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  • 1
    Online Resource
    Online Resource
    Hindawi Limited ; 2018
    In:  Mathematical Problems in Engineering Vol. 2018 ( 2018-11-08), p. 1-15
    In: Mathematical Problems in Engineering, Hindawi Limited, Vol. 2018 ( 2018-11-08), p. 1-15
    Abstract: A new methodology for the identification of the values of unknown disturbance signals acting in the input and output measurements of the dynamic linear system is presented. For the solution of this problem, the new idea of the use of two different state observers, which are coworking simultaneously in parallel, was elaborated. Special integral type observers are operating on the same finite time window of the width T and both can reconstruct the exact value of the vector state x(T) on the basis of input-output measurements in this interval [0, T]. If in the input-output signals the disturbances are absent (measurements of I/O signals are perfect) then both observers (although they are different) reconstruct the exact and the same state x(T). However, if in the measurement signals the disturbances are present then these observers will reconstruct the different values of the final states x1(T)=x(T)+e1(T) and x2(T)=x(T)+e2(T). It is because they have different norms and hence they generate different errors in both estimated states. Because of the disturbances, the real state x(T) is unknown, but it is easy to calculate the state difference: x1(T)-x2(T)=e1(T)-e2(T). It occurs that, based on this difference, the values of all the disturbances acting during the control process can be identified. In the paper, the theory of the exact state observation and application of such observers in online mode is recalled. The new methodology for disturbances identification is presented.
    Type of Medium: Online Resource
    ISSN: 1024-123X , 1563-5147
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2018
    detail.hit.zdb_id: 2014442-8
    SSG: 11
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  • 2
    In: Control Engineering Practice, Elsevier BV, Vol. 146 ( 2024-05), p. 105884-
    Type of Medium: Online Resource
    ISSN: 0967-0661
    Language: English
    Publisher: Elsevier BV
    Publication Date: 2024
    detail.hit.zdb_id: 1501351-0
    detail.hit.zdb_id: 1150140-6
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  • 3
    Online Resource
    Online Resource
    Walter de Gruyter GmbH ; 2019
    In:  International Journal of Applied Mathematics and Computer Science Vol. 29, No. 4 ( 2019-12-01), p. 739-757
    In: International Journal of Applied Mathematics and Computer Science, Walter de Gruyter GmbH, Vol. 29, No. 4 ( 2019-12-01), p. 739-757
    Abstract: The paper presents new concepts of the identification method based on modulating functions and exact state observers with its application for identification of a real continuous-time industrial process. The method enables transformation of a system of differential equations into an algebraic one with the same parameters. Then, these parameters can be estimated using the least-squares approach. The main problem is the nonlinearity of the MISO process and its noticeable transport delays. It requires specific modifications to be introduced into the basic identification algorithm. The main goal of the method is to obtain on-line a temporary linear model of the process around the selected operating point, because fast methods for tuning PID controller parameters for such a model are well known. Hence, a special adaptive identification approach with a moving window is proposed, which involves using on-line registered input and output process data. An optimal identification method for a MISO model assuming decomposition to many inner SISO systems is presented. Additionally, a special version of the modulating functions method, in which both model parameters and unknown delays are identified, is tested on real data sets collected from a glass melting installation.
    Type of Medium: Online Resource
    ISSN: 2083-8492
    Language: English
    Publisher: Walter de Gruyter GmbH
    Publication Date: 2019
    detail.hit.zdb_id: 2136386-9
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  • 4
    Online Resource
    Online Resource
    Walter de Gruyter GmbH ; 2016
    In:  International Journal of Applied Mathematics and Computer Science Vol. 26, No. 3 ( 2016-9-1), p. 585-602
    In: International Journal of Applied Mathematics and Computer Science, Walter de Gruyter GmbH, Vol. 26, No. 3 ( 2016-9-1), p. 585-602
    Abstract: The paper presents a new method for diagnosis of a process fault which takes the form of an abrupt change in some real parameter of a time-continuous linear system. The abrupt fault in the process real parameter is reflected in step changes in many parameters of the input/output model as well as in step changes in canonical state variables of the system. Detection of these state changes will enable localization of the faulty parameter in the system. For detecting state changes, a special type of exact state observer will be used. The canonical state will be represented by the derivatives of the measured output signal. Hence the exact state observer will play the role of virtual sensors for reconstruction of the derivatives of the output signal. For designing the exact state observer, the model parameters before and after the moment of fault occurrence must be known. To this end, a special identification method with modulating functions will be used. A novel concept presented in this paper concerns the structure of the observer. It will take the form of a double moving window observer which consists of two signal processing windows, each of width T . These windows are coupled to each other with a common edge. The right-hand side edge of the left-side moving window in the interval [ t − 2 T, t − T ] is connected to the left-hand side edge of the right-side window which operates in the interval [ t − T, t ]. The double observer uses different measurements of input/output signals in both the windows, and for each current time t simultaneously reconstructs two values of the state—the final value of the state in the left-side window z T ( t − T ) and the initial value of the state z 0 ( t − T ) in the right-side window. If the process parameters are constant, the values of both the states on the common joint edge are the same. If an abrupt change (fault) in some parameter at the moment t A = t − T occurs in the system, then step changes in some variables of the canonical state vector will also occur and the difference between the states will be detected. This will enable localization of the faulty parameter in the system.
    Type of Medium: Online Resource
    ISSN: 2083-8492
    Language: English
    Publisher: Walter de Gruyter GmbH
    Publication Date: 2016
    detail.hit.zdb_id: 2136386-9
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  • 5
    Online Resource
    Online Resource
    Walter de Gruyter GmbH ; 2012
    In:  International Journal of Applied Mathematics and Computer Science Vol. 22, No. 2 ( 2012-06-1), p. 379-388
    In: International Journal of Applied Mathematics and Computer Science, Walter de Gruyter GmbH, Vol. 22, No. 2 ( 2012-06-1), p. 379-388
    Abstract: The paper presents two methods used for the identification of Continuous-time Linear Time Invariant (CLTI) systems. In both methods the idea of using modulating functions and a convolution filter is exploited. It enables the proper transformation of a differential equation to an algebraic equation with the same parameters. Possible different normalizations of the model are strictly connected with different parameter constraints which have to be assumed for the nontrivial solution of the optimal identification problem. Different parameter constraints result in different quality of identification. A thorough discussion on the role of parameter constraints in the optimality of system identification is included. For time continuous systems, the Equation Error Method (EEM) is compared with the continuous version of the Output Error Method (OEM), which appears as a special sub-case of the EEM.
    Type of Medium: Online Resource
    ISSN: 1641-876X
    Language: Unknown
    Publisher: Walter de Gruyter GmbH
    Publication Date: 2012
    detail.hit.zdb_id: 2136386-9
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  • 6
    Online Resource
    Online Resource
    University of Applied Sciences in Tarnow, Poland ; 2018
    In:  Science, Technology and Innovation Vol. 3, No. 2 ( 2018-12-27), p. 62-68
    In: Science, Technology and Innovation, University of Applied Sciences in Tarnow, Poland, Vol. 3, No. 2 ( 2018-12-27), p. 62-68
    Abstract: In the paper an overview of state estimators and state observers used in linear systems, will be presented. The state estimators and observers can be used in many applications like the state reconstruction for the control purposes or for the diagnosis and fault detection in technical processes or for the virtual measurements of inaccessible variables of the system as well as for the best filtration of the differential equation solution. As the standard most commonly the Kalman filter and Luenberger type observers are used. Although the Kalman filter guarantees optimal filtering quality of the state, reconstructed from the noisy measurements, both Kalman filter and the Luenberger observer guarantee only asymptotic quality of the real state changes and tracking, basing on the current measurements of the system output and input signals. Unfortunately, the value of the estimation error at any moment of time cannot be calculated. The discussion on differences between continuous and two types of discrete Kalman Filter will be presented. This paper is plan to be the introduction to presentation of the another type of the state observers which have the structure given by the integral operators. Based on measurements of the system output and input signals on some predefined finite time interval, they can reconstruct, after this interval, the observed state exactly.
    Type of Medium: Online Resource
    ISSN: 2544-9125
    Language: English
    Publisher: University of Applied Sciences in Tarnow, Poland
    Publication Date: 2018
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  • 7
    Online Resource
    Online Resource
    University of Applied Sciences in Tarnow, Poland ; 2019
    In:  Science, Technology and Innovation Vol. 5, No. 2 ( 2019-6-30), p. 23-33
    In: Science, Technology and Innovation, University of Applied Sciences in Tarnow, Poland, Vol. 5, No. 2 ( 2019-6-30), p. 23-33
    Abstract: In the paper, the exact state observers will be presented. The state estimators and observers can be used in technical processes for many purposes like the fault detection and diagnosis, the implementation of the state controllers, and soft reconstruction of inaccessible for measurements variables of the system. As the standard, for continuous systems the differential estimators of Kalman filter or Luenberger type observer are commonly used. However, if the initial conditions of the real state are unknown, both estimators guarantee only an asymptotic quality of the real state tracking. The paper presents another type of the state observers, which for continuous system have the structure given by two integral operators. Based on measurements of the system input and output signals on some predefined finite time interval T, they can reconstruct the initial state exactly. In on-line version, the exact state reconstruction is performed continuously for every t, based on special procedure executed within two moving windows of width T, on sliding time interval [t-T, t].
    Type of Medium: Online Resource
    ISSN: 2544-9125
    Language: English
    Publisher: University of Applied Sciences in Tarnow, Poland
    Publication Date: 2019
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  • 8
    Online Resource
    Online Resource
    Elsevier BV ; 1995
    In:  IFAC Proceedings Volumes Vol. 28, No. 10 ( 1995-07), p. 297-302
    In: IFAC Proceedings Volumes, Elsevier BV, Vol. 28, No. 10 ( 1995-07), p. 297-302
    Type of Medium: Online Resource
    ISSN: 1474-6670
    Language: English
    Publisher: Elsevier BV
    Publication Date: 1995
    detail.hit.zdb_id: 2976778-7
    detail.hit.zdb_id: 2839185-8
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  • 9
    Online Resource
    Online Resource
    Elsevier BV ; 2000
    In:  IFAC Proceedings Volumes Vol. 33, No. 15 ( 2000-06), p. 757-762
    In: IFAC Proceedings Volumes, Elsevier BV, Vol. 33, No. 15 ( 2000-06), p. 757-762
    Type of Medium: Online Resource
    ISSN: 1474-6670
    Language: English
    Publisher: Elsevier BV
    Publication Date: 2000
    detail.hit.zdb_id: 2976778-7
    detail.hit.zdb_id: 2839185-8
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  • 10
    Online Resource
    Online Resource
    Elsevier BV ; 1996
    In:  IFAC Proceedings Volumes Vol. 29, No. 1 ( 1996-06), p. 5316-5321
    In: IFAC Proceedings Volumes, Elsevier BV, Vol. 29, No. 1 ( 1996-06), p. 5316-5321
    Type of Medium: Online Resource
    ISSN: 1474-6670
    Language: English
    Publisher: Elsevier BV
    Publication Date: 1996
    detail.hit.zdb_id: 2976778-7
    detail.hit.zdb_id: 2839185-8
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