Jean-Marc Biannic's Courses

ONERA/DCSD - Flight Dynamics and Control Department

Robustness Analysis: A practical approach to µ analysis

For numerical and technical reasons, control system design is generally performed on simplified models which fail to capture the exact behavior of the real plant. In the aerospace industry, before implementation and flight tests, control laws must be extensively checked on simulation platforms. This time-consuming process requires numerous simulations and statistical analysis.

The main purpose of robustness analysis is to provide cheaper solutions to perform "pre-validations" of the control systems. Among existing solutions in the control literature, µ analysis techniques are clearly the most mature today. Although these techniques are restricted to the class of uncertain LTI models, they offer a very nice framework for which efficient tools have been recently developed to handle high-order systems (possibly involving numerous flexible modes) and numerous uncertainties. With the development of the SMT Toolbox first, and more recently the SMART Library of the SMAC Toolbox, ONERA/DCSD has played a keyrole in the field of robustness analysis which is now taught at ISAE/SUPAERO.



Two sets of slides are available below.


See also "Selected talks" for more slides in english on this topic.


An academic study case:


To get shortly familiar with the µ analysis approach and the most recent tools now available with the SMART Library of the SMAC Toolbox, a simple study case is proposed below. It consists of a robustness evaluation of a satellite attitude control system despite uncertainties affecting the flexible modes of a solar array. For this example, the restricted version of the toolbox is sufficient.


Related Software: