State feedback
Undergraduate
State feedback is a control law that uses the full state, $u = k(x)$ instead of only a partial measurement of the state.
Examples
Examples
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$u = -K x$, with the full state measured
High school
$u = -K x$ is state feedback because the input uses the whole state. For a controllable system, $K$ can place the closed-loop eigenvalues anywhere.
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$u = -K y$, when $y = x$
High school
$u = -K y$ is also state feedback, because here the output is the whole state.
Non-examples
Things that may be mistaken for examples.
-
$u = -K \hat{x}$, where an observer computes $\hat{x}$ from $y$
Undergraduate
By the separation principle, a stabilizing state feedback combined with a converging observer stabilizes the system.
- $u = -k y$, for $\dot x_1 = x_2$, $\dot x_2 = u$ with $y = x_1$ Undergraduate
Properties
- For a controllable linear system, linear state feedback can place the closed-loop eigenvalues anywhere (pole placement).
Distinctions involving this term
- State feedback vs. output feedback: A feedback controller computes its input from information about the system, which may be more or less complete. State feedback uses the full state, which is rarely measured directly. Output feedback uses only the measured output, and it may need an observer or other dynamics to do what state feedback can.