q6 assignment 1 lcs
DESCRIPTION
Matlab AssignmentTRANSCRIPT
syms k1 k2 l1 l2 m2 I
>> A=[0 1 0 0;-(k1*l1^2 + k2*l2^2)/I 0 (k2*l2)/I 0;0 0 0 1;(k2*l2)/m2 0 -k2/m2 0]
A =
[ 0, 1, 0, 0]
[ -(k1*l1^2 + k2*l2^2)/I, 0, (k2*l2)/I, 0]
[ 0, 0, 0, 1]
[ (k2*l2)/m2, 0, -k2/m2, 0]
>> B = [0;l2/I;0;0]
B =
0
l2/I
0
0
>> C = [0 0 1 0]
C =
0 0 1 0
>> D = 0
D =
0
>> I = eye(4,4)
I =
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
z = s*I-A
z =
[ s, -1, 0, 0]
[ (k1*l1^2 + k2*l2^2)/I, s, -(k2*l2)/I, 0]
[ 0, 0, s, -1]
[ -(k2*l2)/m2, 0, k2/m2, s]
>> z1 = inv(z)
z1 =
[ (I*s*(m2*s^2 + k2))/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2), (I*(m2*s^2 + k2))/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2), (k2*l2*m2*s)/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2), (k2*l2*m2)/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2)]
[ -(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2)/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2), (I*(m2*s^3 + k2*s))/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2), (k2*l2*m2*s^2)/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2), (k2*l2*m2*s)/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2)]
[ (I*k2*l2*s)/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2), (I*k2*l2)/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2), (k1*m2*l1^2*s + k2*m2*l2^2*s + I*m2*s^3)/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2), (m2*(k1*l1^2 + k2*l2^2 + I*s^2))/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2)]
[ (I*k2*l2*s^2)/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2), (I*k2*l2*s)/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2), -(k1*k2*l1^2 + I*k2*s^2)/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2), (m2*s*(k1*l1^2 + k2*l2^2 + I*s^2))/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2)]
>> tf=C*z1*B+D
tf =
(k2*l2^2)/(k1*m2*l1^2*s^2 + k1*k2*l1^2 + k2*m2*l2^2*s^2 + I*m2*s^4 + I*k2*s^2)