Michael Buchholz

Identification of a bilinear and parameter-varying model for lithium-ion batteries by subspace methods

In this paper, subspace methods are used to identify a dynamic model for high-power lithium-ion cells for hybrid vehicles which is valid within the whole operating range. The lithium-ion battery cells regarded in this contribution have non-linear dynamic behavior which basically depends on battery cell temperature. Therefore, bilinear and parameter-varying model parts are necessary, which can be summarized within one linear-parameter varying (LPV) model. In combination with subspace methods, the presented modeling approach allows a global identification of the model. In contrast to many publications, the identification of the model is based on measurements where common dynamic current-voltage profiles from normal vehicle operation were applied to battery cells. Although the resulting system model has only low complexity, it is still able to describe the battery cell behavior within the entire temperature operation range due to the chosen LPV structure.

A New Approach of Dynamic Friction Modelling for Simulation and Observation

Abstract This paper presents a new dynamic friction model based on a static friction model and a linear parameter-varying first-order lowpass filter. The static model considers viscous, Coulomb, and Stribeck friction and is defined by continuous functions, yielding a smooth force transition at standstill. The adaptive filter changes its time constant dependent on the actual velocity and supplements the static model with hysteresis and memory effect. The combination of both parts offers a high accuracy in simulations using high sample rates and shows a numerically robust behaviour and a good qualitative representation of the friction for small sample rates, making it applicable for practical control tasks using an observer-based approach.

ADAPT-lpv Software for Identification of Nonlinear Parameter-Varying Systems

Abstract The ADAPT-lpv software for the identification of linear parameter-varying (LPV) and/or nonlinear systems is a direct and simple extension of the canonical variate analysis (CVA) method as implemented in the ADAPTx software for identification of linear time-invariant systems. The computational structure and problem size is very similar to ADAPTx except that the matrix row dimension (number of lagged variables of the past) is multiplied by the effective number of parameter-varying functions. This is in contrast with the exponential explosion in the number of variables using current subspace methods for LPV systems. Compared with current methods, initial results indicate much less computation, maximum likelihood accuracy, and better numerical stability. The method can automatically remove a number of redundancies in the nonlinear models producing near minimal state orders and polynomial degrees by hypothesis testing. There is detailed discussion of the computational methods and structure of the software modules. The software is demonstrated on a widely studied aircraft flutter problem.

Flatness based velocity tracking control of a vehicle on a roller dynamometer using a robotic driver

This paper presents a velocity tracking control of a robotic driver that is used for driving industry test cycles on roller dynamometers. As existing commercial robotic drivers show a high complexity, use outdated mechanics and are nevertheless quite expensive, a new robotic driver is developed. The aim is to track a well defined velocity trajectory of a test cycle with high accuracy in an arbitrary vehicle, whereby no learning cycle for determining the specific vehicle behaviour is allowed. To meet all these conditions, at first a single-wheel model for the longitudinal dynamics of a vehicle is proposed. Additionaly, an approximation for the engine torque is given, enabling the adaption of the resulting model by changing only few parameters. Based on this model, a flatness based velocity tracking control for operating the acceleration pedal is introduced.

Slip-Constrained Model Predictive Control Allocation for an All-Wheel Driven Electric Vehicle

Abstract This contribution describes a real-time model predictive control allocation algorithm for over-actuated electric vehicles with individually driven wheels. The proposed method allows to exploit the inherent redundancy present in these systems to optimally allocate yaw moment and longitudinal force while considering actuator dynamics and complying with rate and wheel slip constraints. A linear formulation of the underlying model with varying parameters allows to take changing driving situations into account while guaranteeing fast computation times. The algorithm is tested and validated on a comprehensive vehicle model.

Recursive subspace identification of linear parameter-varying systems

In this paper, a recursive algorithm for blackbox identification of linear parameter-varying (LPV) systems is proposed. The algorithm belongs to the class of subspace identification methods and is based on an existing LPV subspace identification algorithm with block-processing, which is modified and extended to the recursive estimation scenario. These modifications are related to existing methods of recursive subspace identification for linear and time-invariant (LTI) systems, but offer additional room for improvement of the identification results in the LPV case. Therefore, an extension of the recursive algorithm is introduced that avoids the simplifying assumption of one dominating local linear model in the LPV system, which is made in the block-processing algorithm. It is shown that with this extension the recursive algorithm can lead to even better identification results than the corresponding algorithm with block-processing.

Adaptive model-based velocity control by a robotic driver for vehicles on roller dynamometers

This paper presents an adaptation algorithm for a model-based velocity control of a vehicle driven by a robotic driver. In order to ensure that a robotic driver follows a desired velocity trajectory with an arbitrary vehicle, the overlaid controls must be robust as well as highly accurate. Controllers of existing robotic drivers must be adjusted manually or several learning cycles have to be driven. As each learning cycle is very time-consuming and the vehicle has to be conditioned again, a self-adaptation of the applied controls during normal cycle driving is proposed in this paper. This adaptive control depends only on little previous knowledge for initialization and yields a significant improvement of the accuracy already after a short time of driving. Results of the adaptive control both from simulations and from measurements on a roller dynamometer are shown.

Modelling PEM fuel cell stacks for FDI using linear subspace identification

A long life time and safe operation are important issues when polymer electrolyte membrane fuel cell (PEMFC) stacks are used as power supply in technical systems. Therefore, methods are needed to detect deviations from the chosen operating point before any damage to the stack or the environment occurs. In applications like vehicles, the fuel cell operation is highly dynamic, and special diagnosis cycles can not be used during operation. Thus, a diagnosis system is needed which uses the high dynamic data from operation. However, due to limitations of computational power, this diagnosis system must be as simple as possible. In this paper, the linear canonical variate analysis (CVA), which is a subspace identification method, is used as a means for modelling the non-linear PEMFC stack. The linear state-space models can be shown to represent well the input-output behavior of the stack. Additionally, two concepts are proposed using state-space models from linear CVA for diagnosis purposes.

A New Local Control Strategy for Control of Discrete-Time Piecewise Affine Systems

In this paper we propose an enhanced local control strategy for the control of discrete-time piecewise affine systems on full-dimensional polytopes. The control strategy is divided into a local control and a supervisory control problem. The local control problem is to reach and cross one selected facet of a polytope ensuring that the next sample of the time-discrete trajectory is picked up in the adjacent polytope. The procedure is based on conditions, given as inequalities, for the discrete-time gradient of the system, evaluated in the vertices of the polytopes. Solving an optimization problem with respect to the inequality conditions, a performance index is minimized. The performance index represents a minimal retention period of the trajectory in the polytope or the minimal quadratic sum of the input signal. The control law is then obtained by a simple matrix inversion. The supervisory control problem is to find a suitable combination of polytopes and local control strategies that transfers the trajectory to the polytope that contains the operating point.

Online Velocity Trajectory Planning for Manual Energy Efficient Driving of Heavy Duty Vehicles Using Model Predictive Control

This paper presents a novel approach to online velocity trajectory planning for manual energy efficient driving which involves Model Predictive Control (MPC) for map-based anticipatory driving of heavy duty vehicles. The proposed model leads to a Quadratic Programming (QP) optimization problem with sparse matrix structure, allowing to be solved robustly and efficiently. By reducing the optimization problem to a QP standard form, existing and well-proven QP solvers can be used to calculate a reliable solution for a real-time vehicle control application. Evaluations show that the calculation time of the MPC optimization process with a two kilometer long preview horizon is, compared to other literature, significantly reduced to 1.8 milliseconds, while in real-world driving experiments an average fuel consumption reduction of 11.4% compared to normal driving is measured.