By Denis Dochain
Giving an summary of the demanding situations within the keep watch over of bioprocesses, this finished publication provides key leads to a number of fields, together with: dynamic modeling; dynamic houses of bioprocess types; software program sensors designed for the online estimation of parameters and kingdom variables; keep watch over and supervision of bioprocesses.
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Extra resources for Automatic Control of Bioprocesses (Control Systems, Robotics and Manufacturing)
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18) i=1 ˆ are the vectors of the N values measured and the predictions of the where yi and yi (θ) model at the instants ti (i = 1 to N ) and Qi is a weighted (square) matrix, respectively. 19) i=1 where Ci represents the matrix for the covariance of the measurement errors (Qi is often chosen to be equal to Ci−1 ). , for maximizing the difference between J(θ + δθ) and Jopt (θ)), it will be necessary to maximize the term enclosed in the brackets [·]. 21) The terms ∂y ∂θ are the sensitivity functions of the output variables.
In the case of a model with two parameters (μmax and Ks in the case of Monod’s model, for example), these curves are ellipses. As underlined by Munack [MUN 89], the axes of the ellipses correspond to the characteristic vectors of the Fisher matrix and their length is proportional to the square root of the inverse of the corresponding eigenvalue. Thus, the ratio of the greatest eigenvalue to the smallest one (as absolute value) is a measure for the form of the function close to the optimum estimated values of the parameters.