TU Braunschweig


Nonlinear robust control of longitudinal vehicle dynamics

Projektbearbeiter: Lothar Ganzelmeier, Jörg Helbig, Uwe Becker, Eckehard Schnieder


During the last decades the subject of design and analysis of various longitudinal and lateral control laws for autonomous vehicles has been studied extensively. Even though much effort have been spent on various control laws a mostly neglected aspect of autonomous vehicle control is regarded. The main objective of a longitudinal controller is to ensure that the vehicle drives with the desired velocity. Hereby the largest problem is the nonlinear behavior of a combustion engine. Even within one gear the combustion engine modifies its characteristic significantly by passing through all different engine speeds. Especially during the acceleration phase this effect is particularly relevant and has to be taken into account for stability and performance aspects in controller design. Most scientific works made so far deal with this problem and suggest a wide range of different solutions. The basic approach of this work however goes one step beyond. With the aim to control non-identical vehicles with absolutely different engine concepts and characteristics, much harder boundary conditions are found by the controller. For this reason it is a large challenge for every control task to operate appropriate under such a wide variety of vehicle dynamics.

Nonlinear Robust Control Objectives:

Nonlinear H? control is an extention of the linear H? method, which has been used successfully since the end of the 1980?.In contrast to linear control theory nonlinear H? control theory is formulated in the time domain and depends on ideas and methods of differential games and nonlinear partial differential The approach generally considers nonlinear systems of the given form where w stands for some unmeasured disturbance vector. The aim is then to design a feedback control that stabilizes the closed-loop system and attenuates the effect of w on some regulated output z. The shown standard nonlinear H? control formulation is used. Mathematical and computational aspects of nonlinear H? control or of L2 gain synthesis are considered. For output-feedback H? control a nonlinear state feedback controller is combined with a nonlinear observer based on the plant dynamics. The solution of the resulting Hamilton-Jacobi-Isaac differential inequalities is approximated by power series and implemented in Matlab.

Longitudinal Control:

These aspects of robust stability were determined by practical experiments. The plots show the results of one longitudinal controller achieved for two non-identical cars with different engine concepts. It concretely is a VWLupo and a VWPassat with the above presented petrol and diesel engine. Both vehicles are stimulated with a step input for the desired velocity. The closed loop system response is plotted over its input signal. Additional to these signals the percentage of the resulting accelerator pedal is shown, too. Despite of more mass one can see the much higher dynamic resulting from the higher torque output of the diesel engine. This leads to some more acceleration pedal activities in the area where the engine develops its highest torque. Nevertheless the controller is able to stabilize the input step. It can be outlined that the very strongly varying parameters are covered by the robustness of the designed controller. Therefore the presented controller not only handles the changing engine torque over different engine speeds but also various characteristics for different engine concepts.

Handout: Nichtlineare robuste Regelung der Längsdynamik von Kraftfahrzeugen