Controller design for a class of underactuated mechanical systems

This study proposes a strategy for the control of a class of underactuated mechanical systems. The Olfati transformation is applied firstly to represent the system into a special cascade form. Since, in general cases, some of the terms in the system dynamic equation represented in the new space might become too complex to derive, they are regarded as uncertainties. These uncertainties would enter the system in a mismatched fashion, and their variation bounds are not available; therefore, most conventional robust or adaptive designs fail to stabilise the closed-loop dynamics. A backstepping-like adaptive controller based on function approximation technique (FAT) is designed so that the system in the new space can be stabilised with uniformly ultimately bounded performance which further implies the same stability property to the system in the original space. Simulation cases for the control of an inverted pendulum and a translational oscillator/rotational actuator (TORA) system are presented to justify the proposed design.

[1]  Anthony M. Bloch,et al.  Optimal control of underactuated nonholonomic mechanical systems , 2006, 2006 American Control Conference.

[2]  Bing Chen,et al.  Direct adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems , 2007, Fuzzy Sets Syst..

[3]  An-Chyau Huang,et al.  FAT-based adaptive control for pneumatic servo systems with mismatched uncertainties , 2008 .

[4]  An-Chyau Huang,et al.  Adaptive multiple-surface sliding control for non-autonomous systems with mismatched uncertainties , 2004, Autom..

[5]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[6]  An-Chyau Huang,et al.  A FAT-based adaptive controller for robot manipulators without regressor matrix: theory and experiments , 2005, Robotica.

[7]  A. Megretski,et al.  Controller design for a class of underactuated nonlinear systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[8]  Rogelio Lozano,et al.  Non-linear Control for Underactuated Mechanical Systems , 2001 .

[9]  Mrdjan Jankovic,et al.  TORA example: cascade- and passivity-based control designs , 1996, IEEE Trans. Control. Syst. Technol..

[10]  An-Chyau Huang,et al.  Adaptive Control of Robot Manipulators: A Unified Regressor-Free Approach , 2010 .

[11]  An-Chyau Huang,et al.  Adaptive sliding control for single-link flexible-joint robot with mismatched uncertainties , 2004, IEEE Trans. Control. Syst. Technol..

[12]  Mingjun Zhang,et al.  A hybrid switching control strategy for nonlinear and underactuated mechanical systems , 2003, IEEE Trans. Autom. Control..

[13]  Bin Yao,et al.  Neural network adaptive robust control of nonlinear systems in semi-strict feedback form , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[14]  An-Chyau Haung,et al.  FAT-based adaptive sliding control for flexible arms: Theory and experiments , 2006 .

[15]  Ümit Özgüner,et al.  Sliding mode control of a class of underactuated systems , 2008, Autom..

[16]  Arjan van der Schaft,et al.  Dynamics and control of a class of underactuated mechanical systems , 1999, IEEE Trans. Autom. Control..

[17]  Thierry Floquet,et al.  Second‐order sliding mode control of underactuated mechanical systems I: Local stabilization with application to an inverted pendulum , 2008 .

[18]  Zhihong Man,et al.  Comments on "Adaptive multiple-surface sliding control for non-autonomous systems with mismatched uncertainties" , 2008, Autom..

[19]  Dan Wang,et al.  Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form , 2005, IEEE Transactions on Neural Networks.

[20]  An-Chyau Huang,et al.  Adaptive Control for Flexible-Joint Electrically Driven Robot With Time-Varying Uncertainties , 2007, IEEE Transactions on Industrial Electronics.

[21]  Petar V. Kokotovic,et al.  Locally optimal and robust backstepping design , 2000, IEEE Trans. Autom. Control..

[22]  Reza Olfati-Saber,et al.  Normal forms for underactuated mechanical systems with symmetry , 2002, IEEE Trans. Autom. Control..

[23]  Guido Herrmann,et al.  Neural Network Control of Nonlinear Time-Delay System with Unknown Dead-Zone and Its Application to a Robotic Servo System , 2010, FIRA RoboWorld Congress.

[24]  Jing Wang,et al.  Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems , 2002, IEEE Trans. Neural Networks.

[25]  An-Chyau Huang,et al.  Sliding control of non-linear systems containing time-varying uncertainties with unknown bounds , 2001 .