Arne Wahrburg

Partial-state synchronization of linear heterogeneous multi-agent systems

This article is devoted to the synchronization of heterogeneous, and hence non-identical, linear systems. The proposed solution results in a fully distributed control law solely relying on local measurements. In order to achieve this, it is shown that the problem can be decomposed into three sub-problems: First, the synchronization of identical exosystems provides a feasible trajectory which turns out to be the synchronization manifold. Second, a decentralized observer is proposed for estimating the absolute state based on the local measurements performed. Third, this estimate is used to derive a tracking control law, based on the full information output regulation problem, to follow the generated exosystem reference. The concept is illustrated by an example.

Parametric design of robust fault isolation observers for linear non-square systems

Abstract In this article, two different approaches to design fault isolation observers (FIOs) for linear systems are developed. They extend the existing results to arbitrary fault detectability indices and allow to isolate simultaneously occurring actuator and sensor faults by employing only a single, specifically parameterized observer. While the presented parametric eigenstructure assignment approach gives a comprehensive interpretation of the degrees of freedom arising in non-square systems with additional sensors, the time-domain solution proves to be well suited for optimizing disturbance rejection. Furthermore, this paper presents an approach to optimize the robustness of FIOs with respect to disturbances in finite frequency ranges. This enables to reduce conservatism if knowledge of relevant disturbance frequencies is available.

Robust fault isolation observers for non-square systems - a parametric approach

Abstract In this article, a linear matrix inequality (LMI)-based design for robust fault isolation observers (FIOs) for linear systems with arbitrary fault detectability indices is presented. A parametric design is used to achieve stable fault isolation in square systems as well as non-square systems. Based on this design, the influence of arbitrary disturbances is attenuated by a proper optimization of the observer gain matrices. The applicability of the proposed design is verified in simulations of a helicopter model.

Robust observer-based fault detection and isolation in the standard control problem framework

Abstract This paper deals with the design of robust fault detection and isolation observers where only a single observer is employed to isolate different faults. To this end, the problem of parameterizing such observers is shown to be equivalent to designing a structurally constrained controller in the standard control problem framework. Thereby, the problem is reformulated as a well known classical control problem, which enables the use of existing tools to optimize robustness with respect to arbitrary exogenous disturbances. To account for parametric uncertainties, an approximate model matching approach is used.

Consideration of Gyroscopic Effect in Fault Detection and Isolation for Unbalance Excited Rotor Systems

Fault detection and isolation (FDI) in rotor systems often faces the problem that the system dynamics is dependent on the rotor rotary frequency because of the gyroscopic effect. In unbalance excited rotor systems, the continuously distributed unbalances are hard to be determined or estimated accurately. The unbalance forces as disturbances make fault detection more complicated. The aim of this paper is to develop linear time invariant (LTI) FDI methods (i.e., with constant parameters) for rotor systems under consideration of gyroscopic effect and disturbances. Two approaches to describe the gyroscopic effect, that is, as unknown inputs and as model uncertainties, are investigated. Based on these two approaches, FDI methods are developed and the results are compared regarding the resulting FDI performances. Results are obtained by the application in a rotor test rig. Restrictions for the application of these methods are discussed.

Observer-based fault isolation for statically non-isolable linear systems

This contribution deals with the design of fault isolation observers (FIOs). Their purpose is to detect and isolate faults acting on linear systems by means of only a single observer. While parameterizations for such observers have been proposed for statically isolable systems, we generalize the existing results to linear systems without the restriction of a non-singular fault detectability matrix. To achieve fault isolation in such systems, we introduce virtual system extensions, which enable stable isolation. These virtual augmentations are then realized by dynamically extended fault isolation observers (DFIOs). Apart from that the proposed design allows to isolate both actuator and sensor faults.

Robust fault isolation using dynamically extended observers

In this paper we propose a new method to design robust fault isolation observers (FIOs). The technique exploits the duality between non-interacting control and observer-based fault isolation and provides additional degrees of freedom by means of dynamically extended observers. A general procedure to design such observers is given. The additional design variables are then exploited to increase robustness with respect to high-frequency disturbances while ensuring fast fault response times. The applicability of the proposed method is demonstrated in simulations.

Fault isolation for linear non-minimum phase systems using dynamically extended observers

This article is devoted to the design of fault isolation observers (FIOs). Their purpose is to detect and isolate faults occuring in linear systems by means of only a single, specifically parameterized observer. While parameterizations for such observers have been proposed for minimum phase systems, we generalize the existing results to linear systems without such restrictions. To achieve stable fault isolation, we introduce virtual system extensions, which enable stable isolation despite right half-plane zeros. These virtual augmentations are then realized by dynamically extended fault isolation observers (DFIOs). Apart from that, the proposed design allows to isolate both actuator and sensor faults. The applicability of the proposed approach is shown in both simulations and lab experiments with a gantry crane.

On robust fault-isolation observers with relaxed structural constraints

This article is devoted to observer-based fault isolation in linear, time-invariant systems. In contrast to most existing results, fault isolation is achieved by only a single, specifically parameterized observer, yielding a low order fault isolation system. The design is based on eigenstructure assignment methods. By relaxing the structural constraints imposed to the observer eigenstructure, additional degrees of freedom are obtained. These are employed to increase robustness of the fault isolation observer with respect to exogenous disturbances by means of convex optimization problems. The results are verified by simulations of an example system.

Robust partial fault isolation for linear systems using observers

This paper deals with observer-based fault isolation in linear systems. Only a single observer is implemented to achieve fault isolation, which results in a small implementation effort. If it is known that not all potential faults can occur at the same time, it suffices to achieve partial instead of full fault isolation. In this paper we show how existing methods for full fault isolation can be extended to partial fault isolation based on a parametric eigenstructure assignment approach and elaborate on the arising degrees of freedom. Furthermore we show that under a certain condition there is a simple (bi-)linear relationship between the observer parameterizations for full and partial fault isolation. This gives rise to an efficient algorithm optimizing robustness of partial fault isolation observers with respect to disturbances. The method is successfully applied in both simulations and a lab experiment with a gantry crane.