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![Guaranteed parameter estimation set for the case of internal fouling model. so the value of n takes values from a continuous interval. The true value of the rate constant is K = 2 and P 0 = [0, 2] × [0, 20]. The time-optimal operation, in both cases, commences with the concentration mode (α = 0). Hence accurate parameter estimates are needed to determine the optimal switching time to the singular control. We employ BARON (Tawarmalani and Sahinidis, 2004) for solving the optimization problems (13)-(15) to global optimality with maximum 1 × 10 −4 relative gap.](profile/Radoslav-Paulen/publication/320494122/figure/fig1/AS:653371602112520@1532787337447/Guaranteed-parameter-estimation-set-for-the-case-of-internal-fouling-model-so-the-value.png)
Guaranteed parameter estimation set for the case of internal fouling model. so the value of n takes values from a continuous interval. The true value of the rate constant is K = 2 and P 0 = [0, 2] × [0, 20]. The time-optimal operation, in both cases, commences with the concentration mode (α = 0). Hence accurate parameter estimates are needed to determine the optimal switching time to the singular control. We employ BARON (Tawarmalani and Sahinidis, 2004) for solving the optimization problems (13)-(15) to global optimality with maximum 1 × 10 −4 relative gap.
Source publication
In this paper we study a model-based time-optimal operation of a batch diafiltration process in the presence of fouling where the fouling model is adapted on-line using the set-membership (guaranteed) parameter estimation. The membrane fouling poses one of the major problems in the field of membrane separation processes. The studied objective in th...
Context in source publication
Context 1
... the assessment of the obtained results, we first consider the resulting set of guaranteed parameter estimates P e , which is shown in Fig. 2. The figure shows projections of the conditions (13b) into parametric space. Here each pair of red and blue curves represents a contribution by one measurement and coincides with two inequality conditions in (13b). The obtained set (the white region in between red and blue curves) provides good estimates of both the values of n and K. ...
Citations
Consider a SISO dynamic system as follows: \(y_k=\Phi _k^\mathrm{T}{\boldsymbol{\theta }}+v_k; k=1,2,\ldots ,N,\) where \(\{y_k\} \in \mathbb {R}\), \({\boldsymbol{\theta }} \in {\mathbb {R}^{m}}\), \(\Phi _{k} \in \mathbb {R}^{m}\) are the output observation sequence, unknown parameter vector and observable data vector, respectively. \(\{v_k\} \in \mathbb {R}\) is a unknown but bounded measurement noise sequence that satisfies \(v_k^2 \leqslant \sigma ^2\). The parameter vector and the system information vector are defined by.
