Overcoming the Dissipation Condition in Passivity-based Control for a class of mechanical systems

Abstract

A well-known problem in the application of the Interconnection and Damping Assignment technique for the stabilization of underactuated mechanical systems is dissipation in unactuated coordinates, since it may impede the definiteness requirements for the closed-loop system. Recently, the expansion of the closed-loop Hamiltonian function by a cross term between coordinates and momenta has been explored showing promising results. However, the large number of free parameters is an issue for the tuning of the closed-loop system, and the solution of the matching partial differential equations (PDEs) remains a difficult task. In this work, we aim at giving the closed-loop augmented Hamiltonian more structure in order to simplify the controller parametrization. The result is desired behavior at the equilibrium avoiding the solution of PDEs. Simulations and experiments demonstrate the applicability of the method.

IDA-PBC with adaptive friction compensation for underactuated mechanical systems

“…While control via energy shaping is inherently robust to disturbances, the practical importance of friction in underactuated mechanical systems has motivated a considerable stream of research. The effect of viscous friction was studied within the CL approach by (Chang, 2010;Woolsey et al, 2004), while continuous and linear friction forces were considered in IDA-PBC by (Delgado & Kotyczka, 2014;Gómez-Estern & Van der Schaft, 2004). Furthermore, the compensation of nonlinear and discontinuous friction forces on actuated joints was investigated in (Ryalat & Laila, 2016;Sandoval, Kelly, & Santibáñez, 2011;Zhang & Liu, 2016).…”

An Adaptive Controller Based on Interconnection and Damping Assignment Passivity-Based Control for Underactuated Mechanical Systems: Application to the Ball and Beam System

“…In addition, the influence of viscous friction was studied by using the controlled Lagrangian method [26], and the closed-loop system was more stable. In [27], the IDA-PBC strategy was used to analyze continuous friction.…”

Robust dynamic state feedback for underactuated systems with linearly parameterized disturbances

“…A 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 . Stability and robustness of disturbed PCH systems with dissipation were investigated in Reference .…”