Example 09
ss( , , , ,), damp( ), impulse( ), bode( ), rlocus( )
GIVEN: A Linear Time Invaraient (LTI) system
xdot = [A] {x} + [B] {u}
y = [C] {x} + [D] {u}
REQUIRED: Create Space State model
SOLUTION:
A = [-0.0558 -0.9968 0.0802 0.0415
0.5980 -0.1150 -0.0318 0
-3.0500 0.3880 -0.4650 0
0 0.0805 1.0 0];
B = [ 0.0729 0.0001
-4.700 1.2300m
1.5300 10.6300
0 0];
C = [0 1 0 0
0 0 0 1];
D = [0 0
0 0];
The command ss would create state space representation of your continueous
system.
The open-loop eigenvalues of the continuous-time system can be obtained using
the command damp(sys).
The command pzmap would plot the open-loop eigenvalues in the s-plane:
The time response of the system due to an impulsive function is obtained by:
impulse(sys,60)
The bode plot of the yaw-rate can be plotted with bode(sys(1,1))
The root locus for the (1,1) channel can be ploted with the command rlcous(sys(1,1)).
example09.m
A = [-0.0558 -0.9968 0.0802 0.0415
0.5980 -0.1150 -0.0318 0
-3.0500 0.3880 -0.4650 0
0 0.0805 1.0 0];
B = [ 0.0729 0.0001
-4.700 1.2300
1.5300 10.6300
0 0];
C = [0 1 0 0
0 0 0 1];
D = [0 0
0 0];
states = {'beta' 'yaw' 'roll' 'phi'};
inputs = {'rudder' 'aileron'};
outputs = {'yaw rate' 'bank angle'};
sys = ss(A,B,C,D,'statename',states,...
'inputname',inputs,...
'outputname',outputs);
damp(sys)
impulse(sys,20)
bode(sys(1,1))
sys11=sys(1,1)
rlocus(sys11)
sgrid
[k,poles] = rlocfind(-sys11)
Example
Homework:
Select different value for k.
Please send questions or suggestions about this web page to beatnic@aset.psu.edu
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