1. a The optimization procedure starts with a nominal andnon-optimumcontroller. The derivatives of Equations (14-16) are used in the gradient method to compute new values for the independent variables. The procedure continues until convergence (to a minimum performance index) is achieved. It may be mentioned i n this paper that for a f u l l state optimal controller, the dependency condition of the feedback network
2. be any linear combination of the integrated y-signals, each of which has proper phasing based on optimal control. In other words, without losing generality, the optimization procedure is reduced to the determination of matrix C. Typical control laws developed in this manner are based on the following test conditions: (I) Configuration B (Empty Wing-Tip Launcher
3. L = 1750 f t .
4. In the wind tunnel tests conducted i n 1979, Control Law (NL) was tested to 1.70 times the dynamic pressure corresponding to open loop flutter (1.70 Qf). Extrapolation of the damping trend data indicated a potential to reach 2.40 Qf before flutter. Control Law (NLP) was also tested to 1.70 Q . Its predicted flutter dynamic pressure base 5 on extrapolation was 2.04 Qf. In developing optimized control laws, Law (NL) was often used as the starting point. In Figure 4, the root loci of the key modes which contribute to flutter are plotted for the three optimized control laws. The parameter used in the plots is the dynamic pressure Q. A l l control laws show a reasonable stability margin up to Q = 160 psf, or 2.13 Qf. In Figure 5, the root loci of the closed loop system corresponding to the previously tested control laws, NL and NLP, are plotted. An examination of Figures 4 and 5, data shows that Laws No. 1 and (NL), both leading edge control laws, apparently have the same level of stability margin a t Q = 160 psf. On the other hand, Laws No. 2 and 3, both optimized two surface control laws, feature a superior stability margin a t Q = 160 psf as compared with the previously tested Law (NLP).