Automatic Control of Bioprocesses - Measurement, Monitoring, Modelling, and Control of Bioprocesses - page 41

2.2 Soft Sensors
Economist and business consultant Peter Drucker once said: ''If you can't measure
it, you can't manage it.'' Although he did not mean bioprocesses, it can also be
applied here. Keeping that in mind, soft sensors will here be introduced to
''manage the immeasurable.'' Soft sensors or virtual sensors are employed to
calculate variables from one or more of the directly measured variables. Com-
monly employed indirect measurements based on theoretical models are oxygen
uptake rate (OUR), oxygen transfer rate (OTR), carbon dioxide production rate
(CPR), and the respiration coefficient, which are calculated from exhaust gas
measurements and the aeration rate. The identification of critical needs to suc-
cessfully develop state-of-the-art soft sensors is presented by Luttmann et al. [ 4 ].
They particularly discuss soft sensor methods for bioprocess engineering and
pharmaceutical applications.
Data-driven soft sensors use chemometric models for the estimation of process
variables [ 2 , 3 , 5 ]. An example is the calculation of the glucose concentration and
dry cell mass concentration from fluorescence data [ 6 ]. When using these data-
driven approaches, one has to be careful not to leave the calibration range.
Therefore, theoretical model-based soft sensors usually have a broader range of
application. An important class of these soft sensors is based on state observers.
2.2.1 State Observer
A state observer uses a dynamic theoretical model (state model) of the process to
estimate process variables (state variables). Using available measurements, the
state observer corrects the estimated state variable in such a way that its values will
converge to the true process values. For the implementation of a state observer,
detailed knowledge of the process is necessary. The advantage of state observers is
the determination of immeasurable process variables which can be used for pro-
cess automation.
An example is given by Jenzsch et al. [ 7 ]. They estimated the biomass using a
mass-balance-based state observer by employing the relation between OUR, CPR,
and base consumption. One kind of standard state observer is the Luenberger
observer [ 8 ] and the Kalman filter. A special class of Kalman filter is discussed in
the next section.
2.2.2 Extended Kalman Filter
To smooth noisy measurement signals as well as to estimate immeasurable process
variables, different Kalman filters have been applied for controller implementation.
For this purpose, process knowledge is required in the form of a dynamic state
model, a measurement model, and known measurement noise. The main idea of