23. Internationales Stuttgarter Symposium

Automobil- und Motorentechnik

4. - 5. Juli 2023

Session: VEHICLE DYNAMICS & SIMULATION | | 11:30 - 12:00

Design of a Model-Based Optimal Multivariable Control for the Individual Wheel Slip of a Two-Track Vehicle

Robert Rosenthal, TH Köln

The concept of autonomous driving has become increasingly relevant. This is why innovative drive concepts for motor vehicles need to be developed. Therefore, a model-based optimal multivariable control for the wheel slip is presented in this paper. This allows to specify the slip, and thus the tire force, individually for each wheel. The plant model consists of a planar and stiff multibody two-track model of a vehicle, a complex tire model as well as a simple air resistance and motor model. In addition, the contact forces of the individual wheels are calculated dynamically. A special feature of the multibody model is that the vehicle's position variables are defined by integrating the velocity variables. The linearized model derived from the nonlinear model is used to design a linear optimal static state space controller (LQR) including reference and disturbance feedforward. The contact point velocities of the tires are defined as the controlled variables, since they are proportional to the slip and thus to the driving forces in the operating range of the controller. In addition, the rates of change of the contact point velocities are also chosen as controlled variables in order to set the damping of the closed loop. The four drive torques represent the control variables. Therefore, a true multivariable control is created. As the first step of the analysis, the linearized closed-loop system is investigated regarding stability, robustness, and its dynamic behavior in the reference and disturbance transfer paths. The control system shows a high bandwidth, a well damped dynamic behavior and a large phase margin. In the second step of the analysis, various simulations of realistic experiments, such as an accelerated cornering maneuver or a fishhook maneuver, are performed with the nonlinear closed-loop system. The results of these experiments confirm the high robustness and good dynamic behavior of the control system in most cases. Moreover, the results illustrate how the control considers the dynamic contact forces of the wheels in order to achieve the desired slip at any time. Lastly, dominant transfer paths are identified based on the feedback matrices of the state space controller, showing which input and state variables have relevant influence on the control variables. Based on these, single variable control systems for the individual wheels can be derived.