PERFORMANCE CRIETERIA FOR LINEAR CONSTANT-COEFFICIENT SYSTEMS WITH RANDOM INPUTS

A critical siirvey and assessment has been made of performance measures and associated criteria for linear constant-coefficient systems v/ith random inputs. The suitahility of each criterion for flight control system optimization using "pencil and paper" methods has been investigated by considering its validity, selectivity, and ease of application. Simplifications are introduced by substituting for actual flight control systems lower order equivalent systems having similar dynamics, and by replacing certain random inputs and criteria Vifith transient analogs and "compatible" deterministic criteria. The latter simplification enables the calculation of random input performance measures to be replaced by calculations involving more easily visualized deterministic quantities. It is shown that, for stationary inputs, a wide variety of criteria reduce to minimum mean square error. This criterion is easy to use and has a compatible deterministic form, but yields lightly dainped systems and is unselective (i.e., the mean square error of a wide variety of off-optimum systems is little higher than that of the optimum). Hov/ever, no criterion was found that had the advantages of minimum mean square error without comparable or worse disadvantages. For certain nonstationary problems, the probabilistic square error criterion appears promising. Numerous improved techniques for evaluating criteria and several exanples are presented. It is concluded that none of the criteria that have been proposed to date are suitable as sole criteria for flight control system optimization. PUBLICATION REVIEW This report has been reviewed and is approved. FOR THE COMIANDER C. B. WESTBROOK ^^ Chief, Aerospace Mechanics Branch Flight Control Laboratory