Types of exogenous inputs
A control system is affected by signals that it does not generate itself, and these signals have different names depending on their role. Exogenous inputs are any inputs from outside the system. A control input is chosen; a disturbance acts on the dynamics; measurement noise only corrupts what is measured. A perturbation is a change to the system itself, which may or may not be modeled as an input.
Definitions
Consider a system that changes over time. An exogenous input is any signal that comes into the system from outside it, such as a control input or a disturbance.
Consider a control system. An exogenous input is any signal that enters the system from outside, rather than being determined by the system’s own state. This includes control inputs, reference signals, disturbances, and noise.
Examples
-
A gust of wind hitting a quadcopter drone
The gust is a disturbance, and so an exogenous input, because it changes the drone’s actual motion and is not chosen.
- Jitter in a quadcopter drone’s GPS position readings
-
The motor commands of a quadcopter drone
The motor commands are a control input, and so an exogenous input to the motors, because the flight controller chooses them.
Consider a system that you want to steer, like a car. A control input is a quantity you choose in order to steer the system.
In a control system, a control input is an input $u$ chosen by the controller at each time to change the behavior of the system.
Non-examples
- A gust of wind hitting a quadcopter drone
-
Jitter in a quadcopter drone’s GPS position readings
Jitter in a quadcopter drone’s GPS position readings is not a control input because it is not chosen.
Consider a system that is trying to follow a course, like a drone flying to a target. A disturbance is an outside influence that pushes the system off course.
Consider a control system $\dot{x} = f(x, u, d)$, with inputs from outside. A disturbance is an unwanted exogenous input, such as $d$, that affects the dynamics of the system. It changes the actual state of the system.
Non-examples
-
Jitter in a quadcopter drone’s GPS position readings
The GPS jitter is not a disturbance because it does not directly change the state of the drone (its position or velocity).
-
The motor commands of a quadcopter drone
The motor commands of a quadcopter drone are not a disturbance, because they are chosen, not imposed.
Missing definition: measurement_noise
Missing definition: perturbation
Examples
| Example | exogenous input | control input | disturbance | measurement_noise | perturbation | Why |
|---|---|---|---|---|---|---|
| The motor commands of a quadcopter drone | ✓ | ✓ | ✗ | ✗ | – | |
| A gust of wind hitting a quadcopter drone | ✓ | ✗ | ✓ | ✗ | – | |
| Jitter in a quadcopter drone’s GPS position readings | ✓ | ✗ | ✗ | ✓ | – | |
| A payload that makes a quadcopter drone 10% heavier than modeled | ✗ | – | – | ✗ | ✓ |