Biomedical Engineering Reference
In-Depth Information
been applied to real processes. Santos et al. [ 59 ] are working on simulated E. coli
NMPC-controlled cultivations. They assume the measurement of the substrate
concentration and keep the specific growth rate at the maximum oxidative capacity
as well as inhibiting product formation. They applied a special NMPC scheme
named min-max-based robustness consideration. Another new NMPC method as
well as a comparative performance assessment were presented by Kawohl et al.
[ 10 ]. They compared the performance of NMPC and NMPC-EKF for input signal
prediction to a method called online trajectory planning (OT). OT is basically an
NMPC in which the estimation horizon is extended to the end of the cultivation. If
the system is strongly disturbed, this method has certain advantages for the esti-
mation in order to return to optimal productivity, albeit at the cost of computa-
tional power. The experiments were carried out through Monte Carlo simulations,
simulating experiments through disturbance scenarios. The aim of the experiments
was to maintain the optimal productivity of the product penicillin. The authors
show the potential of this closed-loop control by improving the mean productivity
by 25 % for the MPC and 28 % for the OT method compared with open-loop
control, where these methods especially increase the minimum productivity due to
disturbances.
3.6.1 ANN-Fuzzy Hybrid-Based Estimation for NMPC Control
A possibility to decrease the complexity of nonlinear models in control algorithms
such as MPC is provided by locally linear models, which are applied in a hybrid
structure by combining the abilities of a neural network and fuzzy logic. The basic
structure is displayed in Fig. 6 . Each neuron in the hidden layer consists of a
membership function and a local linear model (LLM). The arguments of the
membership function are the input value x i . The function value itself indicates the
validity of the corresponding LLM, which is in fact a multilinear regression model.
The estimate of this model type is the sum of the LLM output weighted by the
normalized membership function.
The algorithm was successfully applied by Ashoori et al. [ 57 ] to generate a
neuro-fuzzy model to replace equations in a mass balance model for penicillin
formation. The authors assessed the resulting computational costs as very
acceptable for a real-time process. They showed results which are comparable to
results generated by the whole model. Although the method is rarely applied for
biotechnological applications, it provides opportunities to overcome frequently
mentioned computational limits.
Simulation studies for optimal model training, parameter identification, and
comparisons between closed-loop performance are presented by Xu et al. [ 60 - 62 ].
Among others, they employed the LOLIMOT algorithm to achieve optimal
parameters for the membership function as well as for the LLM. The LOLIMOT
algorithm is an incremental tree-based learning algorithm. A detailed description
can be found in Nelles [ 63 ]. The algorithm adds consecutive locally linear model
neurons and thereby optimizes the error of calibration. Obviously, a large number
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