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\sum_k \big[ q^{\uparrow}(t_k) - \tilde q^{\uparrow}(t_k) \big]^2   \rightarrow \min 


The constraints are:

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\tau \geq  0 , \quad  0 \leq f \leq 1

CRMP – Multi-tank Producer-based Capacitance Resistance Model

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\sum_k \sum_j \big[ q^{\uparrow}_j(t_k) - \tilde q^{\uparrow}_j(t_k) \big]^2   \rightarrow \min 


The constraints are:

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\tau_j \geq  0 , \quad f_{ij} \geq  0 , \quad \sum_i^{N^{\uparrow}} f_{ij} \leq 1

ICRM  – Multi-Tank Integrated Capacitance Resistance Model

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LaTeX Math Block
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\sum_k \sum_j \big[ Q^{\uparrow}_j(t_k) - \tilde Q^{\uparrow}_j(t_k) \big]^2   \rightarrow \min 


The constraints are:

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\tau_j \geq  0 , \quad f_{ij} \geq  0 , \quad \sum_i^{N^{\uparrow}} f_{ij} \leq 1


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titleDerivation
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p_{wf}(t) = p_r(t) - \frac{q(t)}{J}
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p_r(t) = p_i + \frac{1}{c_t \, V_{\phi}} \, \Bigg[ \int_0^t q_i(\tau) d\tau - \int_0^t q(\tau) d\tau  \Bigg]

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