Nonlinear Adaptive Control for Electromagnetic Actuators

The authors study here the problem of adaptive ”soft-landing” control for electromagnetic actuators. The soft landing requires accurate control of the actuator’s moving element between two desired positions. They propose a non-linear adaptive controller to solve the problem of robust trajectory tracking for the moving element, when considering model uncertainties with linear parametrisation. The controller is an integral input-to-state stability (iISS) backstepping controller, merged with gradient descent estimation filters to estimate model uncertainties with linear parametrisation. They show that it ensures bounded tracking errors for bounded estimation errors. Furthermore, iISS result allows us to represent the bound on tracking error as a decreasing function of the estimation error. They demonstrate the effectiveness of this controller with numerical tests. IET Control Theory & Applications This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c © Mitsubishi Electric Research Laboratories, Inc., 2015 201 Broadway, Cambridge, Massachusetts 02139 1 Nonlinear Adaptive Control for Electromagnetic Actuators Mouhacine Benosman Mitsubishi Electric Research Laboratories 201 Broadway Street, Cambridge, MA 02139, USA Gökhan M. Atınç Mechanical Science and Engineering Department University of Illinois at Urbana-Champaign, USA Abstract We study here the problem of adaptive ‘soft-landing’ control for electromagnetic actuators. The soft landing requires accurate control of the actuator’s moving element between two desired positions. We propose a nonlinear adaptive controller to solve the problem of robust trajectory tracking for the moving element, when considering model uncertainties with linear parametrization. The controller is an integral Input-to-State Stability (iISS) backstepping controller, merged with gradient descent estimation filters to estimate model uncertainties with linear parametrization. We show that it ensures bounded tracking errors for bounded estimation errors. Furthermore, iISS result allows us to represent the bound on tracking error as a decreasing function of the estimation error. We demonstrate the effectiveness of this controller with numerical tests.