Question

\ddot{z} + 6\dot{z} + 40z = 6\dot{w} + 40w \ddot{w} + 100\dot{w} + 4000w = 12\ddot{z} + 80\dot{z} + 80\dot{u} + 4000u (2) Define the state variables as the outputs of the integrators and write the state variable equations including the equation for the output of interest, the output of interest is y = w - z \dot{X} = AX + Bu y = CX + Du A =? B =? C =? D =? (3) Enter this state space system into MATLAB and use the damp command to get the eigenvalues. Eigenvalues = ? (5%) Damping ratios = ? (5%) Time constants = ? (5%) Damped natural frequencies = ?

          \ddot{z} + 6\dot{z} + 40z = 6\dot{w} + 40w
\ddot{w} + 100\dot{w} + 4000w = 12\ddot{z} + 80\dot{z} + 80\dot{u} + 4000u
(2) Define the state variables as the outputs of the integrators and write the state variable
equations including the equation for the output of interest, the output of interest is y = w - z
\dot{X} = AX + Bu     y = CX + Du
A =?
B =?
C =?
D =?
(3) Enter this state space system into MATLAB and use the damp command to get the
eigenvalues.
Eigenvalues = ?
(5%) Damping ratios = ?
(5%) Time constants = ?
(5%) Damped natural frequencies = ?

z̈ + 6ż + 40z = 6ẇ + 40w
ẅ + 100ẇ + 4000w = 12z̈ + 80ż + 80u̇ + 4000u
(2) Define the state variables as the outputs of the integrators and write the state variable
equations including the equation for the output of interest, the output of interest is y = w - z
Ẋ = AX + Bu y = CX + Du
A =?
B =?
C =?
D =?
(3) Enter this state space system into MATLAB and use the damp command to get the
eigenvalues.
Eigenvalues = ?
(5%) Damping ratios = ?
(5%) Time constants = ?
(5%) Damped natural frequencies = ?

Added by Kevin B.

Question

Please give Ace some feedback