01
Closed-Loop Control
In a closed-loop system, measurements are used to determine corrective control actions. This contrasts with open-loop control, where the controller does not use the resulting output to correct its command.
u = C(s)e
02
Stability
A control system is stable when its response remains bounded under appropriate bounded inputs and its internal dynamics behave acceptably according to the chosen stability definition.
- Transient response describes short-term behavior following a change.
- Steady-state error measures long-term tracking deviation.
- Overshoot measures excursion beyond the desired value.
- Settling time measures how quickly the response approaches its final region.
- Robustness describes sensitivity to model uncertainty and disturbances.
03
State-Space Representation
ẋ = Ax + Bu
y = Cx + Du
State-space models represent dynamic systems through internal state variables and are especially useful for multivariable and modern-control analysis.