In the robotics field control laws taking into account the nonlinearities caused by the mechanical structure have been proposed, assuming that the drive system is linear. These control laws are well-adapted to the case of electric actuators. Electrohydraulics or electropneumatics drive systems introduce other nonlinearities coming both from the servo-valve and the actuator. In most cases these nonlinearities are neglected and the control laws usually used for these drive systems are based on a reduced third-order model obtained by a tangent linearization. A more satisfying solution is to introduce the nonlinearities of the drive system in the control law. This paper deals with the nonlinear control of an electropneumatic servodrive and is based on the nonlinear control theory in continuous time. It takes into account the main specific nonlinearities. The proposed control law consists of an exact input-output linearization via a static nonlinear state feedback. In our case, this control law leads to a one-dimensional unobservable subspace in closed-loop. A physical interpretation of this nonlinear control is given. This interpretation enables us to improve the understanding of the behavior of an electropneumatic servodrive. In order to compare the results obtained from an experimental device, the synthesis of a linear control law in discrete and continuous time is presented. A study in discrete time of the root locus versus position of the closed loop system with the linear control law, shows oscillations in the neighbourhood of the end of the actuator stroke. The experimental results confirm this fact. With nonlinear control these oscillations are suppressed.

The Einstein Equivalence Principle (EEP) is one of the foundations of the theory of General Relativity and several alternative theories of gravitation predict violations of the EEP. Experimental constraints on this fundamental principle of nature are therefore of paramount importance. The EEP can be split in three sub-principles: the Universality of Free Fall (UFF), the Local Lorentz Invariance (LLI) and the Local Position Invariance (LPI). In this paper we propose to use stable clocks in eccentric orbits to perform a test of the gravitational redshift, a consequence of the LPI. The best test to date was performed with the Gravity Probe A (GP-A) experiment in 1976 with an uncertainty of 1.4 × 10 −4 . Our proposal considers the opportunity of using Galileo satellites 5 and 6 to improve on the GP-A test uncertainty. We show that considering realistic noise and systematic effects, and thanks to a highly eccentric orbit, it is possible to improve on the GP-A limit to an uncertainty around (3−4)×10 −5 after one year of integration of Galileo 5 and 6 data.