Constrained optimal control of an electronic throttle

Abstract

The overall vehicle performance is strongly influenced by the quality of the control of the electronic throttle – a DC motor driven valve that regulates the inflow of air to the vehicle's engine. Designing a controller for the throttle system is a challenging task since one has to cope with two strong non-linearities: the gearbox friction and the so-called “limp-home” non-linearity. In this paper we address these issues by solving a constrained optimal control problem formulated for the discrete-time piecewise affine (PWA) model of the throttle. In an off-line, dynamic programming procedure we obtain the look-up table like solution to the optimal control problem. Such a solution allows the real-time controller implementation that would otherwise be impossible to achieve due to the small sampling time needed for the application at hand.

We address the issue of the PWA friction modelling in more detail by considering both static and dynamic friction models. Two different control strategies are studied: constrained finite time optimal control (CFTOC), used in the regulator case, and constrained time-optimal control (CTOC), used in the reference tracking case. We report experimental results with both control strategies. The reference tracking controller significantly outperformed a tuned PID controller with a feedforward compensation of non-linearities in terms of the response speed while preserving the response quality regarding the absence of an overshoot and the static accuracy within the measurement resolution.

Acknowledgments

We wish to thank to Danijel Pavković for sharing his knowledge about the throttle, to Miroslav Barić for help with the Real-Time Linux, and to Davor Hrovat and Joško Deur for helpful discussions regarding the experimental results. This research was supported by the Swiss National Science Foundation and the Ministry of Science, Education and Sports of the Republic of Croatia.