Majji, Manoranjan (2009-05). System Identification: Time Varying and Nonlinear Methods. Doctoral Dissertation. Thesis uri icon

abstract

  • Novel methods of system identification are developed in this dissertation. First set of methods are designed to realize time varying linear dynamical system models from input-output experimental data. The preliminary results obtained in a recent paper by the author are extended to establish a new algorithm called the Time Varying Eigensystem Realization Algorithm (TVERA). The central aim of this algorithm is to obtain a linear, time varying, discrete time model sequence of the dynamic system directly from the input-output data. Important results relating to concepts concerning coordinate systems for linear time varying systems are developed (discrete time theory) and an intuitive understanding of equivalent realizations is provided. A procedure to develop first few time step models is detailed, providing a unified solution to the time varying identification problem. The practical problem of identifying the time varying generalized Markov parameters required for TVERA is presented as the next result. In the process, we generalize the classical time invariant input output AutoRegressive model with an eXogenous input (ARX) models to the time varying case and realize an asymptotically stable observer as a byproduct of the calculations. It is further found that the choice of the generalized time varying ARX model (GTV-ARX) can be set to realize a time varying dead beat observer. Methods to use the developed algorithm(s) in this research are then considered for application to the identification of system models that are bilinear in nature. The fact that bilinear plant models become linear for constant inputs is used in the development of an algorithm that generalizes the classical developments of Juang. An intercept problem is considered as a candidate for application of the time varying identification scheme, where departure motion dynamics model sequence is calculated about a nominal trajectory with suboptimal performance owing to the presence of unstructured perturbations. Control application is subsequently demonstrated. The dynamics of a particle in a rotating tube is considered next for identification using the time varying eigensystem realization algorithm. Continuous time bilinear system identification method is demonstrated using the particle example and the identification of an automobile brake model.
  • Novel methods of system identification are developed in this dissertation. First
    set of methods are designed to realize time varying linear dynamical system models from
    input-output experimental data. The preliminary results obtained in a recent paper by the
    author are extended to establish a new algorithm called the Time Varying Eigensystem
    Realization Algorithm (TVERA). The central aim of this algorithm is to obtain a linear,
    time varying, discrete time model sequence of the dynamic system directly from the
    input-output data. Important results relating to concepts concerning coordinate systems
    for linear time varying systems are developed (discrete time theory) and an intuitive
    understanding of equivalent realizations is provided. A procedure to develop first few
    time step models is detailed, providing a unified solution to the time varying
    identification problem.
    The practical problem of identifying the time varying generalized Markov
    parameters required for TVERA is presented as the next result. In the process, we
    generalize the classical time invariant input output AutoRegressive model with an
    eXogenous input (ARX) models to the time varying case and realize an asymptotically stable observer as a byproduct of the calculations. It is further found that the choice of
    the generalized time varying ARX model (GTV-ARX) can be set to realize a time
    varying dead beat observer.
    Methods to use the developed algorithm(s) in this research are then considered
    for application to the identification of system models that are bilinear in nature. The fact
    that bilinear plant models become linear for constant inputs is used in the development
    of an algorithm that generalizes the classical developments of Juang.
    An intercept problem is considered as a candidate for application of the time
    varying identification scheme, where departure motion dynamics model sequence is
    calculated about a nominal trajectory with suboptimal performance owing to the
    presence of unstructured perturbations. Control application is subsequently
    demonstrated.
    The dynamics of a particle in a rotating tube is considered next for identification
    using the time varying eigensystem realization algorithm. Continuous time bilinear
    system identification method is demonstrated using the particle example and the
    identification of an automobile brake model.

publication date

  • May 2009