The POG technique for modelling engine dynamics based on electrical analogy

Abstract

In this paper the Power-Oriented Graphs (POG) technique is used for modelling an internal combustion engine. The POG technique is focused on a new modular, physically based and lumped parameter approach, leading to a complete and coherent engine model structure. The aim of the authors, starting from an analogy with electrical systems, is to simplify the approach eliminating the space dynamics (multi-zone combustion and wave effects), while preserving the time dynamics. In this way, it is possible to obtain an engine description similar to an electrical circuit, with all the useful consequences in term of existence and numerical availability of the solution. The advantages are in the specific correspondence that is found between the engine components and variables (as throttle valve, cylinder, inertial flows) with electrical counterparts (current, voltage, resistance). The main benefit achievable with this methodology is the simplicity to compose the whole engine model and customize it including the differential equations of the engine in state space form, using the POG technique. The POG technique is a graphical modelling technique which uses only two basic blocks (the "elaboration" and "connection" blocks) for modelling physical systems. The state space mathematical model of a system can be "directly" obtained from the corresponding POG representation. The POG model of the considered combustion engine shows its internal structure from a "power" point of view. GLOSSARYp gas pressure [N/m 2 ] T gas temperature [K] T sl temperature of lateral surface of cylinder [K] T sb temperature of basic surface of cylinder [K] m air mass flow rate [kg/s] Q ext heat flow rate [kJ/s] V volume [m 3 ] θ spark advance [deg] c x specific heat capacities (x = p or v)[J/(kgK)] γ ratio of specific heats , c p /c v [−] h i enthalpy [kJ/kg] m f uel fuel mass [kg] η cb combustion efficiency [−] λ air/fuel ratio [−] S heat release [W/kg] m c choked air mass flow rate [kg/s] m nc not choked air mass flow rate [kg/s] C D discharge coefficient [−] A T effective flow area [m 2 ]