Sensitivity analysis of automatic flight control systems using singular-value concepts

A recently developed sensitivity analysis technique for linear control systems, which is based on the gradients of the return-difference-matrix singular values, is improved by introducing system scaling, and extended to include digital systems. System scaling is used to improve the reliability of the singular values as measures of relative stability. Digital systems are included in the analysis through the derivation of new equations for the matrix singular-value gradients. An example of the applicability of the method to high-order, digital, multiloop systems is presented using the X-29A lateral-directional control laws. Results for the X-29A are discussed, as well as the range of validity of these results. ations in the model. Fewer techniques exist, however, for deter- mining how additional wind-tunnel or flight testing should be conducted if it is deemed necessary. References 1 and 2 present such a technique: a sensitivity analysis that determines the spe- cific model parameters that are most important to the stable operation of a continuous control system. The procedure is based on the singular values of the return difference matrix, and the gradients of these singular values with respect to sys- tem and controller parameters. In Refs. 1 and 2, singular-value gradients were demonstrated to be a viable way to determine which parameters, of the many that describe a control system, most strongly effect that system's relative stability. This paper presents the extension of this analysis to digital systems, and attempts to improve the accuracy of the singular- value plot (d-plot) as a measure of system relative stability. These extensions, with a few other modifications to the analy- sis, allow complex, high-order, digital systems to be analyzed. This paper will begin by discussing real diagonal scaling as a partial solution to the problem of the overconservative nature of singular values. It will then give a brief review of the tech- nique introduced in Ref. 1, followed by a derivation of the singular-value gradients (<r -gradients) for digital systems. Next, the technique is applied to the linear model of the X-29A Advanced Technology Demonstrator; a -plot results are given and the sensitivity analysis technique is demonstrated. The linearity of singular-valu e plots is then investigated to deter- mine the range of usefulness of predictions that are based on a -gradients.