Construction of Parallel Piecewise-Linear Interval Models for Nonlinear Dynamical Objects
Roman S. Voliansky, Олександр Валентинович Садовой, Nina Volianska, Oleksiy Sinkevych · 2019
The paper is devoted to the developing of the methodological framework for modeling of nonlinear dynamical objects. Such a framework allows performing the coordinate transformation and formulating the algorithm of its usage to transform the series mathematical models of the nonlinear dynamical objects into the interval piecewise-defined linear models and then translate them into parallel ones. The abovementioned algorithm is based on reducing domains size where the nonlinearities of studied objects exist. We offer to reduce these domains by defining intervals on which nonlinear functions can be bounded on the bottom and on the top by linear functions. Thus, we suggest replacing nonlinear functions with their top and bottom piecewise-linear boundaries which are determined by minimization of the above-mentioned domains' areas. Previously suggested boundaries are used to define the transfer functions of the considered objects but one can use them for the stability analysis and the synthesis of closed-loop systems with desired dynamic as well. Then, we apply partial fraction decomposition of the transfer functions to perform transformation of the mathematical models into parallel form. Usage of the proposed approach is one of the ways to decrease calculation time and to improve multi-core CPU usage while simulation of nonlinear dynamical objects is being performed as well as to simplify the study of transients and steady-state modes of considered objects and to construct closed-loop control systems for a wide range of the nonlinear dynamical objects.