A linearized model of a vertical takeoff and landing (VTOL) aircraft is [24] x = Ax +

Chapter 0, Problem CP11.5

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A linearized model of a vertical takeoff and landing (VTOL) aircraft is [24] x = Ax + Bill] + B22, where and -0.0389 0.0271 0.0482 -1.0100 0.1024 0.3681 0 0 = 0.4422" 3.5446 -6.0214 ()_ ' 0.0188 -0.4555 0.0019 -4.0208 -0.7070 1.4200 1 0 B 2 = 0.1291 ~ -7.5922 4.4900 ()_ The state vector components are (i) .v, is the horizontal velocity (knots), (ii) x2 is the vertical velocity (knots), (iii) . is the pitch rale (degrees/second), and (iv) ,v4 is the pitch angle (degrees). The input ii\ is used mainly to control the vertical motion, and u2 is used for the horizontal motion. (a) Compute the eigenvalues of the system matrix A. Is the system stable? (b) Determine the characteristic polynomial associated with A using the poly function. Compute the roots of the characteristic equation, and compare them with the eigenvalues in part (a). (c) Is the system controllable from ii] alone? What about from 2 alone? Comment on the results.