Orientation of radio-telescope secondary mirror via adaptive sliding mode control

In this work a parallel manipulator (Stewart platform) is used to align and maintain the position of the secondary mirror of a radio-telescope. The six degrees of freedom platform gives the significant advantage of reaching the maximum performance for the positioning tasks. The near-singularity condition of the platform is analyzed and is handled by implementation of a new control law based on sliding mode with inner regularization procedure. Herein, the finite-time convergence of closed-loop system derived from designed control in the presence of external as well as internal disturbances/uncertainties is proved. The effectiveness of the proposed controller is verified via numerical simulation. We show that Sliding Mode Control with a gain matrix adaptation based on the Equivalent Control method can significantly reduce the undesirable chattering effect an therefore avoid the possible damages.

[1]  Oguz Ustun,et al.  A neuro-fuzzy controller for speed control of a permanent magnet synchronous motor drive , 2008, Expert Syst. Appl..

[2]  Chung-Shi Tseng,et al.  Robust PID control design for permanent magnet synchronous motor: A genetic approach , 2008 .

[3]  Hongbo Zhou,et al.  Neural network-based sliding mode adaptive control for robot manipulators , 2011, Neurocomputing.

[4]  Judith E. Deutsch,et al.  A Stewart Platform-Based System for Ankle Telerehabilitation , 2001, Auton. Robots.

[5]  Tzu-Chun Kuo,et al.  Adaptive Sliding-Mode Control for NonlinearSystems With Uncertain Parameters , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  Alexander S. Poznyak,et al.  Tethered space orientation via adaptive sliding mode , 2016 .

[7]  R. D. Brandt,et al.  Self-tuning of PID controllers by adaptive interaction , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[8]  Hee-Jun Kang,et al.  An online self-gain tuning method using neural networks for nonlinear PD computed torque controller of a 2-dof parallel manipulator , 2013, Neurocomputing.

[9]  Qingling Zhang,et al.  Novel sliding surface design for nonlinear singular systems , 2016, Neurocomputing.

[10]  Gu Hongbin,et al.  Adaptive Sliding Control of Six-DOF Flight Simulator Motion Platform , 2007 .

[11]  Hee-Jun Kang,et al.  An adaptive tracking controller for parallel robotic manipulators based on fully tuned radial basic function networks , 2014, Neurocomputing.

[12]  P. Deuflhard.  A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting , 1974 .

[13]  B. Y. Duan,et al.  Singularity analysis of fine-tuning Stewart platform for large radio telescope using genetic algorithm , 2003 .

[14]  K. Srinivasan,et al.  Kinematic and dynamic analysis of Stewart platform-based machine tool structures , 2003, Robotica.

[15]  Ying Zou,et al.  A compound control method based on the adaptive neural network and sliding mode control for inertial stable platform , 2015, Neurocomputing.

[16]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[17]  Daniel G. Sbarbaro-Hofer,et al.  An adaptive sliding-mode controller for discrete nonlinear systems , 2000, IEEE Trans. Ind. Electron..

[18]  Christopher Edwards,et al.  Sliding Mode Control and Observation , 2013 .

[19]  Jae-Bok Song,et al.  Position control of a Stewart platform using inverse dynamics control with approximate dynamics , 2003 .

[20]  Wilfrid Perruquetti,et al.  Dynamic modeling of a parallel robot. Application to a surgical simulator , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[21]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[22]  Yuri B. Shtessel,et al.  Sliding Mode Disturbance Observer-Based Control for a Reusable Launch Vehicle , 2005 .

[23]  Yuri B. Shtessel,et al.  Sliding mode control with gain adaptation—Application to an electropneumatic actuator , 2013 .

[24]  William K. Durfee,et al.  Design and implementation of a laboratory test bed for space robotics: the VES mod II , 1994 .

[25]  B. Bandyopadhyay,et al.  Stabilization of Stewart platform using Higher Order Sliding Mode control , 2012, 2012 7th International Conference on Electrical and Computer Engineering.

[26]  Kan-Jian Zhang,et al.  Theoretical and numerical analysis of learning dynamics near singularity in multilayer perceptrons , 2015, Neurocomputing.

[27]  Sing Kiong Nguang,et al.  Adaptive sliding mode control for a class of MIMO nonlinear systems with uncertainties , 2014, J. Frankl. Inst..

[28]  Vadim I. Utkin,et al.  Adaptive sliding mode control with application to super-twist algorithm: Equivalent control method , 2013, Autom..

[29]  Ahmad Bagheri,et al.  Simulation and tracking control based on neural-network strategy and sliding-mode control for underwater remotely operated vehicle , 2009, Neurocomputing.

[30]  Nasser Sadati,et al.  Adaptive multi-model sliding mode control of robotic manipulators using soft computing , 2008, Neurocomputing.