An attempt to make robust controller synthesis work on a real system

Marc Trotoux, Control and Dynamical Systems, Caltech

A recent approach in uncertainty modeling, to construct model validating uncertainty sets, has been applied to an aircraft testbed at Caltech. This approach aims at reducing the gap between system identification methods and robust control by constructing model validating sets in the LFT robust control framework. The inevitable leap of faith going from model development and control design to closed loop performance for a real system is, hence, minimized. Furthermore, if the identified set of plants is physically meaningful, one expects the best possible closed loop performance via optimal robust controller synthesis. Otherwise, an "optimal" robust controller can lead to poorer performance than expected. As a precursor to generating a model validating set of plants, one needs to identify a nominal plant and a disturbance/noise model and assume an uncertainty structure about this nominal model. If the tests for the existence of a model validating set are satisfied, it is then possible to parameterize all the models which are model validating with this particular LFT uncertainty structure. This parameterization is used as a basis for a systematic way to perform uncertainty tradeoff to minimize the set of model validating plants, to allow good closed-loop performance with robust controller synthesis.

This talk will first discuss the parameterization of the model validating sets, the tests for feasibility and the optimization over a particular set of plants. A tool-box, implementing numerically the algorithm, will be illustrated by simulation results on two examples: a transparent SISO system and a realistic MIMO analytical model of the ducted fan. Finally, the results obtained on the Caltech testbed will be presented and in particular the comparison between the predicted and the measured closed loop performance for a mu controller.