Robust Stabilization of a Servomechanism With Respect To Time-Delay

Barış Samim Nesimioğlu [1] , Sabri Yılmaz [2] , Emre Dincel [3]


In this paper, a servomechanism under teleoperation is considered. Since the teleoperation itself can result in large amount of time-delays and this amount can change operation to operation, it can be difficult to control such mechanisms in order to accomplish the desired tasks. From the robust control viewpoint, a methodology that guarantees the stability in worst case is essential. Based on a simple methodology to find the delay independent stabilizing proportional (P) controller regions, just by forming the magnitude polynomial and employing the root locus technique, the stability of the robot is guaranteed, even in the worst case: the system becomes stable even if the connection has huge amount of time-delays. This fact is evidenced first by the simulations. To simulate the real system, as there is no information about the motor parameters, the motor is modeled by a global optimization methodology, named Genetic Algorithm in order to obtain a valid model for the system as accurate as possible. Then the resulting P controllers are applied to the real system, the results of which are found in accordance with the simulation results; the stability of the operation is not affected by the time-delay. 
Teleoperation System Control, Time-Delay Systems, Robust Control, Low-Order Controllers, Delay Independent Stability
  • [1] Hokayen P.F. & Spong, M.W., Bilateral teleoperation: A historical survey, Automatica, Vol.42, 2006, pp. 2035-2057.
  • [2] Cui J. et. al. A Review of Teleoperation System Control, Proc. FCRAR, Boca Raton, Florida, USA 2003.
  • [3] Alfi A. & Farrokhi, F., A Simple Structure for Bilateral Transparent Teleoperation Systems With Time Delay, Journal of Dynamic Systems Measurement and Control, Vol. 130 Number 4, 2008.
  • [4] Arcara P. & Melchiorri, C., Control Schemes for Teleoperation with time delay: A comparative study, Robotics and Autonomous Systems, Vol 38, 2002, pp. 49-64.
  • [5] Al-Mutairi, N.B. Adaptive Fuzzy Modulation for Networked PI Control Systems, Ph.D. Dissertation, Dept. Elec. and Comp. Eng., North Carolina State University, 2002.
  • [6] Alfi, A., Bakhshi, A., Yousefi, M. & Talebi, H.A. Design and Implementation of Robust-Fixed Structure Controller for Telerobotic Systems, J. Intell Robot Syst, 2016. doi: 10.1007/s10846-016-0335-2.
  • [7] Slawinski, E., Mut V. & Santiago D., PD-like controller for delayed bilateral teleoperation of wheeled robots International Journal of Control, 2016, doi: 10.1080/00207179.2016.1144234.
  • [8] Silva, G.J., Datta, A. & Bhattacharyya, S.P. PID Controllers for Time-Delay Systems, Birkhäuser: Boston, 2005.
  • [9] Walton M., & Marshall, J.E., Direct Method for TDS Stability Analysis, IEE Proceedings – Control Theory & Applications, Vol. 134, Number 2, pp. 101 – 107, 1987.
  • [10] Nesimioglu, B.S. & Soylemez, M.T., A simple derivation of all stabilizing proportional controllers for first order time-delay systems, Asian Journal of Control, Vol. 14, Number 2, 2012, pp. 598-604.
  • Olgac N., & Sipahi, R., A Practial Method for Analyzing the Stability of Neutral Type LTI-Time Delayed Systems, Automatica, Vol. 40, 2003 pp. 847 – 853.
  • Hohenbichler, N., All Stabilizing PID Controllers for Time Delay Systems, Automatica, Vol. 45, Number 11, 2009, pp. 2678 – 2684.
  • Lee, B.N., Wang Q.G. & Lee, T.H., Development of D-decomposition method for computing stabilizing gain ranges for general delay systems, Journal of Process Control, Vol. 25, 2015, pp. 94-104.
  • Nesimioglu B.S. & Soylemez, M.T. All‐Stabilizing Proportional Controllers for First‐Order Bi‐Proper Systems with Time Delay: An Analytical Derivation, Asian Journal of Control, Vol.18 Number 6, 2016, pp. 2203-2220.
  • Wang, D.J. A PID Controller Set of Guaranteeing Stability and Gain and Phase Margins for Time-Delay Systems, Journal of Process Control, Vol. 22, 2012, pp. 1298 – 1306.
  • Nesimioglu, B.S, Yilmaz, S., & Dincel E., Robust stabilization of a servomechanism with respect to time-delay, International Conference on Advanced Technology & Sciences (ICAT), 1-3 September 2016, Turkey, Konya.
  • Le, B.N., Wang, Q.G., Lee, T.H. & Nie, Z. On computation of stabilizing loop gain and delay ranges for bi-proper delay systems, ISA Transactions, Vol.53, pp. 1705 – 1715, 2014.
  • Nesimioglu, B.S. & Soylemez, M.T., Calculation of All Gains Providing Time-Delay Independent Stability via Root Locus, Int. Conf. on Control Decision and Information Technologies (CoDIT), Metz, France, pp. 566-571, 2014.
  • Thowsen A. Delay independent stability of linear systems, IEE Proceedings D-Control Theory and Applications, Vol. 129, Number 3, 1982 pp. 73-75.
  • Ergenc, A.F., A New Method for Delay-Independent Stability of Time-Delayed Systems, 9th IFAC Workshop on Time Delay Systems, Published by Elsevier Ltd., 7-9 June 2010, Czech Republic, Prague.
  • Michiels, W., & Niculescu S. I., Characterization of Delay-Independent Stability and Delay Interference Phenomena, SIAM Journal of Control and Optimization, Vol.45, Number 6, 2007, pp. 2138-2155.
  • Dynamixel MX 106T User’s Manual, http://support.robotis.com/en/product/dynamixel/mx_series/mx-106.htm
  • Garg, D.P. & Kumar, M. Optimization techniques applied to multiple manipulators for path planning and torque minimization, Engineering Applications of Artificial Intelligence, Vol. 15, 2002 pp. 241-252.
Subjects Engineering
Journal Section Research Article
Authors

Author: Barış Samim Nesimioğlu
Institution: KTO KARATAY ÜNİVERSİTESİ
Country: Turkey


Author: Sabri Yılmaz
Institution: İSTANBUL TEKNİK ÜNİVERSİTESİ
Country: Turkey


Author: Emre Dincel

Dates

Publication Date : December 1, 2016

Bibtex @research article { ijamec270376, journal = {International Journal of Applied Mathematics Electronics and Computers}, issn = {}, eissn = {2147-8228}, address = {}, publisher = {Selcuk University}, year = {2016}, volume = {}, pages = {250 - 257}, doi = {10.18100/ijamec.270376}, title = {Robust Stabilization of a Servomechanism With Respect To Time-Delay}, key = {cite}, author = {Nesimioğlu, Barış Samim and Yılmaz, Sabri and Dincel, Emre} }
APA Nesimioğlu, B , Yılmaz, S , Dincel, E . (2016). Robust Stabilization of a Servomechanism With Respect To Time-Delay. International Journal of Applied Mathematics Electronics and Computers , (Special Issue-1) , 250-257 . DOI: 10.18100/ijamec.270376
MLA Nesimioğlu, B , Yılmaz, S , Dincel, E . "Robust Stabilization of a Servomechanism With Respect To Time-Delay". International Journal of Applied Mathematics Electronics and Computers (2016 ): 250-257 <https://dergipark.org.tr/en/pub/ijamec/issue/25619/270376>
Chicago Nesimioğlu, B , Yılmaz, S , Dincel, E . "Robust Stabilization of a Servomechanism With Respect To Time-Delay". International Journal of Applied Mathematics Electronics and Computers (2016 ): 250-257
RIS TY - JOUR T1 - Robust Stabilization of a Servomechanism With Respect To Time-Delay AU - Barış Samim Nesimioğlu , Sabri Yılmaz , Emre Dincel Y1 - 2016 PY - 2016 N1 - doi: 10.18100/ijamec.270376 DO - 10.18100/ijamec.270376 T2 - International Journal of Applied Mathematics Electronics and Computers JF - Journal JO - JOR SP - 250 EP - 257 VL - IS - Special Issue-1 SN - -2147-8228 M3 - doi: 10.18100/ijamec.270376 UR - https://doi.org/10.18100/ijamec.270376 Y2 - 2016 ER -
EndNote %0 International Journal of Applied Mathematics Electronics and Computers Robust Stabilization of a Servomechanism With Respect To Time-Delay %A Barış Samim Nesimioğlu , Sabri Yılmaz , Emre Dincel %T Robust Stabilization of a Servomechanism With Respect To Time-Delay %D 2016 %J International Journal of Applied Mathematics Electronics and Computers %P -2147-8228 %V %N Special Issue-1 %R doi: 10.18100/ijamec.270376 %U 10.18100/ijamec.270376
ISNAD Nesimioğlu, Barış Samim , Yılmaz, Sabri , Dincel, Emre . "Robust Stabilization of a Servomechanism With Respect To Time-Delay". International Journal of Applied Mathematics Electronics and Computers / Special Issue-1 (December 2016): 250-257 . https://doi.org/10.18100/ijamec.270376
AMA Nesimioğlu B , Yılmaz S , Dincel E . Robust Stabilization of a Servomechanism With Respect To Time-Delay. International Journal of Applied Mathematics Electronics and Computers. 2016; (Special Issue-1): 250-257.
Vancouver Nesimioğlu B , Yılmaz S , Dincel E . Robust Stabilization of a Servomechanism With Respect To Time-Delay. International Journal of Applied Mathematics Electronics and Computers. 2016; (Special Issue-1): 257-250.