Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization

Abstract

An alternative method to analyze a class of nonlinear systems in a bond graph approach is proposed. It is well known that the analysis and synthesis of nonlinear systems is not a simple task. Hence, a first step can be to linearize this nonlinear system on an operation point. A methodology to obtain linearization for consecutive points along a trajectory in the physical domain is proposed. This type of linearization determines a group of linearized systems, which is an approximation close enough to original nonlinear dynamic and in this paper is called dynamic linearization. Dynamic linearization through a lemma and a procedure is established. Therefore, linearized bond graph models can be considered symmetric with respect to nonlinear system models. The proposed methodology is applied to a DC motor as a case study. In order to show the effectiveness of the dynamic linearization, simulation results are shown.

Fabrication of Silica Optical Fibers: Optimal Control Problem Solution

“…According to [20,21], if some nonlinear system is linearized in the neighborhood of its stationary state, then the analysis of such a linearized system can replace the analysis of the original system. In this case, the stationary value of the fiber radius is conveniently considered as the optimal geometric characteristic.…”