The stabilization problem the flow parameters of the production line
Creators
- 1. National Technical University "Kharkiv Polytechnic Institute", Kharkiv, Ukraine
- 2. V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
Description
The problem of designing a system for optimal control of random deviations of flow parameters of a production line from the planned value is considered. The PDE-model of the production line was used as a foundation for the development of an algorithm for optimal control of the parameters production line. The method of Lyapunov functions was used to construct a system of operational control of flow parameters of production lines. The problem of stabilization of the value flow parameters of the production line (the task of operational control of the flow production) is formulated. The equations for the production line parameters in small disturbances are obtained. To assess the technological resources of the production system, which spent on the formation of control actions, the integral of the production line quality was introduced, the minimum value of which corresponds to the rapid damping of the flow parameters disturbance. Taking into account the specified quality criterion, the Lyapunov function of the production line is determined. Control actions are found that ensure the asymptotic stability of a given planned state of the production line flow parameters for a steady and transient mode of operation.
Files
The_stabilization_problem.pdf
Files
(295.6 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:f7dc503e9f69b0d35f0cefee6b5e329a
|
295.6 kB | Preview Download |
Additional details
References
- 1. Shkurba V.V. Discrete production planning in an automated control system. / V.V.Shkurba et al. - Kiev: Technics, 1975. - P. 296
- 2. Kempf K. Optimization models for production planning. Planning Production and Inventories in the Extended Enterprise: A State of the Art Handbook. / K.Kempf, P.Keskinocak, R.Uzsoy –Springer-Verlag, New York, 2010. – P. 587
- 3. Hopp W.J. Factory Physics: Foundations of Manufacturing Management. / W. J. Hopp, M.L. Spearman. – Irwin/McGraw-Hill, Boston, 2001. – P. 698. https://doi.org/10.1080/15320370108500206
- 4. Sinitsa L.M. Organization of production. / L.M. Tit. - Minsk: UP IVC Minfin, 2003. –C. 512
- 5. Korobetsky Yu.P. Simulation models in flexible systems. / Yu.P. Korobetsky, S.K. Ramazanov. - Lugansk: Ed. VNU, 2003. - P. 280
- 6. Pihnastyi O.M. Statistical theory of control systems of the flow production / O.M. Pihnastyi. –LAP LAMBERT Academic Publishing. –2018. - 436 p. –ISBN: 978-613-9-95512-1
- 7. Berg R. Partial differential equations in modelling and control of manufacturing systems/ R.Berg. –Netherlands, Eindhoven Univ. Technol., 2004. –P. 157
- 8. Pihnastyi O.M. Questions of stability of macroscopic parameters of technological processes of mass production / V.P. Demutskiy, O.M.Pihnastyi // Reports of the National Academy of Sciences of Ukraine. –Kiev: Publishing House "Academperiodika". - 2006. –№ 3. –С. 63-67
- 9. Malkin I.G. The theory of stability of motion / I.G. Malkin. - Moscow: Nauka, 1966 .-- P. 531.
- 10. Lyapunov A.M. General problem of motion stability / A.M. Lyapunov. - M .: Gostekhizdat, 1950 .-- P. 395