By T. Lombaerts
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Lm P( j 2) lies on or within the boundary of this contour. The nominal plant transfer function, with K 1 and ao 1 , is o 51 Quantitative Feedback Theory and Its Application in UAV’s Flight Control Po (s ) 1 s(s 1) (22) and is represented in Fig. 4°}. Note, once a nominal plant is chosen, it must be used for determining all the bounds B ( j ) . R i Fig. 13. 10 Disturbance bounds B ( j ) : CASE 1 D i Two disturbance inputs are shown in Fig. 7. It is assumed that only one disturbance input exists at a time.
These measurements are therefore of the angular rates of the system. Sensing angular velocity in modern strap-down navigation systems is actually accomplished through exploiting the Sagnac effect rather than the mechanical properties of rotating masses. In this case, the interference patterns generated by light traveling along opposing closed paths is used as a measure of the angular rotation of the system. In any case, the measurements obtained from a gyroscope triad can modeled by the observation equation ω = ω + d + Sω + Nω + ω (118) where is the measurement ω is the angular velocity d is the gyroscope bias S is a matrix representing the gyroscope scale factor N is a matrix representing the non-orthogonality of the axes ω is noise ω The noise terms of both accelerometers and gyroscopes can be further decomposed as = w + c + r + q + d (119) the ﬁve terms representing white, correlated, random walk, quantization and dither noise, respectively.
15)] as close to the origin as possible without significantly affecting the time response. This additional zero raises the curve B for the frequency range above cf . The spread can be further increased by augmenting T L with a negative real pole [see Eq. (16)] which is as close to the origin as possible but far enough away not to significantly affect the time response. Note that the straight-line Bode plot is shown only for T L . This additional pole lowers B for this frequency range. R U L U R R (n2 / a)(s a) (n2 / a)(s z1 ) s 2 2n s n2 ( s 1 )( s 2 ) (15) K K (s a1 )(s a2 )( s a3 ) (s 1 )(s 2 )(s 3 ) (16) TRU (s ) TRL (s ) Thus, the magnitude of ( j ) increases as i , increases above cf .