Experimental Control: A Helicopter Case Study

John Morris, Electrical Engineering, California Institute of Technology

Experimental systems provide a great deal of information relevant to the direction control theory should move. A description of an experimental platform, comprised of a real-time computer and a radio-controlled model helicopter mounted on a six degree-of-freedom stand, is given. This platform was used as a case study for modelling, identification, analysis, and synthesis.

Traditional system identification and control techniques were used to construct hover controllers for the model helicopter. These techniques were not suitable for the construction of robust models for a system of this complexity. In particular, there was no systematic way to augment nominal identified models with uncertainty suitable for the construction of robust controllers.

To address this issue, frequency-domain model validation algorithms and software are developed. These algorithms provide a methodology for verifying the applicability and consistency between experimental data and robust models. Additionally, they provide a method whereby the robust model can be refined by tuning nominal model parameters in a robust setting. This is the first set of software tools which provide this capability for general linear uncertain systems.

A design process was developed which incorporated frequency-domain model validation analysis, mu-analysis and mu-synthesis, simulation, and implementation. This design process proved to be a valuable new tool for designing control systems for the helicopter. In particular, by applying this design process, the size of uncertainty in the robust model for the helicopter was substantially reduced over several iterations, without sacrificing the ability of the model to "cover" the experimental data. After the design cycle was completed, the first controller implemented on the helicopter worked, and was, in fact, the best controller overall. This was strikingly different from the results obtained when using standard robust control techniques, where several controllers destabilized the helicopter when implemented, even though they performed well under simulation.

The contribution of this work is to provide a consistent methodology and framework which connects system identification, the construction of robust models, and controller synthesis with experimental data. For the first time the control engineer can compute measures on the validity of a robust model, with respect to all observed data on the actual physical system, which are directly related to the robustness measures resulting from mu-analysis and mu-synthesis.