Contribution of New Parameter Inverses to Robustification of Fractional-Order Perfect Control for LTI MIMO Discrete-Time State-Space Systems

• Autorzy: Wach Ł. , Hunek W. P.

Identyfikatory

DOI

10.14313/JAMRIS_3-2016/21

• Języki publikacji: EN

Abstrakty

EN

The paper presents results of application of various right inverses to fractional-order discrete-time perfect control in terms of improving its stability and robustness. For that reason the newly introduced σ-inverse and H-inverse are applied finally to obtain the mentioned above control strategy strictly dedicated to LTI MIMO nonsquare systems described by state-space framework. It is highlighted that parameter σ-inverse and H-inverse with different so called ‘degrees of freedom’ outperform the typical minimum-norm right T-inverse. Moreover, this new approach deals with the same class of problems concerning integer-order systems. The simulation studies performed in Matlab/Simulink environment confirm high potential of proposed here method.

Słowa kluczowe

EN

LTI MIMO fractional-order systems; perfect control; inverses of nonsquare matrices; stability

• Wydawca: Łukasiewicz Industrial Research Institute for Automation and Measurements PIAP
• Czasopismo: Journal of Automation Mobile Robotics and Intelligent Systems
• Rocznik: 2016
• Tom: Vol. 10, No. 3
• Strony: 29--33
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Wach Ł.

• PhD student, Opole University of Technology, Department of Electrical, Control and Computer Engineering, Poland

autor

Hunek W. P.

• Group of Control and Decision Systems at the Institute of Control and Computer Engineering, Department of Electrical, Control and Computer Engineering, Opole University of Technology, Poland

Bibliografia

• [1] Wach Ł., Hunek W. P., “Perfect control for fractional-order multivariable discrete-time systems, Theoretical Developments and Applications of Non-Integer Order Systems”. In: Proc. of the 7th Conference on Non-integer Order Calculous and its Applications (RRNR’2015), series: Lecture Notes in Electrical Engineering, vol. 357, Szczecin, Poland, 2015, 233–237. DOI: 10.1007/978-3-319-23039-9_19.
• [2] Hunek W.P., Towards a General Theory of Control Zeros for LTI MIMO Systems, Opole University of Technology Press, Opole, Poland, 2011.
• [3] Hunek W.P., Latawiec K.J., “A study on new right/left inverses of nonsquare polynomial matrices”,International Journal of Applied Mathematics and Computer Science, vol. 21, no. 2, 331–348, 2011.DOI: 10.2478/v10006-011-0025-y.
• [4] Hunek, W.P., Latawiec K.J., Majewski P., Dzierwa P., “An application of a new matrix inverse in stabilizing state-space perfect control of nonsquare LTI MIMO systems”. In: Proc. Of the 19th IEEE International Conference on Methods and Models in Automation and Robotics (MMAR’2014), Międzyzdroje, Poland, IEEE Catalog Number: CFP13MMA-CDR, 451–455.
• [5] Hunek W. P., “New SVD-based matrix H-inverse vs. minimum-energy perfect control design for state-space LTI MIMO systems”. In: Proc. of the 20th IEEE International Conference on System Theory, Control and Computing (ICSTCC’16), 13th–15th October 2016, Sinaia, Romania, 2016. Accepted for publication.
• [6] Ben-Israel A., Greville T. N. E., Generalized Inverses, Theory and Applications, New York: Springer-Verlag, 2 ed., 2003.
• [7] Bańka S., Dworak P., Efficient algorithm for designing multipurpose control systems for invertible and right-invertible MIMO LTI plants. Bulletin of the Polish Academy of Sciences –Technical Sciences, vol. 54, no. 4, 2006, 429–436.
• [8] Bańka S., Multivariable control systems –A polynomial approach, vol. 11, Szczecin: Szczecin University of Technology Press, 2007. (in Polish)
• [9] Hunek W. P., “An application of polynomial matrix σ-inverse inminimum-energy state-space perfect control of nonsquare LTI MIMO systems”. In: Proc. of the 20th IEEE International Conference on Methods and Models in Automation and Robotics (MMAR’2015), Międzyzdroje, Poland, 252–255, 2015.
• [10] Hunek W. P., “An application of new polynomial matrix σ-inverse in minimum-energy design of robust minimum variance control for nonsquare LTI MIMO systems”. In: Proc. of the 8th IFAC Symposium on Robust Control Design (ROCOND’2015), Bratislava, Slovakia, 2015, 149–153.
• [11] Hunek W. P., “Contribution of new matrix H-inverse to stabilizing the perfect control for LTI MIMO state-space systems”. In: Proc. of the 21st IEEE International Conference on Methods and Models in Automation and Robotics (MMAR’2016), Międzyzdroje, Poland, 2016, 64–69.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.