Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes

Viola, G.; Banavar, Ravi N.; Acosta, José Ángel; Astolfi, Alessandro

doi:10.1007/978-3-540-73890-9_11

Cited by 23 publications

(46 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Limiting the algebraic solution to the potential‐energy PDE simplifies the control law (37) and preserves the mechanical structure of the closed‐loop system (32) on the extended state space. Notably, while the kinetic‐energy PDE can be reduced to ordinary differential equations or to algebraic equations for different classes of systems under some assumptions, 4,37 this is not the case for the potential‐energy PDE. Finally, the disturbance compensation controller (40) can in principle be used with different definitions of algebraic solution besides the one proposed in (35).…”

Section: Underactuated Mechanical Systemsmentioning

confidence: 99%

Robust dynamic state feedback for underactuated systems with linearly parameterized disturbances

Franco

Baena

Astolfi

2020

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

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. K E Y W O R D Sadaptive control, disturbance rejection, mechanical systems, passivity-based control, underactuated systems 1 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. 4112wileyonlinelibrary.com/journal/rnc Int J Robust Nonlinear Control. 2020;30:4112-4128.FRANCO et al. 4113A further aspect of energy shaping control that has been attracting increasing attention is robustness to disturbances, which are common to most practical application. Notable results in this area include the study of viscous friction within the controlled Lagrangians formulation, 12,13 and of continuous and smooth physical dissipation within the IDA-PBC framework, 14,15 while friction according to the Dahl model affecting the actuated part of the state was considered in Reference 16. Stability and robustness of disturbed PCH systems with dissipation were investigated in Reference 17. The robust energy shaping control of fully actuated mechanical systems with disturbances was presented in Reference 18, while disturbance attenuation for discrete-time systems was studied in Reference 19. More recently, integral IDA-PBC designs that rely on the classical solution of the PDE were proposed in References 20-22 for a class of underactuated mechanical systems with constant matched disturbances (ie, those affecting the actuated part of the state), and in Reference 23 for bounded matched disturbances. The result in Reference 21 was extended to unmatched constant disturbances in Reference 24, which, however, is only applicable to mechanical systems with constant inertia matrix. The case of nonconstant inertia matrix and variable but bounded disturbances was considered in Reference 25. In addition, the adaptive compensation of constant disturbances within energy shaping control was attempted in References 26,27: while the former still requires solving the PDE, the latter is confined to a limited class of mechanical systems. Besides energy shaping, a sliding mode control for a class of underactuated systems with dry friction was presented in Ref...

show abstract

Section: Underactuated Mechanical Systemsmentioning

confidence: 99%

Robust dynamic state feedback for underactuated systems with linearly parameterized disturbances

Franco

Baena

Astolfi

2020

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

“…is nonzero, seriously complicating the kinetic energy PDE. In [3], a coordinate transformation is proposed such that the PDEs become solvable. Applying the technique developed in [3], we can derive the solution obtained in [6] without partial feedback linearization.…”

Section: B Controller Designmentioning

confidence: 99%

“…The success of the method is limited by the possibility of solving two partial differential equations (PDEs) which identify the kinetic and potential energy functions that can be assigned to the closed-loop. Therefore, current research focusses on developing methods that make IDA-PBC applicable to a broader class of systems; especially [3] shows encouraging progress on the matter, making it possible to derive state-feedback controllers for the Inverted Pendulum on a Cart and the Furuta Pendulum.…”

Section: Introductionmentioning

confidence: 99%

An experimental application of Total Energy Shaping Control: Stabilization of the inverted pendulum on a cart in the presence of friction

Burg

Scherpen

Acosta³

et al. 2007

2007 European Control Conference (ECC)

View full text Add to dashboard Cite

In this paper we report the experimental application of a state-feedback controller derived via the principles of Total Energy Shaping Control for the stabilization of underactuated mechanical systems. The particular application concerns the well-known inverted pendulum on a cart. We describe the first steps taken towards global stabilization of the inverted pendulum with Total Energy Shaping Control. The results show that performance of the nonlinear controller in the neighborhood of the equilibrium position is better compared to a linear H-infinity controller, since the transients are smoother and there is less overshoot. Furthermore, it is shown that the energy shaping controller has a great tuning potential that allows proper functioning of the closed-loop system in the presence of friction. This paper is intended to be the starting point in the development of tools that enable the control engineer to make deliberate choices in tuning the energyshaping controller, based on performance in the presence of friction and in a later stage also for parameter uncertainties, input constraints and other issues that are relevant in a practical environment.

show abstract

“…In order to simplify the PDE problem Viola et al (2007) have introduced a change of coordinates and a modification of the target dynamics. With the objective to completely avoid PDEs, the following leading methods have been proposed: constructive procedures (Donaire et al, 2016a;Borja et al, 2016;Romero et al, 2017), implicit port-Hamiltonian representation (Macchelli, 2014;Castaños and Gromov, 2016) and an algebraic approach Batlle et al, 2007;Nunna et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

Algebraic IDA-PBC for Polynomial Systems with Input Saturation: An SOS-based Approach

Cieza

Reger

2019

View full text Add to dashboard Cite

The necessity to deal with partial differential equations (PDEs) and the dissipation condition are the mainadversities in the application of Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC). Recently,an algebraic solution of IDA-PBC has been explored for a class of affine polynomial systems by using sum of squares(SOS) and semidefinite programming (SDP). In this work, we extend the previous method by incorporating actuatorsaturation (AS) and two minimization objectives in the SDP. Our results are validated on two polynomial systems.

show abstract

Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes

Cited by 23 publications

References 13 publications

Robust dynamic state feedback for underactuated systems with linearly parameterized disturbances

Robust dynamic state feedback for underactuated systems with linearly parameterized disturbances

An experimental application of Total Energy Shaping Control: Stabilization of the inverted pendulum on a cart in the presence of friction

Algebraic IDA-PBC for Polynomial Systems with Input Saturation: An SOS-based Approach

Contact Info

Product

Resources

About