Laurent Truffet

Normalized Knock Indicator for Natural Gas S.I. Engines: Methane Number Requirements Prediction

Design of engines and associated nominal settings are normally computed and optimized so as to provide maximum performance, i.e. compromise between efficiency and emissions. For Combined Heat and Power (CHP) applications fuelled by gas network, this conception is adapted for a large range of gas chemical composition, up to a limit. The indicator used to describe gas quality is the methane number (MN). Hence, engine manufacturers normally supply specific information such as nominal engine settings and its associated limit value for the methane number (MNL ). When the engine is operating under its nominal settings, a low grade gas (MN < MNL ) can lead to engine knock. Knock is caused by auto-ignition of the end gas ahead of the flame in spark-ignition engine. Heavy knock can severely damage engine piston, constituting a main constraint for optimization of engine operating conditions. For an engine setting ES, (the vector ES includes the spark advance SA, the air fuel ratio AFR and the load), methane number requirement (MNR) is defined such as the minimum value of MN above which no-knock is ensured. The objective of this paper is to predict MNR as a function of engine setting for three engines. Simulation results show that the critical value of the considered knock criterion varies from an engine to another. A new normalized knock indicator based on the energy ratio is proposed to enable this comparison: laminar flame speed is assumed to be more sensible to MN variation than internal fluid dynamics (swirl, tumble, and squish) due to engine design.© 2009 ASME

Some Remarks on Links between Positive Invariance, Monotonicity, Strong Lumpability and Coherency in Max-Plus Algebra

In this paper, we make clearly appear links in Max-Plus algebra between four apparently different concepts encountered in various domains, such as Positive invariance, Monotonicity, Strong lumpability and Coherency. The first concept concerns Positive invariance of a particular set by a (linear) map. The second concept concerns Monotonicity of a given matrix. The third concept concerns Strong lumpability and the last concept concerns Coherency. To achieve these objectives, we begin first by recalling the idempotent version of Haar’s lemma, which gives necessary and sufficient conditions for the inclusion of ”one sided” idempotent polyhedra. Then, we generalize this result to the case of the inclusion of ”two sided” idempotent polyhedra. Finally, these results allow to formulate conditions for each concept and to give links between them. Recalling that Strong lumpability and Coherency are used for the aggregation (reduction) of systems. All the proofs are based on residuation theory, which play a central role in duality theory.

State Feedback Control via Positive Invariance for Max-plus Linear Systems using Γ-algorithm

It is now almost classical that max-plus linear systems modelize discrete events systems (DES) of practical interest. The control of such systems is a recent topic of research which has not yet been so developed than control theory in classical algebra. In this paper, we identify and characterize the positive invariance of a max-plus polyhedron set by max-plus linear dynamical systems. We show that positive invariance of max-plus polyhedron set can be expressed under the form of polyhedron sets inclusion. Using Haars Lemma (1918) which provides the algebraic characterization of the inclusion of two polyhedral sets, Necessary and Sufficient Conditions (NSC) are provided under which the positive invariance of a max-plus polyhedron set hold. As an application we propose a method using Γ-algorithm to compute a static state feedback control. Finally, the proposed methods are illustrated by an example.

Bounds on the end-to-end loss probability for queues in Series with Finite Capacity

Abstract We study network of queues in series with finite capacity without blocking of servers but with loss of customers. The contribution of this paper is to obtain upper and lower bounds on the end-to-end loss probability under the assumption that service times are exponentially distributed. This result is obtained using an approach based on sample path comparison. Computational bounds can then be obtained in the special case when the arrival process at the network is Poisson. Numerical results are reported that show the accuracy of the bounds

Numerical Method for Bounds Computations of Discrete-Time Markov Chains with Different State Spaces

In this paper, we propose a numerical method for bounds computations of discrete-time Markov chains with different state spaces. This method is based on the necessary and sufficient conditions for the comparison of one-dimensional (also known as the point-wise comparison) of discrete-time Markov chains given in our previous work [3]. For achieving our objective, we proceed as follows. Firstly, we transform the comparison criterion under the form of a complete linear system of inequalities. Secondly, we use our implementation on Scilab software of Gamma-algorithm to determine the set of all possible bounds of a given Markov chain.

Idempotent version of the Fréchet contingency array problem

In this paper we study the idempotent version of the so-called Frechet correlation array problem. The problem is studied using an algebraic approach. The major result is that there exists a unique upper bound and several lower bounds. The formula for the upper bound is given. An algorithm is proposed to compute one lower bound. Another algorithm is provided to compute all lower bounds, but the number of lower bounds may be a very large number. Note that all these results are only based on the distributive lattice property of the idempotent algebraic structure.