Question

Problem 2: A (battery) system has the state equation $\dot{x} = \begin{bmatrix} 0 & 0 \\ 0 & -\frac{1}{R_p C_p} \end{bmatrix} x + \begin{bmatrix} \frac{1}{Q} \\ \frac{1}{C_p} \end{bmatrix} i$ v = [c, 1]x where Q = 36000, $C_p$ = 500, $R_p$ = 0.2, c = 0.5. (1) Check if the system is observable. (2) Design a state observer to estimate x (we need to estimate the SOC), such that the observation error dynamic system has poles at -1, -2.

          Problem 2: A (battery) system has the state equation
$\dot{x} = \begin{bmatrix} 0 & 0 \\ 0 & -\frac{1}{R_p C_p} \end{bmatrix} x + \begin{bmatrix} \frac{1}{Q} \\ \frac{1}{C_p} \end{bmatrix} i$
v = [c, 1]x
where Q = 36000, $C_p$ = 500, $R_p$ = 0.2, c = 0.5.
(1) Check if the system is observable.
(2) Design a state observer to estimate x (we need to estimate the SOC),
such that the observation error dynamic system has poles at -1, -2.

Problem 2: A (battery) system has the state equation
ẋ =
< b m a t r i x >
x +
< b m a t r i x >
i
v = [c, 1]x
where Q = 36000, Cp = 500, Rp = 0.2, c = 0.5.
(1) Check if the system is observable.
(2) Design a state observer to estimate x (we need to estimate the SOC),
such that the observation error dynamic system has poles at -1, -2.

Added by Jeffrey D.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Linda Winkler

Step 1

The observability matrix is given by: O = [C | C*A | C*A^2 | ... | C*A^(n-1)] where A is the system matrix. In this case, A = [[0, 1], [0, -0.2]] and C = [0.5, 1]. Let's calculate the observability matrix: Show more…

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Problem 2: A battery system has the state equation 0 1 0 x 1 x+ 0 10-0 v=[c,1]x where Q=36000, C=500, R=0.2, c=0.5 (1) Check if the system is observable (2) Design a state observer to estimate x (we need to estimate the SOC such that the observation error dynamic system has poles at -1, -2)