Methods for model reduction

Abstract

This paper describes the evolution of model reduction methods, including the motivations behind this work. For active load alleviation work on the Lockheed L-1011, simplified structural models were generated for control system analysis and synthesis work. This was accomplished using spectral decomposition to decouple states in the original partitioned model. For flying qualities work on other highly augmented aircraft, methods for generating equivalent low order transfer functions from their frequency responses were developed. These started from simple gradient methods for individual frequency responses, and evolved into routines which allowed multiple transfer f unctions of any order to be simultaneously fit. Equivalent transfer f unctions are generated with each mode either fixed to initial conditions, varied for each frequency response, or simultaneously varied across all responses. Pure time delays could also be included. Motivated by very high order systems with structural dynamics, and by full state feedback design methods, state space model reduction techniques are coming into use. Enns developed a model reduction technique based on balancing. This method, and a bandwidth based method by Jonckheere at USC, have been developed for Lockheed. These methods are being used and further refined using realistic system models.