Output feedback
Undergraduate
Consider a control system with state $x$ and measured output $y$. Output feedback is a control law that uses only $y$, either directly, as in $u = k(y)$, or through a dynamic controller.
Examples
Examples
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$u = -K y$, when $y = x$
High school
$u = -K y$ is output feedback, because the input is computed from the measured output $y$.
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$u = -K \hat{x}$, where an observer computes $\hat{x}$ from $y$
Undergraduate
$u = -K \hat{x}$ is output feedback because the observer’s estimate $\hat{x}$ is computed from the output $y$, not from the state.
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$u = -k y$, for $\dot x_1 = x_2$, $\dot x_2 = u$ with $y = x_1$
Undergraduate
$u = -k y$ is output feedback because the input uses only the measured position $y = x_1$, not the velocity. The closed loop $\ddot x_1 = -k x_1$ oscillates for every $k > 0$, so no static output feedback stabilizes the double integrator.
Non-examples
Things that may be mistaken for examples.
- $u = -K x$, with the full state measured High school
Properties
- Some controllable and observable systems cannot be stabilized by static output feedback, but can be by . They can, however, be stabilized by dynamic output feedback, for example by combining an observer with state feedback (the separation principle).
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.