Control of Zeros and Poles in Problems of Synthesis of Regulation Systems. Part II. Compensation Modal Approach
https://doi.org/10.17587/mau.21.611-621
Abstract
The synthesis problem of linear stationary automatic regulation systems (ARS) with the given indicators of the dynamic quality of regulation processes occupies the important place in the theory and practice of the automatic systems’ construction. The given indicators are connected with the type and parameters of transient characteristics of the regulation systems. The initial requirements for the dynamic quality of ARS it is possible by formalize via the representation of the desired structure and parameters of the transfer function (TF) of the system namely amplification coefficient, zeros and poles. In mechanism of formation of the desired TF which is synthesized by ARS it is necessary to take into account the factor of compensation of zeros and poles of the controlled object. Although they are excluded from TF channel "setpoint — output" of the system, but become the poles of the synthesized system and will inevitably develop its dynamics under external perturbations. The effect of compensation of zeros and poles of the control object in ARS is analyzed in the first part of the article. And also the influence of the factor of non-minimal phase zeros for the dynamics of regulation systems is research. The given effect and its negative results are visually shown in the classical compensation approach to the synthesis of regulators by a priori given (desired, standard) TF of closed ARS. The classical polynomial method of the modal compensators synthesis, the principle deficiency of which is the appearance of uncontrolled ("parasitic") zeros is presented in the second part of the article. The new regulation schemes combining the functional possibilities of the compensation and modal approaches are suggested. Two methods of ASR synthesis with desired poles and zeros of the system, excluding the effect of the appearance of "parasitic" zeros, are discussed and analyzed. In the first method the sequential and parallel correction links (CL) are included into the regulator’s structure. The latter one contains small constant time which generate rapidly damped modes. One may neglected by their influence on the regulation processes. The sequential CL is also used in the second method, but instead of parallel CL modal feedback (MFB) is used. In this case the key value has the invariance property of the zeros of object’s TF when closing its MFB. The possibility of compensating unwanted left zeros of an object that fall within the localization region of fast-fading mode spectra is discussed.
About the Authors
A. B. Filimonov
Moscow Technological University
Russian Federation
Moscow
Russian Federation
Moscow
N. B. Filimonov
Lomonosov Moscow State University
Russian Federation
Moscow
Russian Federation
Moscow
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Review
For citations:
Filimonov A.B., Filimonov N.B. Control of Zeros and Poles in Problems of Synthesis of Regulation Systems. Part II. Compensation Modal Approach. Mekhatronika, Avtomatizatsiya, Upravlenie. 2020;21(11):611-621. (In Russ.) https://doi.org/10.17587/mau.21.611-621
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