(Differencialnie Uravnenia i Protsesy Upravlenia)

About
History
Editorial Page
Addresses
Scope
Editorial Staff
Submission Review
For Authors
Publication Ethics
Issues
Русская версия

**Nikolay Evgenievich Zubov**

Dr. Sci. (Eng.), Professor

Professor of Dep. “Automatic Control Systems”, Dean of “Rocket and Space Techniques” faculty at Bauman MSTU

(Russia, 105005, Moscow, 2-nd Bauman Street, Building 5)

**Alexey Vladimirovich Lapin**

Cand. Sci. (Eng.)

Senior Lecturer of Dep. “Automatic Control Systems” at Bauman MSTU

(Russia, 105005, Moscow, 2-nd Bauman Street, Building 5)

**Vladimir Nikolaevich Ryabchenko**

Dr. Sci. (Eng.), Associate Professor

Senior Technologist of JSC “RDC at FGC of UES”

(Russia, 115201, Moscow, Kashirskoe highway, House 22, Building 3)

Professor of Dep. “Automatic Control Systems” at Bauman MSTU

(Russia, 105005, Moscow, 2-nd Bauman Street, House 5)

We consider a task of providing the modal controllability by output vector in linear dynamic systems at not completely measured vector of state applying decomposition method of control synthesis based on Van der Woude approach. It is typical that at meeting the condition «dimension of vector of control plus dimension of vector of observe is more than dimension of object of control» modal controllability of closed-loop system as a whole is provided not for all possible types of matrices with desirable spectrum which are assigned or calculated within decomposition of multi-dimension systems. It is shown that modal controllability by output is determined by whether a matrix with whatever desirable spectrum at zero level exists, which provides a solvability of linear matrix equation of relation between matrices of controllers by state and by output. We offer keeping the desirable spectra to set specified matrices in triangular form or to calculate them basing on equations formed in a certain way. At such approach modal controllability by output is provided regardless of ratios between the parameters of system and spectra at top levels of decomposition and calculation of matrices with desirable spectra is simplified at bottom levels. An example of applying the described approach is given at synthesis of controller by output for linear stationary automatic control system of 6th order containing 3 control inputs and 4 measured outputs. The results of mathematical simulation confirm the feasibility of application of suggested approaches.

- control by output vector
- decomposition method of modal control
- feedback
- matrix with desirable spectrum
- modal controllability

- Leonov, G. A. and Shumafov, M. M. Metody stabilizatsii lineynykh upravlyaemykh sistem [Methods of stabilization of linear controllable systems]. St. Petersburg, St. Petersburg Univ. Press, 2005. (In Russian)
- Gadjiev, M. G. and Misrikhanov, M. Sh., Ryabchenko V. N., Sharov Yu. V. Matrichnye metody analiza I upravleniya perekhodnymi protsessami v electroenergeticheskikh sistemakh [Matrix methods of analysis and control of transients in electric power systems]. Moscow, MPEI Publ. House, 2019. (In Russian)
- Zubov, N. E., Zybin, E. Y., Mikrin, E. A., Misrikhanov, M. Sh., Proletarskii, A. V. and Ryabchenko, V. N., “Output Control of a Spacecraft Motion Spectrum, ” J. Comput. Syst. Sci. Int., vol. 53, iss. 4, pp. 576 - 586, 2014. DOI: 10. 1134/S1064230714040170
- Zubov, N. E., Lapin, A. V., Mikrin, E. A. and Ryabchenko, V. N., “Output Control of the Spectrum of a Linear Dynamic System in Terms of the Van der Woude Method, ” Doklady Mathematics, vol. 96, iss. 2, pp. 457 - 460, 2017. DOI: 10. 1134/S1064562417050179
- Zubov, N. E., Mikrin, E. A. and Ryabchenko, V. N. Matrichnye metody v teorii i praktike sistem avtomaticheskogo upravleniya letatel’nykh apparatov [Matrix methods in theory and practice of flying vehicles automatic control systems]. Moscow, Bauman MSTU Publ., 2016. 666 p. (In Russian)
- Zubov, N. E., Ryabchenko, V. N., Mikrin, E. A. and Misrikhanov, M. Sh., “Output Control of the Spectrum of a Descriptor Dynamical System, ” Doklady Mathematics, vol. 93, iss. 3, pp. 259 - 261, 2016. DOI: 10. 1134/S106456241603008X
- Zubov, N. E., Mikrin, E. A., Misrikhanov, M. Sh. and Ryabchenko, V. N., “Stabilization of Coupled Motions of an Aircraft in the Pitch-Yaw Channels in the Absence of Information about the Sliding Angle: Analytical Synthesis, ” J. Comput. Syst. Sci. Int., vol. 54, iss. 1, pp. 93 - 103, 2015. DOI: 10. 1134/S1064230715010153
- Zubov, N. E., Mikrin, E. A., Misrikhanov, M. Sh. and Ryabchenko, V. N., “Output control of the Longitudinal Motion of a Flying Vehicle, ” J. Comput. Syst. Sci. Int., vol. 54, iss. 5, pp. 825 - 837, 2015. DOI: 10. 1134/S1064230715040140
- Zubov, N. E., Mikrin, E. A., Ryabchenko, V. N. and Fomichev, A. V., “Synthesis of Control Laws for Aircraft Lateral Motion at the Lack of Data on the Slip Angle: Analytical Solution, ” Russian Aeronautics, vol. 60, iss. 1, pp. 64 - 73, 2017. DOI: 10. 3103/S106879981701010X
- Zubov, N. E., Mikrin, E. A., Ryabchenko, V. N. and Proletarskii, A. V., “Analytical Synthesis of Control Laws for Lateral Motion of Aircraft, ” Russian Aeronautics, vol. 58, iss. 3, pp. 263 - 270, 2015. DOI: 10. 3103/S1068799815030034
- Zubov, N. E., Vorob’eva, E. A., Mikrin, E. A., Misrikhanov, M. Sh., Ryabchenko, V. N. and Timakov, S. N., “Synthesis of Stabilizing Spacecraft Control Based on Generalized Ackermann’s Formula, ” J. Comput. Syst. Sci. Int., vol. 50, iss. 1, pp. 93 - 103, 2011. DOI: 10. 1134/S1064230711010199
- Mikrin, E. A., Zubov, N. E., Lapin, A. V. and Ryabchenko, V. N. Analiticheskaya formula vychisleniya regulyatora dlya lineinoi SIMO-sistemy [Analytical formula of calculating a controller for linear SIMO-system] // Differencialnie Uravnenia i Protsesy Upravlenia, No. 1, pp. 1 - 11, 2020. (In Russian)