Reduction of linear dynamic systems using generalized approach of pole clustering method

A new model order abatement method based on the clustering of poles and zeros of a large-scale continuous time system is proposed. The clustering of poles and zeros are used for finding the cluster centres. The abated model is identified from the cluster centres, which reflect the effectiveness of the dominant poles of the clusters. The cluster centre is determined by taking [Formula: see text] root of the sum of the inverse of [Formula: see text] power of poles (zeros) in a particular cluster. It is famous that the magnitude of the pole cluster centre plays an important role in the clustering technique for the simplification of large-scale systems. The magnitude of the cluster centres computed by the modified pole clustering method or some other methods based on the pole clustering techniques is large as compared to the proposed technique. The less magnitude of pole cluster centre reflects the better approximations and proper matching of the abated model with the original system. Therefore, the proposed method offers better approximations matching between actual and abated systems during the transient period compared to some other clustering methods, which supports the replacement of large-scale systems by proposed abated systems. The proposed technique is a generalized version of the standard pole clustering technique. The proposed method guarantees the retention of dominant poles, stability and other fundamental control properties of the actual plant in the abated model. The proposed algorithm is illustrated by the five standard systems taken from the literature. The accuracy and effectiveness of the proposed method are verified by comparing the time responses and various performance error indices.

Virtual Sensors in the Fault Diagnosis Problem

The paper is devoted to the problem of fault diagnosis (isolation and identification) in linear dynamic systems under disturbances. The performances of fault diagnosis depend on the sensors which are in the system under diagnosis. To improve the performances, additional sensors can be applied. But sometimes it is impossible to use such sensors; besides they have low reliability. In this paper, we suggest to use so-called virtual sensors instead of additional ones. To obtain such sensors,Luenberger observers can be used. Such an observer is designed in two steps. On the first step, the model of minimal dimension invariant with respect to the disturbances and estimating a predetermined component of the system state vector and some other components of the system state vector is designed. The second components are necessary to provide stability of the observer by means of generating residual and using feedback. Such components are determined during t he process of the problem solution which is based on the canonical form of matrices describing the model. On the second step, the feedback matrix is found based on the required quality of transient. To obtain this matrix, eigenvalues are selected and coefficients of the characteristic equation are calculated. The rule to find the predetermined component of the system state vector to be estimated by vir tual obser ver is suggested. Theoretical results are illustrated by practical example of well known three tank system.

On the Uncertainty Identification for Linear Dynamic Systems Using Stochastic Embedding Approach with Gaussian Mixture Models

In control and monitoring of manufacturing processes, it is key to understand model uncertainty in order to achieve the required levels of consistency, quality, and economy, among others. In aerospace applications, models need to be very precise and able to describe the entire dynamics of an aircraft. In addition, the complexity of modern real systems has turned deterministic models impractical, since they cannot adequately represent the behavior of disturbances in sensors and actuators, and tool and machine wear, to name a few. Thus, it is necessary to deal with model uncertainties in the dynamics of the plant by incorporating a stochastic behavior. These uncertainties could also affect the effectiveness of fault diagnosis methodologies used to increment the safety and reliability in real-world systems. Determining suitable dynamic system models of real processes is essential to obtain effective process control strategies and accurate fault detection and diagnosis methodologies that deliver good performance. In this paper, a maximum likelihood estimation algorithm for the uncertainty modeling in linear dynamic systems is developed utilizing a stochastic embedding approach. In this approach, system uncertainties are accounted for as a stochastic error term in a transfer function. In this paper, we model the error-model probability density function as a finite Gaussian mixture model. For the estimation of the nominal model and the probability density function of the parameters of the error-model, we develop an iterative algorithm based on the Expectation-Maximization algorithm using the data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.