Optimal Linear Control.
HONEYWELL SYSTEMS AND RESEARCH CENTER MINNEAPOLIS MN
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This is the final report on a multi-year research program to bridge the gap between modern control theory and practical control system design. The results of the total program are summarized and the last years results are described in detail. Characterizations of optimal linear controls have been derived, from which guides for selecting the structure of the control system and the weights in the performance index were developed, so that optimal controls meeting conventional design specifications can be designed for single-input systems. For multi-input systems a method of selecting weights for the performance index on the basis of desired closed-loop modal properties and system bandwidth was developed. For such systems it was also found that optimal controls which use state estimators have no guaranteed stability margins, and a method was developed for adjusting the state estimator design so that good margins could be obtained. It was also found that single-loop stability margins in multi-input systems were inadequate measures of robustness, the quality of stability being preserved for a class of perturbations of system characteristics. A new measure of robustness expressed in terms of singular values was developed which is a valid generalization of the concept of stability margins for single-input systems. A method for estimating bounds on system perturbations in terms of singular values associated with parameter uncertainties and unmodeled dynamics, including some forms of nonlinearities, is described in detail in this report. Illustrative examples have been treated in each phase of the program. In this report such an example is presented, demonstrating the se of singular value analysis in design.
- Numerical Mathematics