Robust Stabilization of a Servomechanism With Respect To Time-Delay

Yıl 2016, , 250 - 257, 01.12.2016

Barış Samim Nesimioğlu , Sabri Yılmaz Emre Dincel

https://doi.org/10.18100/ijamec.270376

Cited By: 1

Öz

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. 

Anahtar Kelimeler

Teleoperation System Control, Time-Delay Systems, Robust Control, Low-Order Controllers, Delay Independent Stability

Kaynakça

• [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.