Fa2004 16.33311-2 Altitude Gain Root Locus: k>0 Altitude gain Root locus: k<0 Figure 2: Altitude root locus #2 Root locus versus h feedback clearly not going to work Would be better off designing an inner loop first. Start with short period model augmented with the 0 state ww-kq9-h00+8c L hw kg ke x+de=-KIlz+de Target pole locations s=-1.8+2.41, s=-0 25 gains:K=[-0.0017-26791-6.5498 Inner loop target poles Figure 3: Inner loop target pole locations - t get there with only a gain� � � � Fall 2004 16.333 11–2 −5 −4 −3 −2 −1 0 1 2 3 4 −4 −3 −2 −1 0 1 2 3 4 0.68 0.54 0.38 0.18 5 0.18 0.986 0.95 0.89 0.8 0.8 0.54 0.38 3 0.68 0.89 4 2 0.95 0.986 1 Altitude Gain Root Locus: k>0 Real Axis Imaginary Axis −5 −4 −3 −2 −1 0 1 2 3 4 −4 −3 −2 −1 0 1 2 3 4 0.68 0.54 0.38 0.18 5 0.18 0.986 0.95 0.89 0.8 0.8 0.54 0.38 3 0.68 0.89 4 2 0.95 0.986 1 Altitude Gain Root Locus: k<0 Real Axis Imaginary Axis Figure 2: Altitude root locus #2 • Root locus versus h feedback clearly NOT going to work! • Would be better off designing an inner loop first. Start with short period model augmented with the θ state δe = −kww−kqq−kθθ+δe c = kw kq kθ x+δc = −KILx+δe c − e – Target pole locations s = −1.8 ± 2.4i, s = −0.25 – Gains: KIL = −0.0017 −2.6791 −6.5498 −5 −4 −3 −2 −1 0 1 2 3 4 −4 −3 −2 −1 0 1 2 3 4 0.8 0.68 0.54 0.38 0.18 0.54 0.18 0.986 0.95 0.89 5 4 0.38 0.89 0.68 2 0.8 3 0.95 0.986 1 Inner loop target poles Real Axis Imaginary Axis Figure 3: Inner loop target pole locations – won’t get there with only a gain