- PII
- 10.31857/S0374064125010104-1
- DOI
- 10.31857/S0374064125010104
- Publication type
- Status
- Published
- Authors
- Volume/ Edition
- Volume 61 / Issue number 1
- Pages
- 133-138
- Abstract
- In this paper we solve the problem of assigning the desired characteristic polynomial of a linear stationary dynamic system with one input and output dynamic feedback in the form of a first-order dynamic compensator. Necessary and sufficient conditions for the existence of the solution of the problem are considered. An explicit formula for the compensator parameters, analogous to the Bass–Gura formula for a state feedback system, is derived.
- Keywords
- линейная система обратная связь по выходу формула Басса–Гура
- Date of publication
- 18.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 10
References
- 1. Datta, B. Numerical Methods for Linear Control Systems / B. Datta. — Boston : Elsevier Academic Press, 2004. — 640 p.
- 2. Лапин, А.В. Обобщение формулы Аккермана для некоторого класса многомерных динамических систем с векторным входом / А.В. Лапин, Н.Е. Зубов, А.В. Пролетарский // Вестн. МГТУ им. Н.Э. Баумана. Сер. Естеств. науки. — 2023. — № 4. — С. 18–38.
- 3. Lapin, A.V., Zubov, N.E., and Proletarskii, A.V., Generalization of ackermann formula for a certain class of multidimensional dynamic systems with vector input, Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2023, vol. 109, no. 4, pp. 18–38.
- 4. Lapin, A.V. Generalization of Bass–Gura formula for linear dynamic systems with vector control / A.V. Lapin, N.E. Zubov // Herald of the Bauman Moscow State Technical University, Series Natural Sciences. — 2020. — V. 89, № 2. — P. 41–64.
- 5. Буков, В.Н. Анализ и синтез матричных линейных систем. Сравнение подходов / В.Н. Буков, С.В. Горюнов, В.Н. Рябченко // Автоматика и телемеханика. — 2000. — № 11. — С. 3–43.
- 6. Bukov, V.N., Goryunov, S.V., and Ryabchenko, V.N., Matrix linear systems: a comparative review of the approaches to their analysis and synthesis, Automation and Remote Control, 2000, vol. 61 (1), no. 11, pp. 1759–1795.
- 7. Brash, F.M. Pole placement using dynamic compensators / F.M. Brash, J.B. Pearson // IEEE Trans. Automat. Contr. — 1970. — V. AC-15. — P. 34–43.
- 8. Bernstein, D.S. Matrix Mathematics: Theory, Facts, and Formulas / D.S. Bernstein. — Second Ed. — Princeton Univ. Press, 2009. — 1184 p.
- 9. Гантмахер, Ф.Р. Теория матриц / Ф.Р. Гантмахер. — 5-е изд. — М. : Физматлит, 2010. — 560 c.
- 10. Gantmacher, F.R., The Theory of Matrices, American Mathematical Society, 1998.