Types of control
A controller can decide its input with or without measuring what the system is doing. Open-loop control computes the input without measuring the output, and closed-loop (feedback) control uses the measured output to correct errors. Feedforward acts on a measured disturbance or a known reference before it affects the output, and is usually combined with feedback.
Definitions
Think of a machine that is trying to reach a goal, like a toaster making toast. In open-loop control, the machine acts without checking the result.
Consider a controller that chooses the input to a system. In open-loop control, the controller chooses the input without measuring the result.
Consider a control system $\dot x = f(x, u)$. In open-loop control, the input $u$ is computed in advance, or from the reference alone, and does not depend on measurements of the system’s output.
Examples
-
A toaster that runs for a fixed time
A toaster that runs for a fixed time is open-loop control because it does not measure how brown the toast is.
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A precomputed optimal input $u(t)$, applied without measurements
A precomputed input is open-loop control because it uses no measurements.
Non-examples
-
A thermostat
A thermostat is not open loop because it reacts to measurements of the temperature.
Think of a machine that is trying to reach a goal, like a heater warming a room. In closed-loop control, the machine checks the result and adjusts its action based on what it measures.
Consider a controller that chooses the input to a system. In closed-loop control, the controller measures the result and adjusts the input to correct errors.
Consider a control system $\dot x = f(x, u)$. In closed-loop control, the input $u$ is computed from measurements of the output (or state), forming a feedback loop. The closed-loop system is the plant together with its controller.
Examples
- A thermostat
- Steering a bike to keep from tipping over
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Cruise control that uses both the speed error and a map of upcoming hills
Cruise control that uses the speed error is closed-loop feedback control, because it corrects the measured speed error.
Non-examples
Think of a system that can see the results of what it does, like a person riding a bike. Feedback is when the system watches its own results and adjusts.
Consider a system with an input and an output. Feedback is using information about the system’s output to decide its input.
Consider a system with an input $u$ and an output $y$ (or state $x$). Feedback is the use of measurements of the output (or state) to determine the input, as in $u = k(y)$.
Examples
-
A thermostat
A thermostat is closed-loop feedback control because it measures the temperature and switches the heater accordingly.
- Steering a bike to keep from tipping over
- Cruise control that uses both the speed error and a map of upcoming hills
Non-examples
-
A toaster that runs for a fixed time
A toaster that runs for a fixed time is not closed-loop or feedback control, because it does not measure how brown the toast is.
-
A precomputed optimal input $u(t)$, applied without measurements
A precomputed input is not feedback control, so any disturbance or model error goes uncorrected.
-
Raising heater power when an outdoor thermometer reports a cold snap
Raising heater power on a cold-snap report is not feedback control, because it does not use the room temperature.
Properties
- Feedback can stabilize unstable systems and reduce sensitivity to disturbances and model errors.
Consider a system that is affected by a disturbance that you can see coming. Feedforward control reacts to the disturbance before it affects the result.
Consider a control system with a measured disturbance or a known reference signal. Feedforward is a control action computed from the disturbance or reference, applied before the disturbance or the change in the reference affects the output.
Examples
-
Cruise control that uses both the speed error and a map of upcoming hills
Cruise control that uses a map of upcoming hills is feedforward control, because it uses the map to anticipate the hills.
- Raising heater power when an outdoor thermometer reports a cold snap
Non-examples
-
A thermostat
A thermostat is not feedforward, because it reacts to the measured temperature after a disturbance has already affected it.
Properties
- Feedforward cannot correct errors it does not anticipate, such as unmeasured disturbances or model errors, so it is usually combined with feedback (a two-degree-of-freedom controller).
Examples
| Example | open loop | closed loop | feedback | feedforward | Why |
|---|---|---|---|---|---|
| A toaster that runs for a fixed time | ✓ | ✗ | ✗ | – | |
| A thermostat | ✗ | ✓ | ✓ | ✗ | |
| A precomputed optimal input $u(t)$, applied without measurements | ✓ | – | ✗ | – | |
| Raising heater power when an outdoor thermometer reports a cold snap | – | – | ✗ | ✓ | |
| Cruise control that uses both the speed error and a map of upcoming hills | – | ✓ | ✓ | ✓ |
Notes
- In loop analysis, the “open-loop transfer function” $L(s)$ is the loop broken at one point. It describes a closed-loop design, not open-loop control.
- Pure feedforward control is a form of open-loop control, so some authors use the terms interchangeably.