Stabilization of a Class of Robot Systems in Fractional-Order Hold Case via Sampling Zero Dynamic Stable Approach

Robots play a significant-and growing-role in many practical fields, for example, the corresponding application in industrial and medicine field. More importantly, for the control of a robot system, a good control performance is natural and necessary requirements. And since the control of system is usually realized by a digital computer, sampling is an inevitable process in actual engineering. However, it is a well known truth that unstable zero dynamics can greatly limit the control performance of the system. This paper investigates the stabilization of a class of robot system based on the corresponding sampled-data model, which generated from the discretization with fractional-order hold (FROH). Further, the sampled-data model of the two degree of freedom (DOF) robot system is obtained and the expression and stable conditions of sampling zero dynamics are also obtained. What is more, the control strategy of the corresponding robot system is acquired using the sampling zero dynamic stable approach. Finally, numerical example is provide to illustrate the effectiveness of the proposed approach in this paper.

[1]  Ning Sun,et al.  Adaptive Control for Pneumatic Artificial Muscle Systems With Parametric Uncertainties and Unidirectional Input Constraints , 2020, IEEE Transactions on Industrial Informatics.

[2]  M. V. A. Raju Bahubalendruni,et al.  Robots in Medicine: Past, Present and Future , 2017, Int. J. Manuf. Mater. Mech. Eng..

[3]  G. Goodwin,et al.  Sampling and Sampled-Data Models: The Interface Between the Continuous World and Digital Algorithms , 2013, IEEE Control Systems.

[4]  Dorothée Normand-Cyrot,et al.  Immersion and invariance stabilization of strict-feedback dynamics under sampling , 2017, Autom..

[5]  Nitai Pal,et al.  Transient Stability Analysis of a Multimachine Power System with TCSC Controller – A Zero Dynamic Design Approach , 2018 .

[6]  Dragan Nesic,et al.  A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models , 2004, IEEE Transactions on Automatic Control.

[7]  Graham C. Goodwin,et al.  On sampled-data models for nonlinear systems , 2005, IEEE Transactions on Automatic Control.

[8]  K. Yuan,et al.  Output tracking of a non-linear non-minimum phase PVTOL aircraft based on non-linear state feedback control , 2002 .

[9]  Shan Liang,et al.  Stability of Limiting Zeros of Sampled-data Systems with Backward Triangle Sample and Hold , 2019, International Journal of Control, Automation and Systems.

[10]  A. Isidori.  Nonlinear Control Systems , 1985 .

[11]  Zulkifli Mohamed,et al.  Humanoid robot arm performance optimization using multi objective evolutionary algorithm , 2014, International Journal of Control, Automation and Systems.

[12]  José António Tenreiro Machado,et al.  Robot Trajectory Planning Using Multi-objective Genetic Algorithm Optimization , 2004, GECCO.

[13]  Leonid M. Fridman,et al.  Zero-dynamics design and its application to the stabilization of implicit systems , 2016, Syst. Control. Lett..

[14]  Cheng Zeng,et al.  A novel approach to stable zero dynamics of sampled-data models for nonlinear systems in backward triangle sample and hold case , 2019, Appl. Math. Comput..

[15]  Juan I. Yuz,et al.  Sampled-Data Models for Linear and Nonlinear Systems , 2013 .

[16]  Seungwan Ryu,et al.  Soft robot review , 2017 .

[17]  S. Hayati,et al.  A robot with improved absolute positioning accuracy for CT guided stereotactic brain surgery , 1988, IEEE Transactions on Biomedical Engineering.

[18]  Paula Gomes,et al.  Surgical robotics: Reviewing the past, analysing the present, imagining the future , 2011 .

[19]  Shan Liang,et al.  The stability properties of the zeros of sampled models for time delay systems in fractional order hold case , 2004 .

[20]  S. Monaco,et al.  Zero dynamics of sampled nonlinear systems , 1988 .

[21]  Shan Liang,et al.  A novel condition for stable nonlinear sampled-data models using higher-order discretized approximations with zero dynamics. , 2017, ISA transactions.

[22]  C. L. Philip Chen,et al.  Adaptive Neural Control for Dual-Arm Coordination of Humanoid Robot With Unknown Nonlinearities in Output Mechanism , 2015, IEEE Transactions on Cybernetics.

[23]  Dragan Nesic,et al.  A framework for nonlinear sampled-data observer design via approximate discrete-time models and emulation , 2004, Autom..

[24]  K. Åström,et al.  Zeros of sampled systems , 1980 .

[25]  Frank L. Lewis,et al.  Dynamic inversion with zero-dynamics stabilisation for quadrotor control , 2009 .

[26]  M. Ishitobi,et al.  Improvement of stability of zeros in discrete-time multivariable systems using fractional-order hold , 2003 .

[27]  Yan Lin,et al.  Robust output tracking control of a class of non-minimum phase systems and application to VTOL aircraft , 2011, Int. J. Control.

[28]  Shan Liang,et al.  Improving the Stability Behavior of Limiting Zeros for Multivariable Systems Based on Multirate Sampling , 2018, International Journal of Control, Automation and Systems.

[29]  Kil To Chong,et al.  A new time-discretization for delay multiple-input nonlinear systems using the Taylor method and first order hold , 2011, Discret. Appl. Math..

[30]  Keyong Shao,et al.  Global Fuzzy Sliding Mode Control for Multi-joint Robot Manipulators Based on Backstepping , 2014 .

[31]  M. De la Sen,et al.  Improving the stability properties of the zeros of sampled systems with fractional order hold , 2000 .

[32]  M. Ishitobi.  Stability of zeros of sampled system with fractional order hold , 1996 .

[33]  Carlos Llopis-Albert,et al.  A review of mobile robots: Concepts, methods, theoretical framework, and applications , 2019, International Journal of Advanced Robotic Systems.

[34]  He Chen,et al.  Neural Network-Based Adaptive Antiswing Control of an Underactuated Ship-Mounted Crane With Roll Motions and Input Dead Zones , 2020, IEEE Transactions on Neural Networks and Learning Systems.