The Lagrange multiplier for the kinetic energy e is shown to be −γcm on a singular arc, where γ (g/J) is derived from engine and driveline characteristics and cm ≈ 1. Using this value as an approximation for constrained arcs as well, the cost function is J(s, x) ≈ −γcme + C(s) that yields the residual cost φ(x) = −γcme. The factor β corresponds to the constant Lagrange multiplier for time and i...

The paper proposes a predictive control strategy in discrete time δ-representation in order to reduce the oscillations in the driveline. These oscillations appear in modern diesel engines when a high engine torque is generated at low engine speed. The main object of this paper is to present a model based control concept in δ domain which seems to improve both the control performance and control...

A flywheel angular velocity model for misfire and disturbance simulation is presented. Applications of the model are, for example, initial parameter calibration and robustness analysis of misfire detection algorithms. An analytical cylinder pressure model is used to model cylinder torque and a multi-body model with torsional flexibilities is used to model crankshaft and driveline oscillations. ...