The article presents algorithms for the synthesis of an optimal control system for
dynamic objects. As a model, we consider a differential equation of a continuous one-dimensional
system in the form of a state space, which has the properties of controllability and observability. The
paper shows the need to use an observation device in order to assess how the properties of the controlled
system change with the slightest change in the parameters of the control object, to assess the sensitivity
of the system to these changes. When finding a solution to the equation formulated to find the parameters
of the control law, computational difficulties arise due to the fact that the system of equations is, as a
rule, ill-conditioned. Considering the ill-posedness of the problem under consideration, regular
procedures were used. The above algorithms make it possible to synthesize a stable control system with
an optimal feedback gain.
The article presents algorithms for the synthesis of an optimal control system for
dynamic objects. As a model, we consider a differential equation of a continuous one-dimensional
system in the form of a state space, which has the properties of controllability and observability. The
paper shows the need to use an observation device in order to assess how the properties of the controlled
system change with the slightest change in the parameters of the control object, to assess the sensitivity
of the system to these changes. When finding a solution to the equation formulated to find the parameters
of the control law, computational difficulties arise due to the fact that the system of equations is, as a
rule, ill-conditioned. Considering the ill-posedness of the problem under consideration, regular
procedures were used. The above algorithms make it possible to synthesize a stable control system with
an optimal feedback gain.
| № | Имя автора | Должность | Наименование организации |
|---|---|---|---|
| 1 | Mamirov U.F. | DSc, Associate professor | Tashkent State Technical University |
| 2 | Igamberdiyev K.Z. | DSc, professor, academician | Tashkent State Technical University |
| 3 | Khankeldiyeva .K. | Assistant | Bukhara engineering - technological institute |
| № | Название ссылки |
|---|---|
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| 2 | 5. Afanasyev V.N.: Theory of optimal control of continuous dynamic systems. Moscow, Publishing House of the Faculty of Physics of Moscow State University, 2011. 168 p. 6. Egupov N.D., Pupkov K.A. Methods of classical and modern theory of automatic control. Textbook in 5 volumes. Moscow, Publishing house of MSTU named after N.E. Bauman, 2004. 7. Mita, T., Pang, B.C., & Liu, K.Z. “Design of optimal strongly stable digital control systems and application to output feedback control of mechanical systems”, International Journal of Control, 45(6), 2071- 2082. 1987. https://doi.org/10.1080/00207178708933868 |
| 3 | 8. Igamberdiev Kh.Z., Yusupbekov A.N., Zaripov O.O.: Regular methods for assessing and managing dynamic objects under conditions of uncertainty. Tashkent, Tashkent State Technical University, 2012. 320 p. 9. Igamberdiev Kh.Z., Sevinov J.U., Zaripov O.O.: Regular methods and algorithms for the synthesis of adaptive control systems with customizable models. Tashkent, Tashkent State Technical University, 2014. 10. Tikhonov A.N., Arsenin V.Ya.: Methods for solving ill-posed problems, Moscow, Nauka, 1986. 288 p. 11. Tikhonov A.N., Goncharsky A.V., Stepanov V.V., Yagola A.G.: Numerical methods for solving illposed problems, Moscow, Nauka, 1990. 12. Tikhonov A.N., Goncharsky A.V.: Ill-posed problems in natural science. Moscow, Moscow University Publishing House, 1987. 299 p. |
| 4 | 13. Mamirov U.F.: Regular synthesis of adaptive control systems for uncertain dynamic objects. Tashkent, Knowledge and intellectual potential, 2021. 215 p. 14. Mamirov U.F. “Sustainable Algorithms For Synthesis Of Regulators In Adaptive Control Systems Of Parametrically Uncertain Objects”, J. Chemical Technology, Control and Management, 2019 (4), PP. 126- 132. https://doi.org/10.34920/2019.3.126-13 |