Reduced order H-infinity missile controller synthesis using critical characteristic capture

Abstract

A methodology has been developed which provides reduced order models which capture critical dynamic response characteristics of full order systems. Performance criteria such as delay time, rise time, peak time and settling time are example measurements which can be used in an optimal parameter estimation technique. Position, velocity and/or acceleration can be matched at any point in a step response trajectory in the most general case. The algorithm functions to estimate coefficients in a chosen linear reduced order model structure. The algorithm is unique since it provides the means to capture any number of point conditions or general characteristics along a full order dynamic response trajectory. Model reduction techniques such as Wilson's cannot directly capture point conditions since they use an optimization criterion which minimizes the difference in response between the full and reduced order trajectories throughout the entire response history. The broad applicability of the Matlab based algorithm is illustrated through application of this technology to synthesis of reduced order H missile autopilots. Graduate Student, Mech. Engineering Member AIAA Senior Project Engineer McDonnell Douglas Aerospace St. Louis, Missouri Associate Professor Aerospace Engineering Associate Fellow, AIAA Introduction A unique approach to model reduction has been developed which provides the means to capture individual dynamic conditions at any point along a full order system's dynamic response trajectory. The approach is based on nonlinear parameter estimation techniques although the resulting reduced order model is linear. Our research objective was to derive an optimal model reduction methodology which captures critical dynamic response characteristics of a full order system in a reduced order model. The methodology differs from typical optimal parameter estimation approaches since it uses chosen dynamic response characteristics as measurements in an optimal parameter estimation technique. The optimization criterion thus consists of a subset of the large scale system's time dependent dynamic response. The present formulation allows matching of position, velocity and/or acceleration at any time point in the step response of the full order system. The parameter estimation technique derives the coefficients in a linear reduced order transfer function structure. The optimality is obtained from the inherent capabilities of the Extended Kalman Filter and careful formulation of a measurement strategy which captures the desired dynamic characteristics. The methodology's practical utility is maximized when it is desired to capture the dynamics associated with particular physical quantities such as delay time, rise time, peak time and settling time position magnitudes. The algorithm also provides the unique capability to form a Copyright © 1995 by Michael K. Sharp and S. N. Balakrishnan. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. reduced order model with desirable attributes when an optimal approach such as Wilson's cannot provide an acceptable model due to the inherent limits of fitting high order dynamics to an extremely low order model. This paper initially presents our problem approach for solution of a general reduction problem. Secondly the Extended Kalman Filter equations are presented as they are programmed in our algorithm. Next the algorithm is presented including a discussion of each function. Finally application to an H°° missile autopilot presents the mechanics for use and verification of our algorithm, substantiates the utility of the methodology and provides a concise example. Fourth Order: