Session: Controls 3

Paper Number: 111398

111398 - Parametric Stability Analysis Applied to Complex Pneumatic Systems Using Convex Optimization 

In an airplane, the air conditioning system has a major role in regulating the air that pressurizes the cabin, defrosts the wings, and cools down electronic components, among other key functions. This system comprises a series of pneumatic valves that control the air from the bleed stage beside the engine all the way to the cabin. The first valve cluster to regulate the airflow is the air bleed subsystem located in a region with demanding specification requirements in terms of pressure and temperature variation. Therefore, it is important to tune the design parameters of these valves during the development phase to satisfy the dynamic requirements and as result, avoid early maintenance and the jeopardy of the systems around them.

Optimization under Linear Matrix Inequalities (LMIs) constraints [1] is widely used to solve engineering problems, especially in the context of control engineering. In a previous paper [2] we investigated the use of this technique for assessing the stability properties of a two-stage pressure regulation valve of the air bleed system. In this former work, it was shown that this approach can be used to determine the admissible range of physical parameters, such as viscous friction or feedback line section, which permit a certain decay rate and damping ratio of the valve response.

The present paper explores the method in a more complex system composed of two pressure regulation valves in a serial assembly. This model assemblage allows a better understanding of the reasons why undesired pressure oscillations occur and how they propagate along the streamline. Consequently, it is possible to better grasp the design parameters’ influence over this phenomenon and how the dynamics of the valves inside the air bleed cluster are intertwined.

The present work largely extends the former results, allowing for a broader analysis including a wide set of critical physical parameters, some of which change the equilibrium point. For such cases, the state space matrix is reformulated to take into consideration its dependence on the analyzed parameter. The procedure will also be applied in terms of more than one parameter at a time to analyze the parameters’ interdependence. This new feature aims to allow the system architects to visualize not only a variation range for each parameter at a time, that guarantees the desired dynamics but also the region in which the design parameters should be to guarantee a such response and the limitations imposed by their design choices.

Bibliography

[1] Boyd, Stephen, El Ghaoui, Laurent, Feron, Eric and Balakrishnan, Venkataramanan. Linear Matrix Inequalities in Systems and Control Theory. Society for Industrial and Applied Mathematics (SIAM), vol. 15, 1994

[2] De Carvalho, Gabriel, Massioni, Paolo, Bideaux, Eric, Sesmat, Sylvie and Bristiel, Frederic. Parametric Stability Analysis of Pneumatic Valves Using Convex Optimization. 2022 IEEE Global Fluid Power Society PhD Symposium, Naples, Italy, October 12-14, 2022, GFPS2022 1570805358

Presenting Author: Gabriel De Carvalho Ferreira Silva Univ Lyon, INSA Lyon, Université Claude Bernard Lyon 1, Ecole Centrale de Lyon, CNRS, Ampère, UMR5005 / Liebherr Aerospace Toulouse

Presenting Author Biography: PhD student at Univ Lyon, INSA Lyon employed by Liebherr Aerospace Toulouse.
Mechanical Engineer from UFRJ, Brazil, with a Master's degree diploma at SIGMA Clermont, France.
R&D experience in Engineering and Project/Installation experience in the technical domain.