Plasma Response Models for Control
Reduced linear models of how the plasma reacts to coil and actuator changes - the basis for designing magnetic control loops.
Why a model
To design a controller you need a model of the plant: how the plasma's position, shape, and current respond to changes in coil currents and voltages. Full nonlinear simulation is too slow and too detailed for control design, so control engineers use reduced linear models valid near an operating point, capturing the dominant dynamics with few states.
The rigid and deformable pictures
The simplest models treat the plasma as a rigid current-carrying filament that can move but not change shape (the RZIP-type model: current, radial and vertical position coupled to the coil circuits). More detailed models allow the boundary to deform, adding shape degrees of freedom. The right level of detail depends on which loop the model serves.
State-space form
These models take the standard linear form: the state derivative equals A times the state plus B times the input, with outputs C times the state. The state includes plasma quantities and coil currents; the input is coil voltages; the output is what the sensors measure. In this form the full toolkit of linear control design - pole placement, robust and optimal control - applies directly.
Validity and uncertainty
A linear model is accurate only near the operating point it was linearized about, and the real plasma differs from any model. Robust control design accounts for this by treating the model as a nominal plant surrounded by an uncertainty set, and demanding stability across the whole set. Controllers are validated against higher-fidelity simulation and, ultimately, experiment.
Scheduling across the discharge
Because the plasma changes through a discharge, a single linear model does not suffice. Gain scheduling uses a family of models along the scenario, switching or interpolating controllers as the operating point moves. The models are computed offline from equilibria along the planned trajectory.