Variation in the transfer function calculations
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Transfer function using matlab commands was calculated in two different methods and the answers are different. Why is it happening?
Reference: http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum§ion=SystemModeling
1. Calculated by using s = tf('s'); P_cart = (((I+m*l^2)/q)*s^2 - (m*g*l/q))/(s^4 + (b*(I + m*l^2))*s^3/q - ((M + m)*m*g*l)*s^2/q - b*m*g*l*s/q); P_pend = (m*l*s/q)/(s^3 + (b*(I + m*l^2))*s^2/q - ((M + m)*m*g*l)*s/q - b*m*g*l/q); sys_tf = [P_cart ; P_pend]; inputs = {'u'}; outputs = {'x'; 'phi'}; set(sys_tf,'InputName',inputs) set(sys_tf,'OutputName',outputs) sys_tf
sys_tf =
From input "u" to output...
4.182e-06 s^2 - 0.0001025
x: ---------------------------------------------------------
2.3e-06 s^4 + 4.182e-07 s^3 - 7.172e-05 s^2 - 1.025e-05 s
1.045e-05 s
phi: -----------------------------------------------------
2.3e-06 s^3 + 4.182e-07 s^2 - 7.172e-05 s - 1.025e-05
Continuous-time transfer function.
2. Calculated by tf(sys_ss)
sys_tf =
From input "u" to output...
1.818 s^2 + 1.615e-15 s - 44.55
x: --------------------------------------
s^4 + 0.1818 s^3 - 31.18 s^2 - 4.455 s
4.545 s - 1.277e-16
phi: ----------------------------------
s^3 + 0.1818 s^2 - 31.18 s - 4.455
Both are different even if we neglect the terms with lease magnitude.
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