Robust dynamic state feedback for underactuated systems with linearly parameterized disturbances

This article investigates the control problem for underactuated port‐controlled Hamiltonian systems with multiple linearly parameterized additive disturbances including matched, unmatched, constant, and state‐dependent components. The notion of algebraic solution of the matching equations is employed to design an extension of the interconnection and damping assignment passivity‐based control methodology that does not rely on the solution of partial differential equations. The result is a dynamic state‐feedback that includes a disturbance compensation term, where the unknown parameters are estimated adaptively. A simplified implementation of the proposed approach for underactuated mechanical systems is detailed. The effectiveness of the controller is demonstrated with numerical simulations for the magnetic‐levitated‐ball system and for the ball‐on‐beam system.

[1]  Enrico Franco,et al.  IDA-PBC with adaptive friction compensation for underactuated mechanical systems , 2019, Int. J. Control.

[2]  Safya Belghith,et al.  Robustness enhancement of IDA-PBC controller in stabilising the inertia wheel inverted pendulum: theory and real-time experiments , 2018, Int. J. Control.

[3]  Alessandro Astolfi,et al.  Robust balancing control of flexible inverted-pendulum systems , 2018, Mechanism and Machine Theory.

[4]  Enrico Franco,et al.  Adaptive IDA‐PBC for underactuated mechanical systems with constant disturbances , 2018, International Journal of Adaptive Control and Signal Processing.

[5]  Damiano Rotondo,et al.  State estimation and decoupling of unknown inputs in uncertain LPV systems using interval observers , 2018, Int. J. Control.

[6]  Lei Guo,et al.  Global output regulation for a class of single input Port-controlled Hamiltonian disturbed systems , 2018, Appl. Math. Comput..

[7]  Mutaz Ryalat,et al.  A Robust IDA-PBC Approach for Handling Uncertainties in Underactuated Mechanical Systems , 2018, IEEE Transactions on Automatic Control.

[8]  Romeo Ortega,et al.  Robust integral action of port-Hamiltonian systems , 2018, ArXiv.

[9]  Wenjing Xie,et al.  A simple robust control for global asymptotic position stabilization of underactuated surface vessels , 2017 .

[10]  José Ángel Acosta,et al.  Stability of active disturbance rejection control for uncertain systems: A Lyapunov perspective , 2017 .

[11]  Bruno Siciliano,et al.  Robust IDA‐PBC for underactuated mechanical systems subject to matched disturbances , 2017 .

[12]  Richard H. Middleton,et al.  Integral Control of Port-Hamiltonian Systems: Nonpassive Outputs Without Coordinate Transformation , 2017, IEEE Transactions on Automatic Control.

[13]  Zhitao Liu,et al.  A new family of interconnection and damping assignment passivity‐based controllers , 2017 .

[14]  Romeo Ortega,et al.  Shaping the Energy of Mechanical Systems Without Solving Partial Differential Equations , 2016, IEEE Transactions on Automatic Control.

[15]  Yuh Yamashita,et al.  Vibration suppression for mass‐spring‐damper systems with a tuned mass damper using interconnection and damping assignment passivity‐based control , 2016 .

[16]  Leyla Goren-Sumer,et al.  Some results on disturbance attenuation for Hamiltonian systems via direct discrete‐time design , 2015 .

[17]  Mutaz Ryalat,et al.  Integral IDA-PBC and PID-like control for port-controlled Hamiltonian systems , 2015, 2015 American Control Conference (ACC).

[18]  Romeo Ortega,et al.  On the matching equations of energy shaping controllers for mechanical systems , 2015, Int. J. Control.

[19]  Romeo Ortega,et al.  Robust energy shaping control of mechanical systems , 2013, Syst. Control. Lett..

[20]  Alessandro Astolfi,et al.  Constructive Interconnection and Damping Assignment for Port-Controlled Hamiltonian Systems , 2013, IEEE Transactions on Automatic Control.

[21]  Rafael Kelly,et al.  Interconnection and damping assignment passivity‐based control of a class of underactuated mechanical systems with dynamic friction , 2011 .

[22]  Romeo Ortega,et al.  Constructive immersion and invariance stabilization for a class of underactuated mechanical systems , 2010, Autom..

[23]  Dong Eui Chang,et al.  The method of controlled Lagrangians: Energy plus force shaping , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[24]  Alessandro Astolfi,et al.  Dynamic scaling and observer design with application to adaptive control , 2009, Autom..

[25]  Yuri Orlov,et al.  Hybrid Sliding-Mode-Based Control of Underactuated Systems With Dry Friction , 2008, IEEE Transactions on Industrial Electronics.

[26]  Alessandro Astolfi,et al.  Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes , 2007, IEEE Transactions on Automatic Control.

[27]  A. Astolfi,et al.  Further constructive results on interconnection and damping assignment control of mechanical systems: the acrobot example , 2006, 2006 American Control Conference.

[28]  Naomi Ehrich Leonard,et al.  Controlled Lagrangian Systems with Gyroscopic Forcing and Dissipation , 2004, Eur. J. Control.

[29]  Romeo Ortega,et al.  Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment , 2002, IEEE Trans. Autom. Control..

[30]  R. Ortega,et al.  The matching conditions of controlled Lagrangians and IDA-passivity based control , 2002 .

[31]  Alessandro Astolfi,et al.  Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[32]  Naomi Ehrich Leonard,et al.  Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem , 2000, IEEE Trans. Autom. Control..

[33]  Mutaz Ryalat,et al.  A simplified IDA-PBC design for underactuated mechanical systems with applications , 2016, Eur. J. Control.

[34]  Paul Kotyczka,et al.  Overcoming the Dissipation Condition in Passivity-based Control for a class of mechanical systems , 2014 .

[35]  Mohamed Becherif,et al.  STABILITY AND ROBUSTNESS OF DISTURBED-PORT CONTROLLED HAMILTONIAN SYSTEMS WITH DISSIPATION , 2005 .

[36]  Alessandro Astolfi,et al.  Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one , 2004, Proceedings of the 2004 American Control Conference.

[37]  Arjan van der Schaft,et al.  Physical Damping in IDA-PBC Controlled Underactuated Mechanical Systems , 2004, Eur. J. Control.

[38]  Alberto Isidori,et al.  Nonlinear control systems: an introduction (2nd ed.) , 1989 .