Robust control using recursive design method for flexible joint robot manipulators

Abstract

A flexible joint robot manipulator can be regarded as a cascade of two subsystems: link dynamics and the motor dynamics. Using this structural characteristic, we propose a robust nonlinear recursive control method for flexible manipulators. The recursive design is done in two steps. First, a fictitious robust control for the link dynamics is designed as if it has a direct control input. As the fictitious control, a nonlinear H ∞ -control using energy dissipation is designed in the sense of 2 L -gain attenuation from the disturbance caused by uncertainties to performance. In the process, Hamilton-Jacobi (HJ) inequality is solved by a more tractable nonlinear matrix inequality (NLMI) method. In the second step, the other fictitious and the actual robust control are designed recursively by using the Lyapunov's second method. The proposed robust control is applied to a two-link robot manipulator with flexible joints in computer simulations. The simulation results show that the proposed robust control has robustness to the model uncertainty caused by changes in the link inertia and the joint stiffness.

Position analysis and nonlinear phenomena of flexible manipulator with generic payload mounted on a moving base

“…The approximate solution is being validated with the findings obtained numerically using time responses, and phase portrait at three critical points C, G, D marked in frequency response characteristics for the primary resonance in Figure 10. The results obtained analytically are in good agreement with those obtained by numerically integrating equation (13).…”

“…In the nonlinear and control analysis, Yeon et al. 13 proposed a robust control using recursive design method for robot manipulators with flexible joints. The performance of the proposed control has been verified through simulations with uncertainty in the inertia and joint stiffness.…”

Backstepping Control for Flexible Joint with Friction Using Wavelet Neural Networks and L2‐Gain Approach

“…Þ is the nominal value of Ξ 1 , and α 1 is a positive gain. Combining (9) and (3a) yields the closedloop link dynamics as…”

“…It is generally known that a servo system contains unknown nonlinear functions, that is, geometric and physical parameter deviations, model uncertainties, unmeasured states and external disturbance, which are modeled as loss of effectiveness. In order to solve the problem of model uncertainty and external disturbance of a flexible joint, adaptive control strategy , higher‐order differential feedback control , adaptive sliding mode control , and a robust H ∞ control have been applied. Chang investigated a robust tracking controller for uncertain flexible‐joint robots with time delays and time‐varying perturbations.…”

Modeling Single Flexible Link Using Hardware Description Language

“…For instance, finite element is employed in [22] and lumped mass model is used in [23], models employed depend on requirements in complexity, accuracy, or simulation time. Verity of controllers types are designed such as optimal [24], robust [25], and classical [26].…”