Gilles Duc

An LMI approach to dencentralized H8 control

We consider the design of a decentralized controller for a linear time invariant (LTI) system. This system is modelled as an interconnection of subsystems. For every subsystem, a linear time invariant controller is sought such that the overall closed loop system is stable and achieves a given H performance level. The main idea is to design every local controller such that the corresponding closed loop subsystem has a certain input-output (dissipative) property. This local property is constrained to be consistent with the overall objective of stability and performance. The local controllers are designed simultaneously, avoiding the traditional iterative process: both objectives (the local one and the global one) are achieved in one shot. Applying this idea leads us to solving the following new problem: given an LTI system, parameterize all the dissipative properties which can be achieved by feedback. The proposed approach leads to solving convex optimization problems that involve linear matrix inequality constraints.

Aerospace launch vehicle control: a gain scheduling approach

This paper presents a methodology for designing an aerospace launch vehicle autopilot. Linear controllers are first designed using a multi-objective method based on the Youla parameterization and the optimization under constraints described by linear matrix inequalities. These controllers are then interpolated in such a way that the stability of the closed-loop plant is guaranteed. Results obtained from a nonlinear simulator against wind disturbances and parameter uncertainties are then given.

Low-order robust attitude control of an earth observation satellite☆

Abstract The attitude control of an observation satellite, which exhibits highly uncertain lightly damped modes, is designed by loop-shaping H ∞ design. Minimum-order controllers solving an LMI formulation of the problem are sought, using a cone complementarity linearisation algorithm. For different control laws, it is explained why the procedure leads to very low-order controllers. To analyse the stability robustness of the control law, different structured singular-value upper bounds and fitting characterisations of sets of uncertainties allow the computational cost of a mixed μ-analysis procedure to be minimised. Finally, the performance of the control laws is studied on a nonlinear simulator.

Robust autopilot for a flexible missile: loop-shaping H∞ design and real ν-analysis

This paper considers the control of a bank to turn missile (developed by Aerospatiale) with very lightly damped bending modes. The autopilot is synthesized using the H∞ loop-shaping design procedure of McFarlane and Glover. Robustness against large modelling uncertainties (including parameters and bending modes) is then investigated using the ν-tool, which circumvents the drawback of frequency gridding occurring in μ-analysis. The autopilot of the missile is finally validated on a nonlinear simulator: the performance and the robustness of the design are clearly underlined.

An interpolation method for gain-scheduling

Presents an efficient method for discrete-time gain-scheduling. The proposed algorithm concerns the interpolation of discrete-time controllers in the particular case of an off-line known trajectory. In spite of this restriction, it allows us to give computable results for a large class of plants. Moreover the specific structure of an observer-based controller is used. In order to illustrate the methodology, an example is given.

Gain Scheduling for an Aerospace Launcher With Bending Modes

Abstract An interpolation method with guaranteed stability is first presented. It can be performed with an LTV (Linear Time Varying) system which parametric trajectory is off-line known. An important point of this method is that it can turn into linear interpolation with some special conditions. This is then performed considering an aerospace application. It concerns a non stationary launcher during the atmospheric phase; the control law has to reject any wind disturbance.

AEROSPACE LAUNCH VEHICLE CONTROL: A GAIN SCHEDULING APPROACH

This paper presents a methodology for designing an aerospace launch vehicle autopilot. Linear controllers are first designed using a multi-objective method based on the Youla parameterization and the optimization under constraints described by linear matrix inequalities. These controllers are then interpolated in such a way that the stability of the closed-loop plant is guaranteed. Results obtained from a nonlinear simulator against wind disturbances and parameter uncertainties are then given.

H∞ control of an electromechanical drive with nonlinearities using a multi-block criterion

Abstract H ∞ optimisation was used to design a controller for an electromechanical drive, subjected to imperfectly known memoryless nonlinearities and uncertain inertia and elasticity of the load. After classical two- and four-block criteria had been tested, more satisfying results were obtained by using a multi-block criterion, which was built by taking advantage of the physical knowledge of the plant.

Loop shaping H∞ design: Application to the robust stabilization of a helicopter

Abstract In this paper, the problem of stabilizing the longitudinal and lateral motions of a helicopter is addressed by using a loop shaping procedure followed by an H ∞ optimisation based on coprime factors. This approach is found to be efficient in order to ensure the robustness of the control law against parameter uncertainties, i.e. neglected dynamics and modifications of operating conditions.

LPV Control for μ-split braking assistance of a road vehicle

In this paper, a system is developed to control the yaw moment and the lateral deviation in the case of braking with different adhesion conditions on the left and right sides. A driving assistance is obtained by using the front and rear steering angles. The control law is designed using an extension of the H∞ loop-shaping method to the case of linear parameter-varying (LPV) plants: it allows to obtain a controller whose dynamics depend on the longitudinal speed. The results are evaluated by implementing this controller on a simulation software developed by RENAULT.