Ma, K.; Valdés-González, H.; Bogle, I.D.L.; (2010) Process design in SISO systems with input multiplicity using bifurcation analysis and optimisation. Journal of Process Control , 20 (3) pp. 241-247. 10.1016/j.jprocont.2009.12.005.

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Abstract

This paper presents an approach using continuation and optimisation methods for modifying a process design to avoid control difficulties caused by input multiplicity. The approach assumes an initial design, with a preassigned SISO control structure, has been obtained and is useful where there is an input multiplicity in the operating region. The condition for input multiplicity is obtained by inflating the state space model with a state representing the locus of the point of zero gain. The multiplicity condition is determined using the bifurcation analysis package, AUTO, which allows the study of the influence of operating conditions and parameters on input multiplicity behaviour to obtain an expression for the point of zero gain as a function of the design and disturbance variables. A process modification problem is formulated within an optimisation framework and solved to determine the minimal design parameter changes necessary to avoid input multiplicity given an assumed maximal disturbance. Results are presented for the application of the algorithm to a CSTR system demonstrating that small changes in some design variables can avoid input multiplicity problems in this case, and that the method can determine the changes necessary.

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