Modal Interval Analysis Research Articles

Fault detection and isolation of the three-tank system using the modal interval analysis

Analytical redundancy is a widely used technique for fault detection. It consists of comparing the behaviour of a real system with a reference obtained by simulation of its model. The main problem is that there are always imprecisions and uncertainties which are not represented in the model so the behaviour of the real system and the behaviour of the model are not exactly the same. One way to represent these uncertainties in the model is using interval models. The results of the simulation of these types of models may be represented by envelopes. This paper proposes an approach to generate envelopes based on interval techniques of the modal interval analysis. As an example, this approach is used to detect and isolate faults in a physical system formed by three interconnected tanks.

Application of Modal Intervals to the Generation of Error-Bounded Envelopes

An interval model can express the imprecision and the uncertainty associated to the modeling of a system. The result of the simulation of one of these models can be represented in the form of envelope trajectories. These envelopes can be characterized by several properties such as completeness or soundness, that lead to the concepts of overbounded and underbounded envelopes. The simulation of such interval models can be performed by several means including qualitative, semiqualitative and quantitative methods. A brief description of the different types of simulators is presented and their respective properties are outlined and compared in relation to model-based fault detection. Whereas the existing simulators do not provide any information about the "error" with respect to the exact envelope, a method to obtain error-bounded envelopes is proposed. It is based on the simultaneous computation of an underbounded and an overbounded envelope by means of Modal Interval Analysis. A way of controlling the error of the envelopes and adjusting it to a desired specified value is presented.

Analysis of the Robustness of Predictive Controllers via Modal Intervals

This paper aims to start exploring the application of interval techniques to deal with robustness issues in the context of predictive control. The robust stability problem is transformed into that of checking the positivity of a rational function. Modal intervals are presented as a useful tool to deal with this kind of function. Modal interval analysis extends real numbers to intervals, identifying the intervals by the predicates that the real numbers fulfill, unlike classical interval analysis which identifies the intervals with the set of real numbers that they contain. Modal interval analysis not only simplifies the computation of interval functions but also allows semantic interpretations of the results. These interpretations are applied to the analysis and design of robust predictive controllers for parametric systems. Necessary, sufficient and, in some cases, necessary and sufficient conditions for robust performance are presented. Specifically, an interval procedure is proposed to compute the stability margin of a predictive control law when applied to a class of plants described by discrete time transfer functions with coefficients that depend polynomially on uncertain parameters.

Semiqualitative Simulation Using Modal Interval Analysis

Imprecision and uncertainty in systems can often be expressed with interval models. The result of the simulation of these models can be represented in the form of envelope trajectories. These envelopes can be characterised by several properties such as completeness and soundness which lead to the concept of overbounded and underbounded envelopes. Simulation of such interval models can be performed by several means including quantitative, qualitative and semiqualitative techniques. Whereas existing simulators do not provide any information about the “error” with respect to the exact envelope, a method to obtain error-known envelopes is proposed. It is based on the simultaneous computation of an underbounded and an overbounded envelope. Both envelopes are computed by means of Modal Interval Analysis. A way of controlling the error of the envelopes and adjust it to the desired value is presented.