DOI: 10.17586/2226-1494-2017-17-1-31-38


ROBUST CONTROL ALGORITHM FOR MULTIVARIABLE PLANTS WITH QUANTIZED OUTPUT

A. A. Margun, I. B. Furtat


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For citation: Margun A.A., Furtat I.B. Robust control algorithm for multivariable plants with quantized output. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2017, vol. 17, no. 1, pp. 31–38. doi: 10.17586/2226-1494-2017-17-1-31-38

Abstract

The paper deals with robust output control algorithm for multivariable plants under disturbances. A plant is described by the system of linear differential equations with known relative degrees. Plant parameters are unknown but belong to the known closed bounded set. Plant state vector is unmeasured. Plant output is measured only via static quantizer. Control system algorithm is based on the high gain feedback method. Developed controller provides exponential convergence of tracking error to the bounded area. The area bounds depend on quantizer parameters and the value of external disturbances.  Experimental approbation of the proposed control algorithm is performed with the use of Twin Rotor MIMO System laboratory bench. This bench is a helicopter like model with two degrees of freedom (pitch and yaw). DC motors are used as actuators. The output signals are measured via optical encoders. Mathematical model of laboratory bench is obtained. Proposed algorithm was compared with proportional - integral – differential controller in conditions of output quantization. Obtained results have confirmed the efficiency of proposed controller.                                  


Keywords: robust control, quantization, parametric uncertainties, multivariable systems, disturbances

Acknowledgements. This work was partially financially supported by the Government of the Russian Federation (Grant 074-U01), the Ministry of Education and Science of the Russian Federation (Project 14.Z50.31.0031), the Russian Federation President Grants (No. 14.Y31.16.9281-НШ and No. 14.W01.16.6325-МД (МД-6325.2016.8)).

References
 
1.     Widrow B. Statistical analysis of amplitude-quantized sampled-data systems. IEEE Transactions, 1961,vol. 79, no.6, pp. 555–568.doi: 10.1109/tai.1961.6371702
2.     Liu В., Kaneko T. Error analysis of digital filters with floating-point arithmetic. Proc. IEEE, 1969,vol. 57, pp.1735–1747.
3.     Curry R.E. Estimation and Control with Quantized Measurements. MIT Press, 1970, 141 p.
4.     Delchamps D.F. Stabilizing a linear system with quantized state feedback. IEEE Transactions on Automatic Control, 1990, vol. 35, no. 8, pp. 916–924. doi: 10.1109/9.58500
5.     Brockett R., Liberzon D. Quantized feedback stabilization of linear systems. IEEE Transactions on Automatic Control, 2000, vol. 45, no. 7, pp. 1279–1289. doi: 10.1109/9.867021
6.     Ortega R., Spong M. Adaptive motion control of rigid robots: a tutorial. Proc. 27th IEEE Conf. on Decision and Control, 1988, vol. 2, pp. 1575–1584. doi: 10.1109/cdc.1988.194594
7.     Slotine J.J., Li W. Applied Nonlinear Control. Prentice Hall, 1991, 461 p.
8.     Berghuis H., Ortega R., Nijmeijer H. A robust adaptive robot controller. IEEE Transactions on Robotics and Automation, vol. 9, no. 6, pp. 825–830. doi: 10.1109/70.265925
9.     Furtat L.B., Tsykunov A.M. Robust control of unsteady-state nonlinear structurally undefined objects. Control Sciences, 2008, no. 5, pp. 2–7. (In Russian)
10.  Bobtsov A.A., Shavetov S.V. Output control of linear parametrically uncertain object in conditions of distturbances and neglected dynamics. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2011, no. 1, pp. 33–39. (In Russian)
11.  Tsykunov A.M. Robastnoe Upravlenie s Kompensatsiei Vozmushchenii [Robust Control with Compensation of Perturbations]. Moscow, Fizmatlit Publ., 2012,298 p.
12.  Bobtsov A.A., Faronov M.V., Furtat I.B., Pyrkin A.A., Wang J. Adaptive output control of multichannel linear stationary systems under parametric uncertainty.Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2014, no. 6, pp. 63–70. (In Russian)
13.  Bobtsov A.A., Faronov M.V., Furtat I.B., Pyrkin A.A., Arustamov S.A. Adaptive control of linear MIMO systems. Proc. 6th Int. Congress on Ultra Modern Telecommunications and Control Systems and Workshops, ICUMT. St. Petersburg, Russia, 2014, pp. 584–589. doi: 10.1109/icumt.2014.7002166
14.  Furtat I.B., Fradkov A.L., Liberzon D. Robust control with compensation of disturbances for systems with quantized output. IFAC Proceedings, 2014, vol. 47, no. 3, pp. 730–735. doi: 10.3182/20140824-6-za-1003.00531
15.  Margun A., Furtat I. Robust control of uncertain linear systems in conditions of output quantization. IFAC Proceedings, 2015, vol. 48, no. 11, pp. 843–847. doi: 10.5220/0005981405140520
16.  Margun A., Furtat I. Robust control of linear MIMO systems in conditions of parametric uncertainties, external disturbances and signal quantization. Proc. 20th Int. Conf. on Methods and Models in Automation and Robotics, 2015, pp. 341–346.
17.  Twin Rotor MIMO System Experiment. Feedback Instruments Ltd., 1998.


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