Journal of Automation and Control, 2015, Vol. 3, No. 3, 62-66 Available online at http://pubs.sciepub.com/automation/3/3/4 © Science and Education Publishing DOI:10.12691/automation-3-3-4 The Block Diagram and Equations of State of the Bond Graph Example Darina Hroncová * , Alexander Gmiterko, Tomáš Lipták Department of Mechatronics, Faculty of Mechanical Engineering, Technical University of Košice, Letná 9, 042 00 Košice, Slovak republic *Corresponding author: darina.hroncova@tuke.sk Abstract The work shows the use the methodology of Bond Graph for modeling electric system of simple RLC circuit. Electrical model is solved by this approach at the level of its physical behavior. In this paper the method of generation of state equations system is discussed. Model of a simple electrical RLC circuit consisting of a resistor, an inductor, and a capacitor is taken. The differential equations describing the dynamics of the system are obtained in terms of the states of the system. Keywords: Modeling of dynamic systems, Bond Graphs, energy modeling, state equation Cite This Article: Darina Hroncová, Alexander Gmiterko, and Tomáš Lipták, “The Block Diagram and Equations of State of the Bond Graph Example.” Journal of Automation and Control, vol. 3, no. 3 (2015): 62-66. doi: 10.12691/automation-3-3-4. 1. Introduction The concept of bond graphs was originated by Paynter. The idea was further developed by Karnopp and Rosenberg in their textbooks, such that it could be used in practice by Thoma, Van Dixhoorn, Breedveld and by others [1,2,3,4]. The language of bond graphs aspires to express general class physical systems through power interactions. The factors of power i.e., effort and flow, have different interpretations in different physical domains. Yet, power can always be used as a generalized coordinate to model coupled systems residing in several energy domains. A causal bond graph contains all information to derive the set of state equations. The procedure to derive these equations is covered by bond graph software like Enport (Rosenberg, 1974), MS1 (Lorenz, 1997), CAMP (Granda, 1985), and 20-SIM (Broenink, 1990, 1995, 1997, 1999; Broenink and Kleijn, 1999). Therefore, in practice, generation of equation need not be done by hand. However, we discuss the generation of equations to indicate what exactly has to be done. 2. Bond Graph of the Electrical System - Description of the Model The language of bond graphs aspires to express general class physical systems through power interactions. The factors of power i.e., effort and flow, have different interpretations in different physical domains. Yet, power can always be used as a generalized coordinate to model coupled systems residing in several energy domains. To demonstrate the bond graph methodology as an example an electrical model of RLC system is analyzed Figure 1a. An RLC circuit is an electrical circuit consisting of a resistor, an inductor, and a capacitor. The RLC part of the name is due to those letters being the usual electrical symbols for resistance, inductance and capacitance respectively [5]. Figure 1. Electrical system: a) electrical model of RLC system; b) reference voltage uref with positive direction; c) efforts (voltages) with unique names u1, u2, u3 3. Systematic Procedure to Derive a Bond Graph of the Electrical System We have discussed the basic bond-graph elements and the bond, so we can transform a domain-dependent ideal- physical model, written in domain-dependent symbols, into a bond graph. For this transformation, there is a systematic procedure, which is presented here. This electrical system contains a voltage source effort SE (SE:uz), a resistor R (R:R), an inductor I (I:L) and a capacitor C (C:1/C). In the step 1 we determine which physical domains exist in the system and identify all basic