in order to increases the reliability of parameter identification. Chapter 4 will present application examples in which various types of a priori information will be incorporated into a black-box approximation technique, primarily such engineering knowledge as material balances and information about chemical reactions.
1.5 Semi-mechanistic Modeling for Control
Chemical processes require control to reach good quality products, high profit and safety. Control of chemical processes presents many challenging tasks including nonlinear dynamical behavior, uncertain and time-varying parame-ters, unmeasured disturbances. [9,27,28] provide good overview about control theory and practice.
There are two main ways of process control:
• the process is controlled manually by an experienced operator,
• the process is controlled by an automatic system.
In the recent years, automatic systems have ousted the manual control tech-nique from the low-level control because the automatic systems are more ac-curate, they are tireless and they do not need salary. On the other hand, the characteristic of chemical processes are typically nonlinear, but they are traditionally operated using PID controllers. Unfortunately, PID controllers are not always able to control every nonlinear system effectively. So a num-ber of nonlinear control system design techniques, including Generic Model Control [29], differential geometric-based control [30], reference system syn-thesis and nonlinear model predictive control [31] and fuzzy model predictive control [32], have been developed during the last years to control chemical processes.
Nonlinear model-based control technics can be divided into two ap-proaches:
• the model predictive approach,
• the model inversion approach.
The model predictive approach is an optimization-based strategy in which a nonlinear model is used to predict the future effect of the variation of the manipulated input in the future. The model inversion approach transforms the original model into a control law in a sort of model inversion method.
Both approaches have advantages and disadvantages. The nonlinear predic-tive approach needs to solve a nonlinear optimization problem in every sample time instant, thus it requires significant computational capacity. In contrast, the model inversion approach only needs to evaluate some analytical func-tions. The model inversion approach, in turn, cannot explicitly handle either constraints on the manipulated input or time delays.
The first step of construction of a model-based controller is to build the model of controlled process, the second step is to formalize the controller from this model, and the last step is to tune the obtained controller. The first step is usually the hardest task, and usually it is the most critical step, because model-based controllers are typically sensitive to model error and parameter uncertainty. Certainly, perfect model does not exist, so some kind of model error compensation method is usually introduced into model-based controllers.
For example, an integral term can eliminate steady-state control error due to parameter uncertainty in Globally Linearizing Control (GLC), set-point can be modified by model error, e.g. by applying Internal Model Control (IMC) structure in Model Predictive Control (MPC).
But it is not always possible to handle the model error effectively with the above mentioned compensation techniques. The nonlinear model-based con-trollers are usually based on first-principle models (white-box models), and there are situations when some parts of the white-box model are in fact not known or when the model uncertainty is significant (it will be illustrated in Chapter 5). Thus the application of model-based controllers may fail because sometimes the process is not known accurately enough. Moreover, the ap-plication of first-principle model in a model-based controller needs complete observability of states (state variables of the model), but on-line measuring of states may be complicated. If a state variable cannot be measured, one has to apply indirect measurement (calculation of a non-measured state variable from other measured variables using the model); however if the model is in-sufficient, indirect measurement will be inaccurate or even impossible. This work suggests including black-box elements as parts of white-box model, see Fig. 1.5, to handle such difficulties. White-box model only leans on mecha-nistic knowledge, so applying black-box modeling makes possible utilizing of
White-box Model-based controller
Controlled System
?
Semi-mech.
Model-based controller
Controlled System
Fig. 1.5. Semi-mechanistic modeling for control
1.5 Semi-mechanistic Modeling for Control 11 information form measurement data. This approach corresponds to the con-cept described in Sect. 1.1.
The proposed modeling approach is usually denoted as semi-mechanistic modeling. Thompson and Kramer [33] used the so-called parallel approach of semi-mechanistic modeling where the error between system output and white-box model is estimated by a neural network. They also described the serial approach where a neural network is used to model the unknown part of the model, see Fig. 1.6.
Fig. 1.6. Serial and parallel combinations of white and black box models
The proposed mechanistic control corresponds to the serial semi-mechanistic model because the black-box element is a part of the white-box model. This approach will be presented in Chapter 5. It will be demonstrated how the white-box modeling approach (first-principle model) and the black-box modeling approach (neural network) can be combined to achieve an ef-fective nonlinear model-based controller. Chapter 5 will also concentrate on practical issues of semi-mechanistic modeling arising from model instability and nonlinearity, model uncertainty and measurement noise.