Sören Hohmann

Steering driver assistance system: A systematic cooperative shared control design approach

Several publications have shown that it is beneficial to design a driver assistance system using a shared control structure. For the steering task this structure can be realized with a setup in which driver and automation can apply a torque on the steering wheel in parallel. Thereby both, driver and assistance system, interact with the vehicle and each other over the haptical channel. In the system the driver is given and cannot be changed. The question is how to design the assistance system controller as an ideal complement to the driver. In this paper a formal design concept is applied to this problem which utilizes the fact that adding a controller to the overall system has to lead to a Nash equilibrium. Remaining degrees of freedom are used to optimize the designed controller with respect to a global objective function that specifies overall system performance. We refer the concept as “cooperative shared control design”. For the concept driver and vehicle are modeled as a differential game. We show systematically that this concept can be used to determine the optimal assistance system if the driver characteristics are known. Simulations prove the applicability of this concept.

An identification method for individual driver steering behaviour modelled by switched affine systems

This paper addresses the issue of modelling and identification of individual driver steering behaviour from a new point of view, incorporating the idea of human motion being built up by an individual and limited repertoire of learned patterns. We introduce a switched affine model structure to explain a measurable motion alphabet in the driving context and show that this leads to a new identification problem that differs from general hybrid identification issues. To solve this problem, we derive a multi-step model output error criterion and propose an algorithm to simultaneously identify switching times and subsystem parameters out of measurable movement data. We show that this algorithm is capable of identifying the true parameters of known systems as well as fitting real movement trajectories even though no a priori information is given about the true system complexity.

Nonlinear Torque Control of a Spark Ignition Engine

Abstract In vehicles the produced engine torque is closely related to the manifold pressure, which is determined by the position of the throttle. In order to satisfy new comfort and safety requirements or to reduce NOx and HC emissions using variable cam timing an intervention of a torque control is needed. We propose two controller design approaches for this task. First, a new continuous nonlinear controller design method, called modified optimal control, is applied. State of the art controllers are implemented in digital signal processors. We therefore derive a hybrid nonlinear time discrete controller, too. Both controllers achieve appropriate dynamics and asymptotic stability of the closed loop in the whole operative range.

Functional Fractional Calculus for System Identification of Battery Cells

Abstract This paper considers a fractional modelbased identification method with the objective to determine the aging of a battery cell. The method avoids lumped approximations of the fractional operator. Moreover with this approach it is possible to identify physically motivated battery cell parameters. The basic idea is to transfer the derivatives from the measurements to the so called modulating functions. With the help of simulations a robust behavior against measurement noise is shown. It is possible to use the method for online battery identification.

Necessary and sufficient conditions for the design of cooperative shared control

In a shared control system humans and machines cooperatively interact. From the control theoretic point of view this can be seen as a system which is controlled by several controllers that are either formed by a human or by a machine. Since all controllers influence the system they affect each other. However, the human parts are given and cannot be changed. Therefore, the question is how to design the non-human controller systematically stable and without experiments. In this paper a design concept for these controllers is proposed which is based on game theoretic modeling. We show that adding a controller to the overall system has to lead to a Nash equilibrium. We further show that remaining degrees of freedom may then be used to optimize the designed controller with respect to a certain global objective function that specifies the demands of the system designers. Based on this idea necessary and sufficient conditions for cooperative shared design are stated. Practical approaches to solve the design problem are presented for real world problems. An example shows the applicability of the concept.

Online Identification of Individual Driver Steering Behaviour and Experimental Results

Using switched systems, we model individual driver steering behaviour from a new point of view. This approach allows to incorporate the idea of human motion being built up by an individual and limited repertoire of learned patterns. The identification of the generating subsystem parameters of such individual motion primitives solely on measured output data requires a new identification method. We propose an algorithm using a multi-step model output error criterion and discuss different implementations in detail. We show that this method is capable of tracking real measurement data of driver steering motion trajectories with low model orders and number of switches respectively. The presented method is online-capable. Experimental driving results proof the concept.

Exact sampled data representation of continuous time nonlinear systems by finite polynomials with exactly determined coefficients

A new time discretization scheme is presented, based on a Taylor series expansion of the continuous time nonlinear system. It is shown that any Taylor series coefficient of the corresponding discrete-time nonlinear system can be calculated exactly. Therefore, the notion of Lie sequences is introduced facilitating the calculation of Taylor-Lie series significantly. Since the resulting coefficient can be expressed in terms of the matrix exponential, numerical algorithms for the determination of each coefficient can be used. An illustrative example quantifies the results.

Comparison of Active Battery Balancing Systems

A quantitative model-based comparison of 10 active balancing circuits is presented for equalizing imbalanced cell energies of lithium-ion batteries. A mean current model approach is introduced for active balancing to describe energy transfers between battery cells for long charge/discharge operation. A Th233;venin model for 96 battery cells is used as a subsystem of a mid-size electric vehicle. In quasi-static simulations, FTP75 driving cycles are continuously repeated until the first cell is discharged from initial full charge. Simulation results are compared for cases of new and aged cells with different capacity distributions concerning equalization speeds and final differences of cell energy.

Fractional algebraic identification of the distribution of relaxation times of battery cells

In this paper, an algebraic model-based approach for the identification of a batterys distribution of relaxation times (DRT) is illustrated. The DRT is directly linked to physically interpretable parameters to determine the aging of a battery cell. The approach derives from Mikusińskis operational calculus. Therefore a novel integration operator and the differentiation rule for fractional systems is presented. The identification is exact in that no approximations of the novel operator are used. The procedure is verified by simulation results.

Cooperative Shared Control Driver Assistance Systems Based on Motion Primitives and Differential Games

In this paper, a cooperative shared control driver assistance system that supports the driver in the steering task is proposed. The aim behind this concept is a cooperation between the driver and the assistance system. Thereby, both, driver and assistance system, can apply a torque on the steering wheel. Mathematically, this structure is described as a differential game. As a primary condition to facilitate cooperation, it is essential to explicitly regard the aims and steering actions of the driver for the calculation of the optimal torque, which the assistance system should apply. This requires an appropriate model of the human driver. A model that describes the driver steering motion as a sequence of motion primitives, which can be identified, is proposed for this task. Next, a real-time capable implementation of this concept is proposed. The concept is validated in a driving study. The study indicates that the system improves the lane keeping performance of the participants and leads to a higher user rating compared with noncooperative driver assistance systems.