A robust linear controller for flexible joint manipulators

Abstract

AbstracI-In this paper a new and completely linear algorithm is proposed for composite robust control of flexible joint robots. Maraver, the robust stability of the closed loop system in presence of structured and unstructured uncertainties is analyzed. To introduce the idea, flexible joint robot aith structured and unstructured uncertainties is modelled and converted into singular perturbation form. A robust linear control algorithm is proposed toor the slow dynamics and its robust stability conditions are derived using Thikhonov's theorem. Then the robust stability of the total system considering the porposed composite controller is analyzed, and sufftcient conditions for robust stability of system is obtained. Finally the elktiveness of the proposed controller is verified through simulations. It is shown that not only the tracking performance of the proposed controller is very suitable, but also the actuator effort is much smaller than previous result.

Fuzzy error governor: A practical approach to counter actuator saturation on flexible joint robots

“…A filter is used to estimate _ uðtÞ from u(t) so that the only required measurement would be u(t). As mentioned in the previous section the composite controller composed of a fast PD controller and a slow PID controller has been shown to be robustly stable in absence of actuator limitation [21,23]. The robust stability of the system after adding a fuzzy supervisor and under the effect of the term k(t), will be studied in this paper at the following section.…”

“…Theorem 1. The fast subsystem, (23), with the matrix A f introduced in (26) is stable provided that the lower bounds on k; _ k and conditions on K PF and K DF stated in Appendix I are met.…”

“…Now for the stability analysis, differentiate V along trajectories (22) and (23). This yields to _ Vðx…”

“…[21,22] have discussed the stability of a composite control law consisting of a PID action on link position error and a PD action on the joint torque in addition to a correcting term. Authors have later removed the correcting term and have presented a new proof in [23]. No one of the mentioned references have considered actuator limitation.…”

A Survey on the Control of Flexible Joint Robots

“…Two more advanced versions of these works can be found in [141,142]. The authors have recently published a simpler version in which the integral manifold term has been skipped over and a new analysis and stability proof on it has been presented [143,144]. Moreover, a composite controller structure, using a linear H ∞ controller for the rigid part in the presence of actuator saturation was proposed in [15].…”