Externally defined variables disturbances

Process input variables are independent variables that affect the output variables of a process. They can be subdivided into two subgroups (1) manipulated variables (also called control variables), which can be adjusted freely by an operator or a control mechanism, and (2) disturbance variables (also called externally defined variables), which are subject to the external environment and thus cannot be controlled. These variables are associated typically with the inlet and outlet streams. In a control system, manipulated variables cause changes to controlled variables. 

A prominent measure of overall success is the profit obtained with a given set of resources in a given time span. Basically, the profit depends on costs, revenues and assets employed, whereby those depend on system-internal and -external influences. In SC simulation the aim is to investigate the behaviour of the system and explain the relations between its components. Here, the focus is on studying internal relations under external disturbances. Let X 6 R denote the vector of controllable independent variables and y 6 R" denote the vector of dependent response variables defined in the model building phase. Furthermore, e 6 R° denotes the vector of uncontrollable variables which are not considered in detail in the model but are captured as environmental effects. The function H -) describes the real relation between dependent and independent as well as environmental variables... 

Following Leffler and Grunwald (11), relaxation can be defined as "the return to equilibrium of a system that has been slightly perturbed by the imposition of a change in one of the variables of state." Relaxation corresponds to an irreversible process which is usually studied by following the temporal evolution of the system after a sudden disturbance. The disturbance consists of the change of one physical variable of the system (i.e., temperature, pressure, external electric or magnetic field, etc.)... 

The catastrophes dynamic model (Fig. 3) determines the interpretation function in the form of bifurcation multitude B(0,t) in the area of control variables multitude GZ(0,t) defining the control dynamic environment integrating impact on external disturbances and peculiarities of the object s dynamics multitude F(W(t),D(t)), determming external environment and stmctural changes in the vessel s behaviour. 

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