A dc-dc converter is a device that takes as an input an

Chapter 4, Problem 66

(choose chapter or problem)

Using wind tunnel tests, insect flight dynamics can be studied in a very similar fashion to that of man-made aircraft. Linearized longitudinal flight equations for a bumblebee have been found in the unforced case to be

\(\left[\begin{array}{c} \dot{u} \\ \dot{w} \\ \dot{q} \\ \dot{\theta} \end{array}\right]=\left[\begin{array}{cccc} -8.792 \times 10^{-3} & 0.56 \times 10^{-3} & -1.0 \times 10^{-3} & -13.79 \times 10^{-3} \\ -0.347 \times 10^{-3} & -11.7 \times 10^{-3} & -0.347 \times 10^{-3} & 0 \\ 0.261 & -20.8 \times 10^{-3} & -96.6 \times 10^{-3} & 0 \\ 0 & 0 & 1 & 0 \end{array}\right]\left[\begin{array}{l} u \\ w \\ q \\ \theta \end{array}\right]\)

where u= forward velocity; w= vertical velocity, q= angular pitch rate at center of mass, and \(\theta\)= pitch angle between the flight direction and the horizontal (Sun, 2005).

(a) Use MATLAB to obtain the system’s eigenvalues.

(b) Write the general form of the state-transition matrix. How many constants would have to be found?