9780071086806, Chapter 11, Problem 7SP

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Chapter 11, Problem 7SP Problem 7. Starting with the polynomial- description of the lateral- directional dynamics, including the roll damper, derive the expression for the numerator of the closed-loop transfer or in terms of the open-loop numerator of this transfer function plus coupling numerator. Then using the data for the A-7A Condition (Appendix use plot the numerator root locus showing the effects of roll damper on the zeros of the transfer (Be sure use the polynomial-matrix description for the dynamics assuming fuselage reference by including the terms indicated in Equations 11 70.) Step step solution Step of 3 Solution: Using stability the -matrix description for the directional dynamics with roll damper was given Eqn. which is B(s) r(s) But this must be converted for use with fuselage reference Consistent with Eqn. 11 as well as (11 SM 4), and (11 SM we add the two terms the B equation plus the modified equation for that are necessary to convert this one consistent with using the fuselage-reference axes and obtain r/s or P(s)y(s) Q(s)y(s) The transfer function then B(s) The effects of the roll damper on the poles of this transfer function for the vehicle in question were shown And the numerator of this transfer function is -L's