New tuning conditions for a class of nonlinear PID global regulators of robot manipulators

Several nonlinear proportional-integral-derivative (PID) controllers for robot manipulators that ensure global asymptotic stability have been proposed in the literature. However, the tuning criteria obtained are expressed in terms of conditions so restrictive that they have avoided, until now, carrying out experimental tests with such controllers. Tuning criteria of some PID controllers for robot manipulators with conditions more relaxed than those presented previously in the literature have been proposed in two recent works by the authors. This was achieved by setting the tuning conditions individually for each joint instead of general conditions for the whole robot. In this paper we extend these results to a class of nonlinear PID global regulators for robot manipulators. The obtained tuning criteria are given in terms of conditions so relaxed that they have allowed to carry out, for the first time, experimental essays with these controllers. Such experiments are presented in this paper using a two-degrees-of-freedom robot manipulator.

[1]  Victor Manuel Hernández-Guzmán,et al.  Improving performance of saturation-based PID controllers for rigid robots† , 2011 .

[2]  Rafael Kelly,et al.  A class of nonlinear PID global regulators for robot manipulators , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[3]  Roberto V. Carrillo-Serrano,et al.  PD control for robot manipulators actuated by switched reluctance motors , 2013, Int. J. Control.

[4]  P. Olver.  Nonlinear Systems , 2013 .

[5]  Rafael Kelly,et al.  Control of Robot Manipulators in Joint Space , 2005 .

[6]  Víctor Santibáñez,et al.  A Natural Saturating Extension of the PD-With-Desired-Gravity-Compensation Control Law for Robot Manipulators With Bounded Inputs , 2007, IEEE Transactions on Robotics.

[7]  R. Ortega,et al.  A semiglobally stable output feedback PI2D regulator for robot manipulators , 1995, IEEE Trans. Autom. Control..

[8]  Fernando Reyes,et al.  Experimental evaluation of model-based controllers on a direct-drive robot arm , 2001 .

[9]  V. Santibáñez,et al.  On Saturated PID Controllers for Industrial Robots: the PA10 Robot Arm as Case of Study , 2010 .

[10]  Víctor Santibáñez,et al.  An estimate of the Domain of attraction for the PID regulator of manipulators , 2007, Int. J. Robotics Autom..

[11]  Suguru Arimoto,et al.  Stability and robustness of PID feedback control for robot manipulators of sensory capability , 1984 .

[12]  Ramón Silva-Ortigoza,et al.  A New Tuning Procedure for PID Control of Rigid Robots , 2008, Adv. Robotics.

[13]  R. Kelly.  Global positioning of robot manipulators via PD control plus a class of nonlinear integral actions , 1998, IEEE Trans. Autom. Control..

[14]  R. Kelly,et al.  PID regulation of robot manipulators: stability and performance , 2000 .

[15]  Víctor Santibáñez,et al.  Analysis via Passivity Theory of a Class of Nonlinear PID Global Regulators for Robot Manipulators , 2011 .

[16]  Rafael Kelly,et al.  Control de movimiento de robots manipuladores , 2003 .

[17]  Rafael Kelly,et al.  A tuning procedure for stable PID control of robot manipulators , 1995, Robotica.

[18]  Suguru Arimoto,et al.  Fundamental problems of robot control: Part I, Innovations in the realm of robot servo-loops , 1995, Robotica.

[19]  Víctor Santibáñez,et al.  Simple extensions of the PD-with-gravity-compensation control law for robot manipulators with bounded inputs , 2006, IEEE Transactions on Control Systems Technology.

[20]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[21]  Víctor Santibáñez,et al.  A saturated PD controller for robots equipped with brushless DC-motors , 2009, Robotica.