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.
Highlights
Nonlinear systems are common in many scientific disciplines and one of the objectives is to analyze and design controllers for the models
This connection is called in this paper dynamic linearization and can be used for many concatenated stages of linearization, which is formalized in the following lemma
Consider a class of nonlinear systems modeled by bond graphs described by (21) whose linearization is expressed by (36) under a nominal operation point due to the linearized bond graph; an approximated performance of the state variables connecting a recursive form of linearized bond graphs according to Figure 4 where uδ (t) is the size of the neighborhood and the initial state is changed by the state variable solution is obtained
Summary
Nonlinear systems are common in many scientific disciplines and one of the objectives is to analyze and design controllers for the models. A methodology to obtain the approximation of the state variables of linearized bond graph models with respect to nonlinear bond graphs for input signal trajectories is proposed. Some of the main advantages of this paper with respect to previously published works are: (1) The classical approach of linearization with piecewise [8], recursive [17] or other schemes [13,14,15,16] are based on algebraic analysis of the equations; if the configuration of these schemes changes, it is not easy to adapt these modifications, while in bond graph linearization the adaptation process is simple; (2) the papers [8,13,14,15,16,17] are dedicated to specific models and the bond graph has a multi-domain energy characteristic; (3) the linearization papers [18,27,30].
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