Unformatted text preview: le. From lecture 3, we know that the equation of motion for a single
pendulum without control input is given by ! = −(!sin(!))/! , and from this we can formulate
the linearized first order difference equation. Here, we have the following linearized difference
equation.
!
!! !
1 − Δt !! ! − 1 + ! !
=
!
!! !
!! ! − 1
Δ!
1
X ! = AX ! − 1 + ! ! (1)
where x! = ! (rad/s), x! = ! (rad), n is a time step index, Δt (s) is the time
interval between time steps, η is process noise (e.g., due to linearization
error, initial condition uncertainty,...
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 Spring '08
 Schaal
 Estimation theory, ΔT, Kalman filter, Filtering problem, briefly comment

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