Determination of Vertices and Edges in a Parametric Polytope to Analyze Root Indices of Robust Control Quality
The research deals with the methodology intended to root robust quality indices in the interval control system, the parameters of which are affinely included in the coefficients of a characteristic polynomial. To determine the root quality indices we propose to depict on the root plane not all edges of the interval parametric polytope (as the edge theorem says), but its particular vertex-edge route. In order to define this route we need to know the angle sequence at which the edge branches depart from any integrated pole on the allocation area. It is revealed that the edge branches can integrate into the route both fully or partially due to intersection with other branches. The conditions which determine the intersection of one-face edge images have been proven. It is shown that the root quality indices can be determined by its ends or by any other internal point depending on a type of edge branch. The conditions which allow determining the edge branch type have been identified. On the basis of these studies we developed the algorithm intended to construct a boundary vertex-edge route on the polytope with the interval parameters of the system. As an illustration of how the algorithm can be implemented, we determined and introduced the root indices reflecting the robust quality of the system used to stabilize the position of an underwater charging station for autonomous unmanned vehicles.
KeywordsRobust control parametric uncertainty parametric polytope interval parameters system analysis
Unable to display preview. Download preview PDF.
This work was supported by the Ministry of Education and Science of the Russian Federation (No. 2.3649. 2017/PCh).
- D. Mihailescu-Stoica, F. Schrodel, R. Vobetawinkel, J. Adamy. On robustly stabilizing PID controllers for systems with a certain class of multilinear parameter dependency. In Proceedings of the 26th Mediterranean Conference on Control and Automation, IEEE, Zadar, Croatia, pp. 1–6, 2018. DOI: https://doi.org/10.1109/MED.2018.8442811.Google Scholar
- B. Y. Juang. Robustness of pole assignment of an interval polynomial using like λ-degree feedback gain based on the Kharitonov theorem. In Proceedings of SICE Annual Conference, IEEE, Taipei, China, pp. 3475–3484, 2010.Google Scholar
- Y. Hwang, Y. R. Ko, Y. Lee, T. H. Kim. Frequency-domain tuning of robust fixed-structure controllers via quantum-behaved particle swarm optimizer with cyclic neighborhood topology. International Journal of Control, Automation and Systems, vol. 16, no. 2, pp. 426–436, 2018. DOI: https://doi.org/10.1007/s12555-016-0766-3.CrossRefGoogle Scholar
- M. S. Sunila, V. Sankaranarayanan, K. Sundareswaran. Comparative analysis of optimized output regulation of a SISO nonlinear system using different sliding manifolds. International Journal of Automation and Computing, vol.14, no.4, pp.450–462, 2017. DOI: https://doi.org/10.1007/s1l633-017-1078-7.CrossRefGoogle Scholar
- M. Khadhraoui, M. Ezzine, H. Messaoud, M. Darouach. Full order ft filter design for delayed singular systems with unknown input and bounded disturbance: Time and frequency domain approaches. International Review on Automatic Control, vol.9, no. 1, pp.26–39, 2016. DOI: https://doi.org/10.15866/ireaco.v9il.7843.CrossRefGoogle Scholar
- J. G. Lu, Y. Q. Chen. Robust stability and stabilization of fractional-order interval systems with the fractional order a: The 0 < a < 1 case. IEEE Transactions on Automatic Control, vol.55, no. 1, pp. 152–158, 2010. DOI: https://doi.org/10.1109/TAC.2009.2033738.MathSciNetCrossRefzbMATHGoogle Scholar
- S. Sumsurooah, M. Odavic, S. Bozhko, D. Boroyevic. Toward robust stability of aircraft electrical power systems: Using a μ-based structural singular value to analyze and ensure network stability. IEEE Electrification Magazine, vol.5, no.4, pp.62–71, 2017. DOI: https://doi.org/10.1109/MELE.2017.2757383.CrossRefGoogle Scholar
- B. K. Sahu, B. Subudhi, M. M. Gupta. Stability analysis of an underactuated autonomous underwater vehicle using extended-routh's stability method. International Journal of Automation and Computing, vol.15, no. 3, pp. 299–309, 2018. DOI: https://doi.org/10.1007/s1l633-016-0992-4.CrossRefGoogle Scholar
- F. D. C. Da Silva, J. B. De Oliveira, A. D. De Araujo. Robust interval adaptive pole-placement controller based on variable structure systems theory. In Proceedings of the 25th International Conference on Systems Engineering, IEEE, Las Vegas, USA, pp. 45–54, 2017. DOI: https://doi.org/10.1109/IC-SEng.2017.73.Google Scholar
- Y. Chursin, D. Sonkin, M. Sukhodoev, R. Nurmuhametov, V. Pavlichev. Control system for an object with interval-given parameters: Quality analysis based on leading coefficients of characteristic polynomials. International Review of Automatic Control, vol.11, no. 4, pp.203–207, 2018. DOI: https://doi.org/10.15866/ireaco.vlli4.15727.CrossRefGoogle Scholar
- B. Senol, C. Yeroglu. Robust stability analysis of fractional order uncertain polynomials. In Proceedings of the 5th IFAC Workshop on Fractional Differentiation and its Applications, Nanjing, China, pp. 1–6, 2012.Google Scholar
- S. A. Gayvoronskiy, T. Ezangina, I. Khozhaev. The analysis of permissible quality indices of the system with affine uncertainty of characteristic polynomial coefficients. In Proceedings of International Automatic Control Conference, IEEE, Taichung, China, pp. 30–34, 2016. DOI: https://doi.org/10.1109/CACS.2016.7973879.Google Scholar
- B. B. Alagoz. A note on robust stability analysis of fractional order interval systems by minimum argument vertex and edge polynomials. IEEE/CAA Journal of Automatica Sinica, vol.3, no.4, pp.411-121, 2016. DOI: https://doi.org/10.1109/JAS.2016.7510088.