Reduced-Order Elastic Airplane Models

A complete aeroelastic airplane model incorporating states for unsteady aerody­namic effects can have well over 100 states. There are two problems with using such extended plant models in controller system design. A practical difficulty is that when control actuator, instrument, and feedback laws are added, the resultant state matrix would be too large and cumbersome for analysis. A second problem arises when some optimization methods are used to design the controller. The resultant optimal controller could require at least as many states as the plant model, an unacceptable result.

Methods have been developed that reduce the number of states to manageable levels, while at the same time preserving dominant modal characteristics over a sufficiently wide frequency band. These methods are referred to as residualization. A simple partial fraction residualization approach is described by Stevens (1992), based on work by Michael Athans. This consists of examining the plant eigenvalues and deciding which ones, usually high – frequency elastic modes, are to be dropped. A partial fraction expansion of the complete system is replaced by that of the reduced system, giving new state equations.

A more advanced residualization method is described by Newman (1994), an extension of a Stanford PhD dissertation by D. F. Enns. This is called residualization with weighted balanced coordinates.