Using MATLAB and Simulink for Control System Simulation and ...

Linearization: 1-D example
Taylor series expansion about ( θθ , "
) = ( θd,0)
and keep the linear term. Consider the 1-D example
from last class:
I"" θ + F sgnθ" + Fθ" − mgl sinθ
= τ
sinθ = sinθ
d + cosθ
d ( θ −θ
d ) − 0.
5sinθ
d ( θ −θ
d
2
)
+ #
Linearized system:
I∆ "" θ + Fv∆θ" −mglg cosθd∆ θ = τ + mglgsinθd
$%&%'
∆ θ = ( θ −θ
)
c v g
d
may be cancelled or
treated as a disturbance