Automatic Control of Bioprocesses - Measurement, Monitoring, Modelling, and Control of Bioprocesses - page 52

respect to computation time. Compared with a nonlinear optimization algorithm
[ 49 - 51 ], the genetic algorithms make a time saving of approximately 25 %.
A nonlinear fuzzy controller was presented by Cosenza and Galluzzo [ 52 ] for
the control of pH and temperature during a penicillin production process. In their
application the authors used the so-called type 2 fuzzy set, where uncertainty in the
membership function is also implemented. If no uncertainty is present, the
membership function is as described above, which is called type 1. In simulations,
the performance of the type 2 fuzzy controller was compared with an ordinary
(type 1) fuzzy controller as well as a PID controller. It was concluded by the
authors that, due to the nonlinearities and uncertainty of the process, the PID
controller cannot be compared with the fuzzy controller equitable. The best results
were obtained with the type 2 fuzzy controller. When increasing the measurement
noise level, the difference between type 1 and type 2 becomes more evident.
A special controller based on fuzzy logic has been developed by Takagi and
Sugeno [ 53 ]. The difference from the abovementioned fuzzy logic systems is that, in
the conclusion part, a function is defined with the input values as arguments. The
conclusion of the whole rule system is the sum of the function values weighted by the
corresponding membership functions. Belchior et al. [ 54 ] implemented an adaptive
Takagi-Sugeno (TS) fuzzy control algorithm for DO of an activated sludge waste-
water treatment process, where the parameters of the conclusion were adapted
online. The controller was constructed by using the Lyapunov synthesis approach
with a parameter projection algorithm. Parallel to the adaptive control algorithm, the
authors implemented a supervisory fuzzy control with a smooth switching scheme
between supervisory and nonsupervisory modes. In simulations, they could dem-
onstrate that the error obtained by the fuzzy controller was less than 2 %, whereas a
PI controller produced peaks greater than 10 %.
3.5 Artificial Neural Network-Based Control
Artificial neural networks copy the functionality as well as the structure of bio-
logical neural networks by using a mathematical model. In such networks, a
possibly very complex input vector (e.g., a visual and/or acoustical signal) can be
transferred via various neurons to condense information. Figure 5 presents a basic
artificial neural network (ANN) with four inputs in the input layer, five neurons in
the hidden layer, and two outputs in the output layer. The structure of an ANN can
vary in the number of layers, the connections of the layers, and the number of
neurons in each layer, depending on the complexity the network is supposed to
map. Even more outputs than available inputs can be generated. To determine
whether an artificial neuron will ''transmit'' a signal, all its weighted input values
are employed as arguments of a transfer function, which can be, e.g., a sigmoidal
function for smooth transitions or a step function for on/off behavior.
Corresponding to a biological neural network, an artificial neural network needs
to be trained for pattern recognition or decision making. During training the