Approximated modeling and minimal realization of transfer function matrices with multiple time delays

Xie, Linbo; Shieh, Leang-San; Tsai, Jason Sheng‐Hong; Zhang, Y.

doi:10.1016/j.jprocont.2012.10.008

Cited by 4 publications

(3 citation statements)

References 32 publications

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“…Singular values of the Hankel matrix are closely related to the controllability and observability of the system [51,53]. Therefore, SVD of H as shown in (18) provides additional information regarding the controllability and observability of the process, which can be used to quantify the importance of each state in the corresponding input-output system described by H [2,15].…”

Section: Methodsmentioning

confidence: 99%

“…This means that if the Hankel singular values decrease rapidly, most of the input-output behavior is provided by the first few states [15,57]. Therefore, by means of singular values analysis, the information contained in H can be reconstructed just by representing the system with the input-output variables related to the highest singular values [2,53].…”

Section: Methodsmentioning

confidence: 99%

“…Given that SVD of the Hankel matrix determines in a qualitative way whether a process is controllable/observable or not, as a way to quantify these process information extracted from (18), the output impactability index of each output variable (OII y k ) was introduced in [2]. Considering that U represents the output space of H as can be noticed from (18), and hence each column of U is related to one output (left singular vector) [34,53], OII y k is defined as (19). The rationale behind this index is based on the concept of Euclidean norm, therefore, the sum of each squared output singular vector entries related to each output at each time instant U 2 kþms;i ðjÞ weighted by the corresponding squared singular value r 2…”

Section: Methodsmentioning

confidence: 99%

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Model-based scale-up methodology for aerobic fed-batch bioprocesses: application to polyhydroxybutyrate (PHB) production

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Mozumder

et al. 2015

Bioprocess Biosyst Eng

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This work presents a general model-based methodology to scale-up fed-batch bioprocesses. The idea behind this approach is to establish a dynamics hierarchy, based on a model of the process, that allows the designer to determine the proper scale factors as well as at which point of the fed-batch the process should be scaled up. Here, concepts and tools of linear control theory, such as the singular value decomposition of the Hankel matrix, are exploited in the context of process design. The proposed scale-up methodology is first described in a bioprocesses general framework highlighting its main features, key variables and parameters. Then, it is applied to a polyhydroxybutyrate (PHB) fed-batch bioreactor and compared with three empirical criteria, that are traditionally employed to determine the scale factors of these processes, showing the usefulness and distinctive features of this proposal. Moreover, this methodology provides theoretical support to a frequently used empirical rule: scale-up aerobic bioreactors at constant volumetric oxygen transfer coefficient. Finally, similar process dynamic behavior and PHB production set at the laboratory scale are predicted at the new operating scale, while it is also determined that is rarely possible to reproduce similar dynamic behavior of the bioreactor using empirical scale-up criteria.

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