Controlling Engine System: a Low-Dimensional Dynamics in a Spark Ignition Engine of a Motorcycle

Abstract

We analyze a time series of the combustion pressure in the idle state, measured from a spark ignition engine of a motorcycle. It is clarified that the engine system can be described by a lowdimensional deterministic dynamics perturbed by some stochastic process. We also propose a method to stabilize the chaotic behaviour of engine's data by adopting the Pyragas' method. We actually use this method in a computer experiment for the control of combustion pressure data to demonstrate the efficiency of the proposed method. As a result of the experiment, we eliminate the fluctuations in the combustion pressure data and obtain a periodic orbit.

Analysis of pressure fluctuations in a natural gas engine under lean burn conditions

“…The dynamics of cycle-to-cycle pressure variations can be quite complex and evolve on multiple timescales. In order to develop effective control strategies for efficient combustion, it is important to understand the dynamics of cycle-to-cycle pressure variations [4][5][6]. Earlier studies on pressure fluctuations were carried out primarily in gasoline and diesel engines [7][8][9][10][11][12][13][14][15][16][17][18].…”

Analysis of repeatability of Diesel engine acceleration

“…Using this advantage of the presented above approach one can adopt this method to engine testing procedures. The efficient feedback control [21][22][23] also requires predictability of engine dynamics, at least in a short time range. The above examined QRA quantities, developed originally for bio-medical applications [19], provides important information about a transient engine response in the time domain.…”

Application of Chaos Theory to Engine Systems

“…We measured several time series such as combustion pressure, intake manifold pressure, and exhaust gas rate for an engine in its idle state, and analyzed them in terms of nonlinear dynamics. From the results of our analysis presented in a previous paper, it is clarified that cycle-to-cycle combustion fluctuation in spark ignition engines can result from the interplay of a lowdimensional chaotic dynamics of engine systems and stochastic processes [4].…”

“…One only has to supply the system with a feedback of the difference between the current value and a delayed value of the observed time series. Recently, we made use of this advantage and theoretically outlined how to apply Pyragas' method to the engine system [4]. We also made experiments of controlling chaos of an engine system [7].…”

“…The data of low-frequency components have a positive Lyapunov exponent, which is an indication of chaos. It is reported that this fluctuation is caused by the interplay of a lowdimensional chaotic dynamics of engine systems and a stochastic process [4]. …”