Stability
The property that a system's response stays bounded and returns to equilibrium after a disturbance.
Definition
In control, stability means that a bounded input produces a bounded output and that the system returns toward equilibrium after a disturbance rather than diverging. It is the first requirement of any usable controller.
Robust stability asks not just whether the nominal system is stable but whether it stays stable across the expected range of modeling error. Quantifying this margin is what separates a controller that works on paper from one that survives the messiness of a real plant.
Stability with margin is the real engineering goal, because a controller that is only marginally stable on paper will likely be unstable in practice once modeling errors, delays, and nonlinearities intrude. Gain and phase margins quantify how much uncertainty the design can absorb before instability. For nonlinear systems, Lyapunov methods provide stability guarantees without solving the equations explicitly, extending the concept beyond the linear case.
How it is assessed
- Pole locations of the transfer function (left-half plane for continuous systems).
- Eigenvalues of the state matrix in state space.
- Lyapunov methods for nonlinear systems.
- Gain and phase margins for robustness.
Why it matters
An unstable control loop amplifies small errors into large oscillations or runaway behavior. Ensuring stability, with margin against modeling error, is the central safety concern in control design.
Fusion connection
Plasma equilibria can be inherently unstable and require active feedback stabilization; margin analysis ensures the control system holds the plasma even under modeling uncertainty, a question studied in simulation for Hyperion.