Model based fault detection for two-dimensional systems

Fault detection and isolation (FDI) are essential in ensuring safe and reliable operations in industrial systems. Extensive research has been carried out on FDI for one dimensional (1-D) systems, where variables vary only with time. The existing FDI strategies are mainly focussed on 1-D systems and can generally be classified as model based and process history data based methods. In many industrial systems, the state variables change with space and time (e.g., sheet forming, fixed bed reactors, and furnaces). These systems are termed as distributed parameter systems (DPS) or two dimensional (2-D) systems. 2-D systems have been commonly represented by the Roesser Model and the F-M model. Fault detection and isolation for 2-D systems represent a great challenge in both theoretical development and applications and only limited research results are available. In this thesis, model based fault detection strategies for 2-D systems have been investigated based on the F-M and the Roesser models. A dead-beat observer based fault detection has been available for the F-M model. In this work, an observer based fault detection strategy is investigated for systems modelled by the Roesser model. Using the 2-D polynomial matrix technique, a dead-beat observer is developed and the state estimate from the observer is then input to a residual generator to monitor occurrence of faults. An enhanced realization technique is combined to achieve efficient fault detection with reduced computations. Simulation results indicate that the proposed method is effective in detecting faults for systems without disturbances as well as those affected by unknown disturbances.The dead-beat observer based fault detection has been shown to be effective for 2-D systems but strict conditions are required in order for an observer and a residual generator to exist. These strict conditions may not be satisfied for some systems. The effect of process noises are also not considered in the observer based fault detection approaches for 2-D systems. To overcome the disadvantages, 2-D Kalman filter based fault detection algorithms are proposed in the thesis. A recursive 2-D Kalman filter is applied to obtain state estimate minimizing the estimation error variances. Based on the state estimate from the Kalman filter, a residual is generated reflecting fault information. A model is formulated for the relation of the residual with faults over a moving evaluation window. Simulations are performed on two F-M models and results indicate that faults can be detected effectively and efficiently using the Kalman filter based fault detection. In the observer based and Kalman filter based fault detection approaches, the residual signals are used to determine whether a fault occurs. For systems with complicated fault information and/or noises, it is necessary to evaluate the residual signals using statistical techniques. Fault detection of 2-D systems is proposed with the residuals evaluated using dynamic principal component analysis (DPCA). Based on historical data, the reference residuals are first generated using either the observer or the Kalman filter based approach. Based on the residual time-lagged data matrices for the reference data, the principal components are calculated and the threshold value obtained. In online applications, the T2 value of the residual signals are compared with the threshold value to determine fault occurrence. Simulation results show that applying DPCA to evaluation of 2-D residuals is effective.Doctoral These

Relationships between digital signal processing and control and estimation theory

Bibliography: leaves 83-97.NASA Grant NGL-22-009-124 and NSF Grant GK-41647.Alan S. Willsky

Control systems analysis for the Fornasini-Marchesini 2D systems model–progress after four decades

The development of a control systems theory for multidimensional linear systems, i.e. systems with more than one independent variable is an area where a very significant volume of research is based on representations for the underlying dynamics introduced in the 1970s. One of these is the Fornasini-Marchesini state-space model published in 1978. This paper reviews the significant developments in the succeeding four decades in both theory and applications, including examples where this model description is an enabler for the analysis of other classes of systems.</p

Measurements, Models, Systems and Design

531 s.

MODELING OF MHD INSTABILITIES IN EXISTING AND FUTURE FUSION DEVICES IN VIEW OF CONTROL

In questo lavoro viene presentata una versione migliorata del codice CarMa, chiamato CarMa-D, per lo studio di Resistive Wall Modes (RWMs) nei reattori a fusione termonucleare. Tale codice \ue8 in grado di rappresentare accuratamente le strutture conduttrici tridimensionali della macchina, e considerare simultaneamente nel modello gli effetti dovuti alla dinamica del plasma, alla toroidal rotation e agli effetti drift-cinetici. CarMa-D \ue8 il risultato dell\u2019accoppiamento dei codici CARIDDI, per lo studio delle correnti indotte nelle strutture conduttrici, e MARS-K per analisi di stabilit\ue0 MHD nel plasma. Punto di forza della strategia di accoppiamento alla base di CarMa-D \ue8 che non si basa sulle ipotesi semplificative su cui si basa la versione statica di CarMa, ovvero non vengono trascurati la massa del plasma, toroidal rotation e l\u2019effetto del damping cinetico. In questo modo la risposta del plasma a perturbazioni esterne dipende dall\u2019andamento temporale della perturbazione stessa: questo andamento viene approssimato per mezzo di funzioni razionali di Pad\ue9 a coefficienti matriciali. Il passo successivo \ue8 dato dalla combinazione della risposta di plasma approssimata con l\u2019equazione delle correnti indotte nelle strutture passive, per ottenere un modello matematico desctitto come un sistema di equazioni differenziali lineari formalmente uguale alla versione statica di CarMa, ma con un numero maggiori di gradi di libert\ue0 per tener conto della dinamica di plasma. La nuova versione del codice supera le principali limitazioni del modello originale, in particolare: (i) considerando la massa del plasma \ue8 possibile modellare modi con dinamiche molto veloci, come l\u2019external-kink ideale, (ii) il modello \ue8 in grado di tener conto rigorosamente di toroidal rotation e damping cinetico. Questi vantaggi rendono CarMa-D uno strumento potente, in grado di studiare fenomeni macroscopici in cui sia la dinamica del plasma, che gli effetti 3-D delle strutture, sono marcati. Inoltre, il modello matematico risultate \ue8 stato generalizzato per tener conto della simulazione pi\uf9 armoniche toroidali simultaneamente (multi-modal CarMa-D). Il codice \ue8 stato poi testato con successo su un equilibrio di riferimento dato da un plasma a sezione circolare, e successivamente per lo studio di stabilit\ue0 per i modi n = 1 e n = 2 su JT-60SA, Scenario 5. Infine, si \ue8 dimostrato come il modello matematico di CarMa-D possa essere scritto in una formulazione state-space, in vista di un successivo impiego nella progettazione di un controllo in retoazione per la stabilizzazione attiva dei RWMs