On One Approach to Analytic Synthesis of Modal Control by Output for Fourth-Order Dynamic Systems with Two Inputs and Two Outputs

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Abstract

The problem of modal control by output for a fourth-order dynamic system with two control inputs and two measured outputs is considered, provided that the controllability index is not equal to the observability index. It is shown that this problem is solvable, despite the fact that the total dimension of the input and output vectors does not exceed the dimension of the state vector. Compact analytic solutions to this problem using matrix zero-divisors and solvability conditions of one-sided linear matrix equations are proposed. Theorems are proved that implement direct (control) and dual (observation) approaches to solving the problem for cases when the controllability index is correspondingly greater and less than the observability index. Examples are given confirming the efficiency of each approach.

About the authors

N. E. Zubov

Bauman Moscow State Technical University

Author for correspondence.
Email: nik.zubov@gmail.com
Russian Federation, Moscow

A. V. Lapin

Bauman Moscow State Technical University

Email: nik.zubov@gmail.com
Russian Federation, Moscow

References

  1. Zubov N.E., Mikrin E.A., Ryabchenko V.N. Controlling a Linear MIMO-System by a Measurement Vector Using Multilevel Decomposition // J. Comput. Syst. Sci. Int. 2020. V. 59. Iss. 2. P. 151–160. https://doi.org/:10.1134/S1064230720020136
  2. Zubov N.E., Mikrin E.A., Ryabchenko V.N., Fomichev A.V. Synthesis of Control Laws for Aircraft Lateral Motion at the Lack of Data on the Slip Angle: Analytical Solution // Russian Aeronautics. 2017. V. 60. Iss. 1. P. 64–73. https://doi.org/:10.3103/S106879981701010X
  3. Zubov N.E., Ryabchenko V.N., Sorokin I.V. Output Control of the Longitudinal Motion Spectrum of a Single-Rotor Helicopter // Russian Aeronautics. 2020. V. 63. Iss. 2. P. 249–259. https://doi.org/:10.3103/S1068799820030319
  4. Zubov N.E., Mikrin E.A., Oleynik A.S., Ryabchenko V.N., Efanov D.E. The Spacecraft Angular Velocity Estimation in the Orbital Stabilization Mode by the Results of the Local Vertical Sensor Measurements // Herald of the Bauman Moscow State Technical University, Series Instrument Engineering. 2014. Iss. 5. P. 3–13.
  5. Van der Woude J.W. A Note on Pole Placement by Static Output Feedback for Single-Input Systems // Systems & Control Letters. 1988. V. 11. Iss. 4. P. 285–287. https://doi.org/:10.1016/0167-6911(88)90072-2
  6. Zubov N.E., Zybin E.Y., Mikrin E.A., Misrikhanov M.Sh., Proletarskii A.V., Ryabchenko V.N. Output Control of a Spacecraft Motion Spectrum // J. Comput. Syst. Sci. Int. 2014. V. 53. Iss. 4. P. 576–586. https://doi.org/:10.1134/S1064230714040170
  7. Lapin A.V., Zubov N.E. Parametric Synthesis of Modal Control with Output Feedback for Descent Module Attitude Stabilization // Int. Russian Autom. Conf. 2019. P. 1–6. https://doi.org/:10.1109/RusAutoCon.2019.8867744
  8. Zubov N.E., Lapin A.V., Mikrin E.A., Ryabchenko V.N. Output Control of the Spectrum of a Linear Dynamic System in Terms of the Van der Woude Method // Doklady Mathematics. 2017. V. 96. Iss. 2. P. 457–460. https://doi.org/:10.1134/S1064562417050179
  9. Zubov N.E., Lapin A.V. Reducing the Problem of the Modal Control by Output for Stationary Forth-Order Systems with Two Inputs and Two Outputs to the Control by State for a System with a Single Input // J. Comput. Syst. Sci. Int. 2023. V. 62. Iss. 1. P. 43–60. https://doi.org/:10.1134/S1064230723010124
  10. Zubov N.E., Zybin E.Yu., Lapin A.V. Analytical Synthesis of an Aircraft’s Lateral Motion Control by Output at the Lack of Measurements of Slip and Roll Angles // J. Comput. Syst. Sci. Int. 2023. V. 62. Iss. 2. P. 354–361. https://doi.org/:10.1134/S1064230723020193
  11. Gantmacher F.R. The Theory of Matrices. Providence: AMS Chelsea Publishing, 2000.
  12. Ryabchenko V.N., Zubov N.E., Sorokin I.V., Proletarskii A.V. Complete Pole Placement Method for Linear MIMO Systems // Mechatronics, Automation, Control. 2018. V. 19. Iss. 1. P. 11–18. https://doi.org/:10.17587/mau.19.11-18.
  13. Zubov N.E., Mikrin E.A., Misrikhanov M.Sh., Ryabchenko V.N. Modification of the Exact Pole Placement Method and its Application for the Control of Spacecraft Motion // J. Comput. Syst. Sci. Int. 2013. V. 52. Iss. 2. P. 279–292. https://doi.org/:10.1134/S1064230713020135
  14. Haidar I., Barbot J.-P., Rapaport A. A Multi Observers Approach when Observability Index is Higher than the State Dimension – a Case Study // IEEE 58th Conf. on Decision and Control. 2019. P. 1571–1576. https://doi.org/:10.1109/CDC40024.2019.9029675
  15. Ackermann J. Der Entwurf linearer Regelungsysteme im Zustandraum // Regeltech, Proz.-Datenverarb. 1972. V. 20. Iss. 1. P. 297–300. https://doi.org/:10.1524/auto.1972.20.112.297

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