AE 582 Robust Control Control in Aerospace Aerospace Systems Systems Homework 4 Handed out: Due:
st
November 21 , 2012 th November 28 , 2012
1) The lateral motion of a ship moving with constant velocity is given by
( s )
i.
Find the transfer function from the rudder to the heading angle G( s )
ii.
Assume that there is 60% uncertainty on the coefficients of the s term of the 3 numerator and s term of the denominator. Find a weighting function W such that the “multiplicative “multiplicative uncertainty” represents the effect of the parametric uncertainties on these coefficients as closely as possible.
( s )
2) For each of the following matrices matrices compute a singular singular value decomposition decomposition and show how the matrix maps the unit circle in x1-x2 plane, by y = Ax, to y1-y2 plane. For each matrix plot the unit circle and the associated ellipse. Show all important singular vector information on the plots. Also find the eigenvalues of these matrices and compare with the singular values.
