σ-Stabilization of a Flexible Joint Robotic Arm via Delayed Controllers

In the present contribution, the problem of establishing tuning rules to proportional retarded controller for LTI systems is addressed. Based on the - decomposition methodology and σ-stability analysis, analytic conditions are determined on the parameters of a delayed controller that guarantee us that the system response reaches the maximal decay rate. The conditions presented in this paper are tested experimentally in tracking tasks of a flexible joint robotic arm.

[1]  Mouhacine Benosman,et al.  Control of flexible manipulators: A survey , 2004, Robotica.

[2]  Z. Bien,et al.  Use of time-delay actions in the controller design , 1980 .

[3]  Nejat Olgac,et al.  Full-state feedback controller design with “delay scheduling” for cart-and-pendulum dynamics , 2011 .

[4]  Boris T. Polyak,et al.  Stability regions in the parameter space: D-decomposition revisited , 2006, Autom..

[5]  D. D. Perlmutter,et al.  Stability of time‐delay systems , 1972 .

[6]  Sabine Mondié,et al.  Integral Retarded Velocity Control of DC Servomotors , 2013, TDS.

[7]  Sabine Mondié,et al.  Design of Maximum Decay Rate for SISO Systems with Delayed Output Feedback Using Elimination Theory , 2015 .

[8]  Sabine Mondié,et al.  Tuning and noise attenuation of a second order system using Proportional Retarded control , 2011 .

[9]  Boris Polyak,et al.  D-decomposition technique state-of-the-art , 2008 .

[10]  Silviu-Iulian Niculescu,et al.  STABILITY CROSSING CURVES OF SISO SYSTEMS CONTROLLED BY DELAYED OUTPUT FEEDBACK , 2006 .

[11]  A. Galip Ulsoy,et al.  Time-Delayed Control of SISO Systems for Improved Stability Margins , 2015 .

[12]  Kestutis Pyragas Continuous control of chaos by self-controlling feedback , 1992 .

[13]  Il Hong Suh,et al.  Proportional minus delay controller , 1979 .

[14]  Elena Gryazina The D-Decomposition Theory , 2004 .

[15]  Sabine Mondié,et al.  Proportional Integral Retarded control of second order linear systems , 2013, 52nd IEEE Conference on Decision and Control.

[16]  C. Abdallah,et al.  Delayed Positive Feedback Can Stabilize Oscillatory Systems , 1993, 1993 American Control Conference.

[17]  V. Kharitonov Time-Delay Systems: Lyapunov Functionals and Matrices , 2012 .

[18]  B. Aguirre‐Hernández,et al.  Tuning of a time‐delayed controller for a general class of second‐order linear time invariant systems with dead‐time , 2019, IET Control Theory & Applications.

[19]  S. Mondié,et al.  Velocity control of servo systems using an integral retarded algorithm. , 2015, ISA transactions.

[20]  Silviu-Iulian Niculescu,et al.  Some insights into the migration of double imaginary roots under small deviation of two parameters , 2018, Autom..

[21]  C. Knospe,et al.  PID control , 2006, IEEE Control Systems.

[22]  Keqin Gu,et al.  Stability and Stabilization of Systems with Time Delay , 2011, IEEE Control Systems.

[23]  Wim Michiels,et al.  Stabilizing a chain of integrators using multiple delays , 2004, IEEE Transactions on Automatic Control.

[24]  Sabine Mondié,et al.  Tuning the leading roots of a second order DC servomotor with proportional retarded control , 2010 .

[25]  S. Niculescu,et al.  Some remarks on stabilizing a chain of integrators using multiple delays , 2003, Proceedings of the 2003 American Control Conference, 2003..

[26]  Sabine Mondié,et al.  Proportional-delayed controllers design for LTI-systems: a geometric approach , 2018, Int. J. Control.

[27]  Sabine Mondié,et al.  Tuning of Proportional Retarded Controllers: Theory and Experiments , 2013, IEEE Transactions on Control Systems Technology.

[28]  Takehiro Mori,et al.  STABILITY PRESERVING TRANSITION FROM DERIVATIVE FEEDBACK TO ITS DIFFERENCE COUNTERPARTS , 2002 .

[29]  Sabine Mondié,et al.  Design of Proportional-Integral-Retarded (PIR) Controllers for Second-Order LTI Systems , 2016, IEEE Transactions on Automatic Control.

[30]  Hamid D. Taghirad,et al.  A SURVEY ON THE CONTROL OF FLEXIBLE JOINT ROBOTS , 2006 .

[31]  Wim Michiels,et al.  Static output feedback stabilization: necessary conditions for multiple delay controllers , 2005, IEEE Transactions on Automatic Control.