On‐line estimation of glucose and biomass concentration in batch fermentation process using particle filter with constraint

Zhao, Zhonggai; Shao, Xinguang; Huang, Biao; Liu, Fei

doi:10.1002/apj.1626

Cited by 2 publications

(2 citation statements)

References 26 publications

(24 reference statements)

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“…To guarantee the ideal growth environment, these variables should be controlled by the addition of acid and base, the circulations of cold water and hot water, and adjustments of air inlet and agitation power, respectively. To provide a public plant for researchers to test novel methods, a simulation model has been developed for penicillin fermentation process by Birol and coworkers as

\frac{d C_{X}}{d t} = μ C_{X} - \frac{C_{X}}{V} \frac{d V}{d t}

\frac{d C_{P}}{d t} = μ_{p p} C_{X} - K C_{P} - \frac{C_{P}}{V} \frac{d V}{d t}

\frac{d C_{S}}{d t} = - \frac{μ}{Y_{x / s}} C_{X} - \frac{μ_{p p}}{Y_{p / s}} C_{X} - m_{x} C_{X} + F - \frac{C_{S}}{V} \frac{d V}{d t}

\frac{d D_{o}}{d t} = - \frac{μ}{Y_{x / o}} C_{X} - \frac{μ_{p p}}{Y_{p / o}} C_{X} - m_{o} C_{X} + K_{l a} (D_{o max} - D_{o}) - \frac{C_{S}}{V} \frac{d V}{d t}

\frac{d V}{d t} = F - F_{loss}

…”

Section: Simulationsmentioning

confidence: 99%

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Constrained particle filtering methods for state estimation of nonlinear process

2014

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Increasingly in practical applications, nonlinearity, non-Gaussianity, and constraint must be considered to obtain good state estimation. A constrained particle filter (PF) approach for state estimation, which involves three alternative strategies to impose the constraints on the prior particles, posterior particles, and state estimation has been proposed. First, to impose constraints on prior particles, a constrained Gibbs sampling method with a constrained inverse transform sampling is proposed to restrict sampling within the constraint region under cases of both univariate and coupling constraints. Second, to ensure validity of posterior particles, resampling is confined to the valid prior particles and the violated ones are discarded, which results in a similar formulation as the existing acceptance/rejection constrained PF method in literature. Third, if the state estimation violates the constraint, different from the existing methods that either discard all violated particles or accept all of them by projecting them onto the constraint region, the proposed method makes a balance between the prior and the likelihood function by adjusting the weights of violated and valid particles, respectively. Compared with the existing methods, the proposed method provides better physical interpretation and involves no restrictive assumptions about the distributions. Simulation results demonstrate effectiveness of the proposed methods.

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\frac{d C_{X}}{d t} = μ C_{X} - \frac{C_{X}}{V} \frac{d V}{d t}

\frac{d C_{P}}{d t} = μ_{p p} C_{X} - K C_{P} - \frac{C_{P}}{V} \frac{d V}{d t}

\frac{d C_{S}}{d t} = - \frac{μ}{Y_{x / s}} C_{X} - \frac{μ_{p p}}{Y_{p / s}} C_{X} - m_{x} C_{X} + F - \frac{C_{S}}{V} \frac{d V}{d t}

\frac{d D_{o}}{d t} = - \frac{μ}{Y_{x / o}} C_{X} - \frac{μ_{p p}}{Y_{p / o}} C_{X} - m_{o} C_{X} + K_{l a} (D_{o max} - D_{o}) - \frac{C_{S}}{V} \frac{d V}{d t}

\frac{d V}{d t} = F - F_{loss}

…”

Section: Simulationsmentioning

confidence: 99%

“…The true initial states and parameters are set as shown in Table and the values of constant parameters in the model can be found in the literature . The biomass grows in the fermenter starting from the initial biomass concentration, substrate concentration and penicillin concentration 0.1, 15, and 0 g/L, respectively.…”

Section: Simulationsmentioning

confidence: 99%