TO ESTIMATION OF ATTRACTION AREA OF EQUILIBRIUM OF NONLINEAR CONTROL SYSTEMS

Abstract

Designing nonlinear control systems is still difficult so many researchers are trying to find
some useful ways and methods to solve this problem. As a result of such research, some methods
have been seen trying to design a good enough control system for nonlinear plants. But a disadvantage
of these methods is the complexity, so it created a need to compare some methods to determine
which one is the easiest method to design a control system for nonlinear plants. It was
found a way to compare two methods, which is comparing the regions of initial conditions of the
systems which are designed using these methods. Two analytical nonlinear control systems design
methods are compared on the example of the design control systems mobile robots. The algebraic
polynomial-matrix method uses a quasilinear model, and the feedback linearization method uses
particular feedback. Both considered methods give a bounded domain of equilibrium attraction,
therefore the obtained control systems can be operated only with bounded initial conditions.
The numerical example of designing the control systems for one object by these methods and the
estimates of the attraction areas of the system’s equilibriums of these systems are given in the
paper. As a result of this paper, it was found that using the algebraic polynomial-matrix method
will get a bigger cross section of initial conditions of the plant’s variable than the same cross section
which is given by the feedback linearization method.