An Energy-Based Nonlinear Control for a Two-Link Flexible Manipulator

Abstract

In this paper, we propose an energy-based nonlinear control for a two-link flexible manipulator. As it is well known, the two-link flexible manipulator is an underactuated system that provides a challenge to control engineers and researchers. Recently, many new control theories and methods are being explored to design controllers for underactuated systems in order to control them more effectively. Among these methods, the energy-based control design method has gained much attention. This method can provide more physical insights in nonlinear control as well as provide a direct candidate for the Lyapunov function, which is very important for proving the stability of closed-loop systems. Especially, the portcontrolled Hamiltonian system and generalized canonical transformation have some advantages over the modeling and control design of nonlinear systems. Therefore, we have chosen to study how to control the two-link flexible manipulator via generalized canonical transformation. Both simulation and experimental results are provided to demonstrate the effectiveness of the controllers.

Infinite dimensional model of a double flexible-link manipulator: The Port-Hamiltonian approach

“…Take the two beams' equations (37) and the nonlinear equations of the boundary conditions (22), and using of the power preserving interconnections (24), define the total system:…”

“…In a similar manner, also the single flexible link manipulator model has been expressed as an infinite dimensional PH system [23]. A juncture element between the previous literature on flexible robot modelling and the PH framework could be found in [24]. Instead of the infinite dimensional boundary valued problem proposed in [23], the authors of [24] propose a finite dimensional model described by a set of nonlinear ODEs derived with Lagrangian equations from the discretized energy of the manipulator.…”

“…A juncture element between the previous literature on flexible robot modelling and the PH framework could be found in [24]. Instead of the infinite dimensional boundary valued problem proposed in [23], the authors of [24] propose a finite dimensional model described by a set of nonlinear ODEs derived with Lagrangian equations from the discretized energy of the manipulator. The aim of this paper is to use the PH formalism to derive a control ori-ented and physically meaningful model of the double flexible-links manipulator for spatial applications, as the Canadarm2 mounted on the International Space Station (ISS) showed in Figure (1).…”

“…Define the pure elastic element (36) and connect it at the end of the elements' chain to change the tip causality and obtain a discretized clamped-clamped beam (37). Interconnect two discretized beam equations (37) to the finite dimensional part of the original model (22) through the energy preserving laws(24), such to obtain the PH PDEs-ODEs finite dimensional model (38).System (38) has been obtained through a structure preserving mixed finite element discretization procedure, instead of the CMST used in the modelling procedure of the existing works[1,24,27]. The CMST allows to derive light models in terms of number of states, but the modes choice highly depends on the operating scenario of the manipulator, i.e.…”

Review of modelling and control of flexible-link manipulators

“…An energy-based control method for TLFMs was proposed. 125 The authors expressed the TLFM as a portcontrolled Hamiltonian system and derived a non-linear control law using generalised canonical transformations. Several researchers studied passivity-based methods for robust control of FLMs.…”