Orthogonal Filters for Model Error Compensation in the Control of Nonrigid Spacecraft

This paper seeks to improve the convergence properties of state estimators as used in spacecraft controller designs, when the linearized models upon which the estimators are based are subject to parameter errors, truncated modes, and neglected disturbances. Instead of choosing mode shapes (which are orthogonal in space) multiplied by time varying coefficients (a conventional approach for modeling elastic modes) to represent the truncated modes, the ''model error vector" discussed herein is approximated, over short "observation windows," T units long, by functions which are orthogonal over the time interval T, where the coefficients of the orthogonal functions are automatically updated via the use of real-time measurements from the system. The device which updates the coefficients of the orthogonal functions is called an orthogonal filter and takes on the form of a state estimator for the synthetic modes of a "model error system" which generates the orthogonal functions. The method is illustrated for a 14th-order model of a flexible spacecraft, resulting in 2nd-, 3rd-, and 4th-order controllers.

[1]  R. Fitzgerald.  Divergence of the Kalman filter , 1971 .

[2]  A. L. C. Quigley,et al.  An approach to the control of divergence in Kalman filter algorithms , 1973 .

[3]  S. Bhattacharyya,et al.  On error systems and the servomechanism problem , 1972 .

[4]  Robert E. Skelton,et al.  On the Use of Model Error Systems in the Control of Large Scale Linearized Systems , 1976 .

[5]  P. W. Likins,et al.  Dynamics and Control of Flexible Space Vehicles , 1970 .

[6]  K. Narendra,et al.  A new canonical form for an adaptive observer , 1974 .

[7]  Y. Ohkami,et al.  Appendage modal coordinate truncation criteria in hybrid coordinate dynamic analysis. [for spacecraft attitude control , 1976 .

[8]  J. Bongiorno,et al.  Observers for linear multivariable systems with applications , 1971 .

[9]  Robert E. Skelton,et al.  Optimal Desaturation of Momentum Exchange Control Systems , 1971 .

[10]  Peter W. Likins,et al.  Techniques of Modeling and Model Error Compensation in Linear Regulator Problems , 1978 .

[11]  P. Kokotovic,et al.  Singular perturbation of linear regulators: Basic theorems , 1972 .

[12]  P. Byrne,et al.  Optimization with trajectory sensitivity considerations , 1976 .

[13]  E. Kreindler,et al.  Formulation of the minimum trajectory sensitivity problem , 1969 .

[14]  V. Larson,et al.  An application of modern control theory to an elastic spacecraft , 1976 .

[15]  E. Davison,et al.  On "A method for simplifying linear dynamic systems" , 1966 .

[16]  P. Likins.  Analytical Dynamics and Nonrigid Spacecraft Simulation , 1974 .