Problems of designing state feedback controllers for objects with transfer function zeros

• Autorzy: Drozdov V. , Abdullin A. , Mamatov A.

Identyfikatory

DOI

10.5277/PED170203

• Języki publikacji: EN

Abstrakty

EN

The analysis of the influence of transfer function zeros on the parameters of state feedback controllers has been conducted. If a transfer function of a control object has zeros which are located closely to poles, the control object tends to singularity, and the influence of the input control signal to the states of the control object becomes weaker. The problem of the state feedback controller synthesis becomes ill-conditioned, which leads to the appearance of extremely large state feedback coefficients. In this case, the state feedback coefficients are sensitive to the parameters of the control object. As a result, the parametric robustness of the control system is reduced. Known methods of structural analysis of control object models are included amongst different methods of the numerical evaluation of the controllability and the observability, as well as methods of the model order reduction. These methods have some disadvantages, such as dependence on the state space representation form of the control object, ignoring a part of the control object model. In this paper, some ways of the preliminary structural analysis of the state space models of control objects have been proposed. The singular (Hankel) matrix is proposed for analyzing the properties of control object models. The singular matrix is the invariant characteristic of the control object in various state space forms and it characterizes the property of the control object completeness. As a result of the research, it was found that the coefficients of the state feedback controller are inversely proportional to the determinant of the singular matrix, and the determinant of the singular matrix is equal to the resultant of the transfer function polynomials. Thus the value of the determinant of the singular matrix depends on the location of the zeros of the transfer function. The method of the structural transformation (decomposition) of the control object for the defining the need of the reducing the order of the control object model is proposed.

Słowa kluczowe

EN

zeros of a transfer function; observability; controllability; Hankel matrix; state feedback controller; resultant; residues

• Wydawca: De Gruyter
• Czasopismo: Power Electronics and Drives
• Rocznik: 2017
• Tom: Vol. 2 (37), No. 2
• Strony: 77--92
• Opis fizyczny: Bibliogr. 22 poz., rys.

Twórcy

autor

Drozdov V.

• ITMO University, Kronverkskiy pr., 49, 197101 St. Petersburg, Russia

autor

Abdullin A.

• ITMO University, Kronverkskiy pr., 49, 197101 St. Petersburg, Russia

autor

Mamatov A.

• ITMO University, Kronverkskiy pr., 49, 197101 St. Petersburg, Russia

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).