Modelling and control for the GARTEUR robust control design challenges
The GARTEUR AG 08 project
As a basic contribution to the design challenge set up, we provided to all participating groups a common RCAM or HIRM aircraft-dynamics simulation model as either SIMULINK S-functions, Fortran or C code. All of this simulation code was automatically generated by Dymola from a single-source symbolic model which was interactively aggregated from components of an early version of our aircraft flight dynamics library. This symbolic model also served as a basis for automated generation of an LFT uncertainty-model description taking into account the given variations bounds of aircraft mass, centre of gravity (both in longitudinal and vertical direction) and control-computer time delay.
Contribution to the RCAM benchmark
Using (ANDECS) MOPS we developed a solution for the RCAM problem with results shown in the following standard evaluation table. A particular feature of this Design Challenge was the availability of common MATLAB evaluation tools developed by NLR for an automated design assessment, which guaranteed a standardized comparison of all design outcomes. All numbers less than one indicate full satisfaction of the requirements.
Our task was also a common stability-robustness evaluation of all design entries. For that purpose we performed a post-design µ-stability robustness analysis which detected that some of the design entries are not stable for all possible parameter combinations within the uncertainty bounds. Since speed deviations led to a very high order uncertainty block description of the LFT-representation, which was not computationally tractable, also a worst-stability parameter search was performed using mathematically optimization within the parameter uncertainty bounds (as criterion the ratio of worst minimum damping over all parameter combinations / minimum damping for the nominal parameter set was used). This additional stability-robustness analysis detected further design entries which become unstable due to deviations from nominal air speed. The results indicated that our MOPS design did quite well among the 12 entries obtained via 8 different methods: it turned out to be the most robust one as measured by both the µ-analysis and the optimisation-based worst stability search.
Contribution to the HIRM benchmark
The design task was split up into a longitudinal and a lateral design problem. For longitudinal control a classical controller structure with auto throttle function was used. The lateral controller is a generically robust LQG/LTR controller. The synthesis parameters available in both structures were tuned in the (old) Computer Aided Control Engineering (CACE) environment ANDECS so as to achieve the desired multi-objective performance and robustness.
The results compare favourably with the various results of the GARTEUR Design Challenge, as reported in the book “Robust Flight Control: A Design Challenge”. The manoeuvring non-linear controlled aircraft was simulated using the available HIRM simulation code. The simulation results were used to produce an animation with a "HIRM-like" object (an X-31, actually). A small sequence showing a 360 degrees velocity-vector-roll can be seen by clicking here. The manoeuvre shown is obtained by maximum lateral stick displacement. Good control behaviour in this case is shown in that the longitudinal axis (green) rotates symmetrically around the velocity vector (red).
You can download publications on our contributions here.