The GARTEUR AG 11 project
The Control Design Engineering Group of DLR was involved in this research by developing the extended High Incidence Research Model (HIRM+) and exploring an optimisation-based approach to clearance. The automatic model building for HIRM+ is illustrated in the Figure below. Several physical aircraft dynamics models for time simulations and trimming purposes have been generated using components from a Modelica Flight Dynamics Library , where a set of uncertain parameters can be independently specified. Besides nonlinear simulation models, inverse dynamics models expressing the trim conditions have been generated as C-codes to ensure fast evaluation of clearance criteria.
The basic feature of the optimisation-based clearance approach is to reformulate the clearance problems as equivalent minimum distance problems for which "anti"-optimisation is performed to determine the worst-case parameter combination/flight condition leading to worst performance. The basic requirements for the applicability of the optimisation-based approach are the availability of suitable parametric models describing the overall nonlinear dynamics of the augmented aircraft and of accompanying efficient and reliable trimming, linearization and optimisation software tools. The optimisation-based approach has no limitations with respect to clearance criteria, being able to address all kinds of clearance requirements which are expressible as mathematical criteria.
The clearance results obtained for the HIRM aircraft augmented with the RIDE control laws cover several linear stability and handling criteria mostly used in the current industrial practice. Two classes of linear stability related criteria have been considered, namely the stability margin criterion and the unstable eigenvalues criterion. The considered handling criteria were the average phase-rate and the absolute amplitude criteria. The analysis results clearly demonstrate the high potential of the optimisation-based approach in reliably solving clearance problems with many simultaneous uncertain parameters.
For example, for the stability margin criterion it must be checked that the Nichols plots of SISO systems resulted by cutting one loop at a time of the closed-loop system does not enter the exact or approximate exclusion regions of the next Figure for gain and phase.
A typical clearance result is shown below, where the worst-case stability degrees, , for 8 extreme flight conditions are plotted against the angle of attack (AoA). Note that values of in the region below 1 correspond to worst-case parameter combinations which lead to violations of the clearance requirements.