable system and detailed. Firstly, the properties of a linear/linearized system is upon commented. Then, nonlinear degeneracy for the normal form of Andronov-Hopf bifurcation is analyzed, and it is deduced that the cubic terms are an integral part of the system. Afterwards, the theoretical study on feedback stabilization is conducted between the normal-form Andronov-Hopf bifurcation and its linearized counterpart, where stabilization using washout-filter-aided feedback is compared, and it is found that by synergistic controller design, the dual-conjugate-unstable eigenvalues can be stabilized by single stable washout filter. Finally, the high-dimensional ethanol fermentation model is taken as a case study to verify the proposed bifurcation control method.

A novel LSSVM-L Hammerstein model structure for system identification and nonlinear model predictive control of CSTR servo and regulatory control

A continuous stirred tank reactor (CSTR) servo and the regulatory control problem are challenging because of their highly non-linear nature, frequent changes in operating points, and frequent disturbances. System identification is one of the important steps in the CSTR model-based control design. In earlier work, a non-linear system model comprises a linear subsystem followed by static nonlinearities and represented with Laguerre filters followed by the LSSVM (least squares support vector machines). This model structure solves linear dynamics first and then associated nonlinearities. Unlike earlier works, the proposed LSSVM-L (least squares support vector machines and Laguerre filters) Hammerstein model structure solves the nonlinearities associated with the non-linear system first and then linear dynamics. Thus, the proposed Hammerstein’s model structure deals with the nonlinearities before affecting the entire system, decreasing the model complexity and providing a simple model structure. This new Hammerstein model is stable, precise, and simple to implement and provides the CSTR model with a good model fit%. Simulation studies illustrate the benefit and effectiveness of the proposed LSSVM-L Hammerstein model and its efficacy as a non-linear model predictive controller for the servo and regulatory control problem.