Robust Control Strategy for a Conduction–Convection System Based on the Scenario Optimization

International audienceThis paper deals with the robust control of an uncertain conduction–convection system in the framework of probabilistic control design based on both the geometric control and the scenario optimization approach. Thus, a robust control strategy that copes with parameter uncertainties is proposed for a heated rod taken as an application example of a conduction–convection system. The design approach consists in two steps. In the first step, assuming a nominal model, a state feedback that yields a stable linear lumped parameter system, of first order, in closed loop is designed by means of geometric control theory. The stability of the resulting closed-loop system is demonstrated based on the perturbation theorem from semigroup theory. The second step consists in defining the input reference of the designed state feedback by a structured robust controller. The parameter tuning of the structured controller is formulated as a semi-infinite (or robust) optimization problem which is, then, relaxed using the scenario approach leading to a standard finite optimization problem. The solution of this scenario optimization problem is achieved using a genetic algorithm. The proposed control strategy is adopted to cope with parameter uncertainties in the problem of heating a steel rod. The effectiveness of the proposed robust control strategy is demonstrated by simulation

Numerical and experimental analysis of a thin liquid film on a rotating disk related to development of a spacecraft absorption cooling system

The numerical and experimental analysis of a thin liquid film on a rotating and a stationary disk related to the development of an absorber unit for a high capacity spacecraft absorption cooling system, is described. The creation of artificial gravity by the use of a centrifugal field was focused upon in this report. Areas covered include: (1) One-dimensional computation of thin liquid film flows; (2) Experimental measurement of film height and visualization of flow; (3) Two-dimensional computation of the free surface flow of a thin liquid film using a pressure optimization method; (4) Computation of heat transfer in two-dimensional thin film flow; (5) Development of a new computational methodology for the free surface flows using a permeable wall; (6) Analysis of fluid flow and heat transfer in a thin film in the presence and absence of gravity; and (7) Comparison of theoretical prediction and experimental data. The basic phenomena related to fluid flow and heat transfer on rotating systems reported here can also be applied to other areas of space systems

A low-rank matrix equation method for solving PDE-constrained optimization problems

PDE-constrained optimization problems arise in a broad number of applications such as hyperthermia cancer treatment and blood flow simulation. Discretization of the optimization problem and using a Lagrangian approach result in a large-scale saddle-point system, which is challenging to solve, and acquiring a full space-time solution is often infeasible. We present a new framework to efficiently compute a low-rank approximation to the solution by reformulating the KKT system into a Sylvester-like matrix equation. This matrix equation is subsequently projected onto a small subspace via an iterative rational Krylov method, and we obtain a reduced problem by imposing a Galerkin condition on its residual. In our work we discuss implementation details and dependence on the various problem parameters. Numerical experiments illustrate the performance of the new strategy also when compared to other low-rank approaches