Franck Cazaurang

Brief paper: Motion planning for flat systems using positive B-splines: An LMI approach

In this paper, the motion planning problem is studied for nonlinear differentially flat systems using B-spline parameterization of the flat output history. In order to satisfy the constraints continuously in time, the motion planning problem is transformed into a B-spline positivity problem. The latter problem is formulated as a convex semidefinite programming problem by means of a non-negative piecewise polynomial function description based on sum of squares decomposition. The contribution of the paper is thus a one-step design procedure for motion planning that satisfies constraints continuously in time where usual B-spline and collocation techniques need post-analysis. Finally, an example of flexible link manipulator motion is presented to illustrate the overall approach.

Modelling of Longitudinal Disturbed Aircraft Model by Flatness Approach

In this paper, an LFT model representing the longitudinal dynamic of the gap between the open loop nominal of an Hight Incidence aircraft Research model named HIRM+ and the disturbed model on a trajectory is given. Five of the most relevant uncertainties on pitch axis are considered. This model describes the gap along a trajectory passing through flight condition FC1, with an angle of attack equal to 6 - . The proposed approach is based on a simplified longitudinal model used to determine a nominal trajectory and corresponding input. The specific outputs are angle of attack fi and pitch angle µ. These outputs allow a parameterisation of state-space trajectory. First the LFT generation by flatness approach is described. Then an LFT model of the open loop model for the above flight condition is given. Thereafter an LFT model of closed loop HIRM+RIDE is proposed to allow the identification of worst case stability margin.

Fault diagnosis in induction machines using the generalized structured singular value

Abstract A model-based approach for off-line fault diagnosis in induction machines is presented. The class of faults to be diagnosed is restricted to broken rotor bars, asymmetry in the rotor cage and asymmetry in the stator, arising due to an inter-turn fault resulting in an opening or shorting of one or more circuits of stator phase windings. The method is based on model invalidation tools and H ∞ /μ -framework models. The experimental model consists of a nominal model estimated by means of a subspace identification algorithm, together with linear fractional norm-bounded perturbations and norm-bounded unknown inputs.

Robust Control of Flat Nonlinear System

Abstract This paper proposes a systematic approach for robust tracking control design of a class of nonlinear systems, refered to dynamic flat systems. First, a nonlinear dynamic feedback is designed to ensure nominal path tracking performance. Next, a compact set of models is elaborated in the vicinity of the nominal path, taking into account both state space disturbances and parametric uncertainties. Finally, a robust linear controller is designed which guarantees the path tracking perfomance objectives for the above so-obtained compact set. Simulations results obtained from speed control of a synchronous actuator demonstrate the potential of the proposed approach.

Robust tracking of nonlinear MIMO uncertain flat systems

This work investigates the problem of robust trajectory tracking of a class of uncertain multi-input/multi-output (MIMO) nonlinear systems. A robust tracking control methodology for such systems using flatness theory is suggested. First, it is shown how feasible desired state-space and the associated nominal control input trajectory are generated by an exosystem subject to reference signal. This signal corresponds to the flat outputs. Next, nonlinear error model due to exogenous disturbance and parametric uncertainties is characterized; using flatness property. A first order linearization is performed along the nominal trajectory to obtain a linear parameter varying (LPV) model. Furthermore, LPV techniques are applied to design a gain-scheduled control system based on user defined performance specifications. Finally, simulation results are presented to demonstrate the effectiveness of the proposed techniques.

ON THE DESIGN OF A FLATNESS-BASED GUIDANCE ALGORITHM FOR THE TERMINAL AREA ENERGY MANAGEMENT OF A WINGED-BODY VEHICLE

This paper suggests a flatness theory-based guidance scheme dedicated to the Terminal Area Energy Management (TAEM) guidance of a Reusable Launch Vehicle. The suggested guidance strategy is based on a Nonlinear Dynamic Inversion (NDI) by flatness approach adapted to the large flight envelope that characterizes the RLV reentry. By this way, after having demonstrated the flatness property of the coupled in-plane and out-of-plane vehicle dynamics, a linear tracking controller is added to the flat model so as to circumvent off-nominal flight conditions. Eventually, the robustness and performances of the considered TAEM guidance scheme are assessed using Monte Carlo simulations under a dedicated simulation tool.

On the computation of π-flat outputs for linear time-varying differential-delay systems

Abstract We introduce a new definition of π -flatness for linear differential-delay systems with time-varying coefficients. We characterize π - and π -0-flat outputs and provide an algorithm to efficiently compute such outputs. We present an academic example of motion planning to discuss the pertinence of the approach.

Model-based fault detection and isolation design for flight-critical actuators in a harsh environment

Safety-impact on flight-critical systems such as flight or engine control systems is a major concern for aircraft equipment designers in civil and military fields. Current avionic equipments related to safety-critical systems are able to detect trivial faults such as loss of power, short circuits, open circuits or threshold overflow. The occurrence of these faults in actuator control loops, if detected, triggers a fail-safe mode. So, although system availability is reduced, the required safety level can still be ensured. This paper emphasizes a design methodology of nonlinear model-based FDI1 algorithms applied to a Hybrid Stepper Motor (HSM). The proposed design methodology combines a nonlinear dynamic inversion and residual generation using standard continuous Kalman Filter. The proposed fault detection method is based on residual mean-checking analysis, where the parameters are tuned with Kriging method.

LPV Modeling of Atmospheric Re-entry Demonstrator for Guidance Re-entry Problem

This paper describes the status of an on-going research work and investigates the problem of entry guidance of the Atmospheric Re-entry Demonstrator (ARD). We propose an entry guidance scheme that uses the flatness property. First, it is shown that the longitudinal dynamics of the ARD is flat and by using flatness property a feasible desired output and the associated nominal control input trajectory are easily generated. Next, a methodology to construct a nonlinear error model, which describes the dynamics of the trajectory tracking error, is derived using coordinate transformations of the flat outputs. A first order linearization of the nonlinear error model is performed along the nominal trajectory in order to formulate the nonlinear ARD longitudinal dynamics as Linear Parameter Varying (LPV) model. LPV control design techniques can then be used to construct the global control law guaranteeing stability and performance.

Dynamic inversion of a Flight Critical actuator for fault diagnosis

Flight-Critical Systems (FCS) integrate usually actuators such as Electro Mechanical Actuators (EMA) controlled by Electronic Engine Control Units (EECU) or Flight Control Units (FCU). They are designed and developed regarding drastic safety requirements. Material Redundancy is therefore a safe design but requires an important amount of space, weight and costs. In this paper, observer-based fault detection methods are applied to a hybrid stepper motor (HSM) nonlinear model. First, state estimations are processed with an Extended Kalman Filter (EKF). After showing that the model is differentially flat, a nonlinear dynamic inversion (NLDI) is applied to the model in order to find its equivalent linear system. A Standard Kalman Filter (SKF) is then applied for fault detection. Faults due to short-circuits in the stator windings are considered.