Wolfgang Reinelt

Comparing different approaches to model error modeling in robust identification

Identification for robust control must deliver not only a nominal model, but also a reliable estimate of the uncertainty associated with the model. This paper addresses recent approaches to robust identification, that aim at dealing with contributions from the two main uncertainty sources: unmodeled dynamics and noise affecting the data. In particular, non-stationary Stochastic Embedding, Model Error Modeling based on prediction error methods and Set Membership Identification are considered. Moreover, we show how Set Membership Identification can be embedded into a Model Error Modeling framework. Model validation issues are easily addressed in the proposed framework. A discussion of asymptotic properties of all methods is presented. For all three methods, uncertainty is evaluated in terms of the frequency response, so that it can be handled by H8 control techniques. An example, where a nontrivial undermodeling is ensured by the presence of a nonlinearity in the system generating the data, is presented to compare these methods.

Back Driving Assistant for Passenger Cars with Trailer

This paper focuses on control strategies that are needed to stabilise a backing trailer and steer it into the desired direction. A model of the trailer and the car is used in order to calculate the desired steering wheel angle. An important constraint is that the driver should not be disturbed by the steering intervention. Measurements are done with a prototype car with an active front steering system. The results show that the drivers manage to fulfill the given driving task faster and with less steering wheel activity than without the assistant.

Robust control of a two-mass-spring system subject to its input constraints

A robust controller is designed for a system consisting of two carts coupled by a spring. Special attention is given to the input saturations. This problem was posed within a benchmark collection for robust control techniques and treated for example at the 1992 ACC. /spl mu/ analysis and simulation studies illustrate our design.

Active Front Steering (Part 2): Safety and Functionality

Active Front Steering (AFS) is a newly developed technology for passenger cars that realises an electronically controlled superposition of an angle to the hand steering wheel angle that is prescribed by the driver. It enables functionalities such as (vehicle velocity) variable steering ratio, steering lead, as well as it provides an interface to support vehicle dynamics control systems. This paper focuses on application dependent safety functions and steering assistance functions. All functions described are model based, their accuracy is demonstrated.

Maximum output amplitude of linear systems for certain input constraints

We determine the maximum output amplitude of a system, when the input is bounded by certain constraints. In particular, amplitude and rate of change (i.e. the first derivative) have to be bounded. We show properties of the worst case input and present an algorithm that allows construction of this input and calculates the maximum amplitude of the output. The solution of this problem is a necessary and important step within a couple of recently developed controller-design procedures, dealing with plants with hard-bounded inputs. Nevertheless, it is interesting as a system theoretic task itself and therefore stated separately.

On Model Error Modeling in Set Membership Identification

A recent perspective on model error modeling is applied to set membership identification techniques in order to highlight the separation between unmodeled dynamics and noise. Model validation issues are also easily addressed in the proposed framework. The computation of the minimum noise bound for which a nominal model is not falsified by i/o data, can be used as a rationale for selecting an appropriate model class. Uncertainty is evaluated in terms of the frequency response, so that it can be handled by H∞ control techniques.

Robust Control of Identified Models with Mixed Parametric and Non-Parametric Uncertainties

A framework for identification oriented robust controller design is developed. The model is identified from open-loop i/o-data and contains parametric uncertainties as well as an additive and norm-bounded error. The set of all robustly stabilising controllers, that additionally guarantee robust performance is characterised by a system of second order cones, which can be efficiently solved by interior point algorithms.

Model error concepts in identification for control

We examine some recent methods for system identification, that also deliver non-parametric error bounds, suited for robust controller design. In particular, we look at stochastic embedding, set membership identification and model error modelling. We briefly review the main ideas together with existing computational solutions and present a comparative example.

Active Front Steering for Passenger Cars: System Modelling and Functions

Abstract Active Front Steering is a newly developed technology for passenger cars that realises an electronically controlled superposition of an angle to the hand steering wheel angle that is prescribed by the driver. It enables functionalities such as (vehicle velocity-) variable steering ratio, steering lead, as well as it provides an interface to support vehicle dynamics control systems. This paper focuses on system modelling and derivation of both steering assistance functions and a safety / diagnostics functions. All functions described are model based. Their models are derived and their accuracy is demonstrated.

Loop shaping of multivariable systems with hard constraints on the control signal

Contents A general framework for the design of multivariable control systems subject to hard constraints on each control channel is developed. The design procedure is based on the ℋ∞ loop shaping and relies on the calculation of the maximum possible control amplitude for a class of reference signals, bounded in amplitude and rate. Special attention is given to adjustment of the design weights in order to meet prescribed bounds on each control signal. A simulation example, the control of the vertical dynamics of an aircraft, illustrates the suggested procedure.