Parameter-Dependent Lyapunov Functions for Linear Systems With Constant Uncertainties

Robust stability of linear time-invariant systems with respect to structured uncertainties is considered. The small gain condition is sufficient to prove robust stability and scalings are typically used to reduce the conservatism of this condition. It is known that if the small gain condition is satisfied with constant scalings then there is a single quadratic Lyapunov function which proves robust stability with respect to all allowable time-varying perturbations. In this technical note we show that if the small gain condition is satisfied with frequency-varying scalings then an explicit parameter dependent Lyapunov function can be constructed to prove robust stability with respect to constant uncertainties. This Lyapunov function has a rational quadratic dependence on the uncertainties

A Passivity-based Nonlinear Admittance Control with Application to Powered Upper-limb Control under Unknown Environmental Interactions

This paper presents an admittance controller based on the passivity theory for a powered upper-limb exoskeleton robot which is governed by the nonlinear equation of motion. Passivity allows us to include a human operator and environmental interaction in the control loop. The robot interacts with the human operator via F/T sensor and interacts with the environment mainly via end-effectors. Although the environmental interaction cannot be detected by any sensors (hence unknown), passivity allows us to have natural interaction. An analysis shows that the behavior of the actual system mimics that of a nominal model as the control gain goes to infinity, which implies that the proposed approach is an admittance controller. However, because the control gain cannot grow infinitely in practice, the performance limitation according to the achievable control gain is also analyzed. The result of this analysis indicates that the performance in the sense of infinite norm increases linearly with the control gain. In the experiments, the proposed properties were verified using 1 degree-of-freedom testbench, and an actual powered upper-limb exoskeleton was used to lift and maneuver the unknown payload.Comment: Accepted in IEEE/ASME Transactions on Mechatronics (T-MECH

Robust design of a passive wind turbine system

The effectiveness of full passive Wind Turbine (WT) systems has been recently demonstrated. Such low cost and reliable structures without active control and with a minimum number of sensors can be efficient only if the system design parameters are mutually adapted through an integrated optimal design approach. Even if there is a good agreement between theoretical design models and an experimental prototype, it is relevant to evaluate the WT efficiency with respect to design variable variations. Thus, this work is devoted more specifically to the sensitivity analysis of a passive WT system according to electrical variable variations of the Permanent Magnet Synchronous Generator (PMSG). It also investigates the interest of a robust design approach for reducing the sensitivity of the WT efficiency to specific variable variations