Stability Investigation of an Idle Speed Control Loop for a Hybrid Electric Vehicle

In this brief, we investigate the stability of an idle speed control (ISC) loop for a hybrid electric vehicle (HEV). The actuators in an HEV powertrain are subject to delays, which can cause instability. Furthermore, in a parallel hybrid setup, these actuators are coupled via a dual mass flywheel, introducing nonlinear behavior through a mechanical dead-zone. The resulting control loop is a Lur´e-type nonlinear system with delays. To investigate its stability, a simple Lyapunov-Krasovskii functional is constructed, taking into account the delays and nonlinear feedback part simultaneously. By means of a quadratic program formulation, conservatism regarding the nonlinearity is reduced. A powertrain model is presented from which an idle speed controller has been designed and successfully implemented on an electronic control unit. Finally, it can be shown that stability for the ISC loop is guaranteed, based on the controller design model of the HEV powertrain.