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- Figure 1.
A. Integrators in series. Let us consider a control plant presented by two integrators connected in series, as shown in Fig. 1:
Figure 1. “Integrators in series” structure.
where T1 and T2 are the parameters of integration. The structure of several integrators (more than 2 integrators) is famous of its instability, i.e. no one linear controller can provide the stability to such system and more over with uncertainly changeable parameters [8, 9]. The example of two integrators in series allows us to see the advantages of using non-linear catastrophe as controller.
Let us choose a feedback control law as following form:
and in order to study stability of the system let us suppose that there is no input signal in the system (equal to zero). Hence, the system with proposed controller can be presented as:
The system (2) has following equilibrium points
, ; (3)