Kinematic analysis of complex gear mechanisms

This paper presents a general kinematic analysis method for complex gear mechanisms. This approach involves the null-space of the adjacency matrix associated with the graph of the mechanism weighted by complex coecients. It allows to compute the rotational speed ratios of all the links and the frequency of all the contacts in this mechanism(including roll bearings). This approach is applied to various examples including a two degrees of freedom car differential

The impact of local masses and inertias on the dynamic modelling of flexible manipulators

After a brief review of the recent literature dealing with flexible multi-body modelling for control design purpose, the paper first describes three different techniques used to build up the dynamic model of SECAFLEX, a 2 d.o.f. flexible in-plane manipulator driven by geared DC motors : introduction of local fictitious springs, use of a basis of assumed Euler-Bernouilli cantilever-free modes and of 5th order polynomial modes. This last technique allows to take easily into account local masses and inertias, which appear important in real-life experiments. Transformation of the state space models obtained in a common modal basis allows a quantitative comparison of the results obtained, while Bode plots of the various interesting transfer functions relating input torques to output in-joint and tip mea-surements give rather qualitative results. A parametric study of the effect of angular configuration changes and physical parameter modifications (including the effect of rotor inertia) shows that the three techniques give similar results up to the first flexible modes of each link when concentrated masses and inertias are present. From the control point of view, “pathological” cases are exhibited : uncertainty in the phase of the non-colocated transfer functions, high dependence of the free modes in the rotor inertia value. Robustness of the control to these kinds of uncertainties appears compulsory

Flexible joint control : robustness analysis of the collocated and non-collocated feedbacks

In this paper, we propose a discussion on the robustness and performance properties of a proportional-derivative controller applied to a very flexible joint. Because of the flexible mode due to in-joint compliance, the classical collocated control does not allow to obtain good rigid mode dynamics with a correct phase margin in low and high frequency, and the non-collocated control does not allow to damp correctly the rotor mode. The simultaneous analysis of discrete root loci and Nichols plots leads to a phase control law with a derivative term built from both input and output velocities. Simulations taking into account various real non-linearities and measurement imperfections are proposed to validate this improved control design

Gain-scheduling through continuation of observer-based realizations-applications to H∞ and μ controllers

The dynamic behavior of gain scheduled controllers is highly depending on the state-space representations adopted for the family of lienar controllers designed on a set of operating conditions. In this paper, a technique for determining a set of consistent and physically motivated linear state-space transformations to be applied to the original set of linear controllers is proposed. After transformation, these controllers exhibits an-observer-based structure are therefore easily interpolted and implemented

Linear dynamic modeling of spacecraft with various flexible appendages and on-board angular momentums

We present here a method and some tools developed to build linear models of multi-body systems for space applications (typically satellites). The multi-body system is composed of a main body (hub) fitted with rigid and flexible appendages (solar panels, antennas, propellant tanks,...) and on-board angular momentums (flywheels, control moment gyros). Each appendage can be connected to the hub by a cantilever joint or a pivot joint. More generally, our method can be applied to any open mechanical chain. In our approach, the rigid six degrees of freedom (d.o.f) (three translational and three rotational) are treated all together. That is very convenient to build linear models of complex multi-body systems. Then, the dynamics model used to design AOCS, i.e. the model between forces and torques (applied on the hub) and angular and linear position and velocity of the hub, can be derived very easily. This model can be interpreted using block diagram representation

Unstationnary control of a launcher using observer-based structures

This paper deals with the design of a gain-scheduled controller for the attitude control of a launcher during atmospheric flight. The design is characterized by classical requirements such as phase/gain margins and flexible mode attenuations as well as time-domain constraints on the response of angle of attack to a worstcase wind profile. Moreover, these requirements must be fulfilled over the full atmospheric flight envelope and must be robust against parametric uncertainties. In order to achieve this goal, we propose a method based on minimal observer-based realizations of arbitrary stabilizing compensators. An original technique to assign the closed-loop dynamics between the state-feedback dynamics and the state-estimation dynamics is presented for the H∞ compensators case. The structure is used to mix various specifications through the Cross Standard Form(CSF) and to perform a smooth gain scheduling interpolation through an Euler-Newton algorithm of continuation

Impedance active control of flight control devices

The work presented in this paper concerns the active control of flight control devices (sleeves, yokes, side-sticks, rudder pedals,...). The objective is to replace conventional technologies by active technology to save weight and to feedback kinesthetic sensations to the pilot. Some architectures are proposed to control the device mechanical impedance felt by pilot and to couple pilot and co-pilot control devices. A first experimental test-bed was developed to validate and illustrate control laws and theirs limitations due to dynamic couplings with the pilot own-impedance

Introduction to Kalman Filtering

This document is an introduction to Kalman optimal Filtering applied to linear systems. It is assumed that the reader is already aware of linear servo-loop theory, frequency-domain Filtering (continuous and discrete-time) and state-space approach to represent linear systems. Generally, Filtering consists in estimating a useful information (signal) from a measurement (of this information) perturbed by a noise. Frequency-domain Filtering assumes that a frequency-domain separation exists between the frequency response of the useful signal and the frequency response of the noise. Then, frequency-domain Filtering consists in seeking a transfer function fitting a template on its magnitude response (and too much rarely, on its phase response). Kalman optimal filtering aims to estimate the state vector of a linear system (thus, this state is the useful information) and this estimate is optimal w.r.t. an index performance: the sum of estimation error variances for all state vector components. First of all, some backgrounds on random variables and signals are required then, the assumptions, the structure and the computation Kalman Filter could be introduced. In the first chapter, we remind the reader how a random signal can be characterized from a mathematical point of view. The response of a linear system to a random signal will be investigated in an additional way to the more well-known response of a linear system to a deterministic signal (impulse, step, ramp, ... responses). In the second chapter, the assumptions, the structure, the main parameters and properties of Kalman Filter will be defined. The reader who wish to learn tuning methodology of the Kalman filtering can directly start the reading at chapter 2. But the reading of chapter 1, which is more cumbersome from a theoritical point of view, is required if one wishes to learn basic principles in random signal processing, on which is based Kalman Filtering. There are many applications of Kalman Filtering in aeronautics and aerospace engineering. As Kalman filter provides an estimate of plant states from an a priori information of the plant behaviour (model) and from real measurement, Kalman Filter will be used to estimate initial conditions (ballistics), to predict vehicle position and trajectory (navigation) and also to implement control laws based on a state feedback and a state estimator (LQG: Linear Quadratic Gaussian control). The signal processing principles on which is based Kalman Filter will be also very useful to study and perform test protocols, experimental data processing and also parametric identification, that is the experimental determination of some plant dynamic parameters

De l'utilisation de la structure estimation/commande pour le pilotage instationnaire d'un lanceur spatial

Dans cet article, nous nous intéressons au développement de techniques ayant trait à la mise sous forme LQG équivalente de correcteurs stabilisants. Dans un premier temps nous nous concentrerons plus particulièrement sur la transformation de correcteurs issus d'une synthèse Hinfinty. Nous proposons une méthode originale pour effectuer le choix des dynamiques d'estimation et de commande du correcteur équivalent en s'appuyant sur les résultats d'une synthèse H2. Puis nous proposerons une définition en temps discret de la Forme Standard de Passage (CSF) qui s'appuie également sur la paramétrisation de Youla sur la structure estimation /commande. Nous la présenterons en tant qu'outil méthodologique pour la mise en forme d'un problème multi-objectif. Nous mettrons en application la CSF sur le problème de pilotage d'un lanceur et nous montrerons l'intérêt de l'utilisation de la structure estimation/commande dans le cadre de l'inter-polation de correcteur pour le pilotage instationnaire

Cross Standard Form for generalized inverse problem: application to lateral flight control of a highly flexible aircraft

This paper introduces the Cross Standard Form (CSF) which can be considered as a generalization of the LQ inverse problem to the H2 and H infinity inverse problems. The CSF allows to formulate a standard problem on which an initial compensator can be obtained by H infinity or H2 synthesis. The definition of the CSF is based on the possibility to construct equivalent observer-based realization of a given compensator. From the robust control application point of view, the general idea is to apply the CSF to a first compensator satisfying nominal performances to initialize a H infinity procedure in order to handle frequency-domain or parametric robustness specifications. These state observer based tools are then applied to design lateral flight control of a highly flexible aircraft