Loop Tuning and Gain Scheduling

Tuning sets a loop's responsiveness; gain scheduling changes the tuning as the plasma moves through very different operating conditions.

Tuning a control loop

A feedback loop's behavior depends on its gains, which set how strongly it responds to error. Too little gain leaves the loop sluggish and unable to reject disturbances; too much makes it oscillate or go unstable. Tuning is the process of choosing gains that give a fast, stable response with adequate margin against instability.

Why one tuning is not enough

The plasma's dynamics change dramatically over a discharge. During ramp-up the plasma is small and cool; at flat-top it is large and hot; the actuator responses and instability growth rates differ between phases. A single fixed tuning that is safe everywhere is too conservative at the operating point, and one tuned for flat-top may be unstable during ramp-up.

Gain scheduling

Gain scheduling solves this by changing the gains as a function of the operating condition, such as plasma current or stored energy. The controller interpolates between tunings validated at several operating points, so it is always near its best tuning for the present state. This is a practical way to control a strongly varying system with well-understood linear tools.

Stability across schedules

Care is needed that switching or interpolating gains does not itself cause instability. The scheduled tunings are designed with overlap and smooth transitions, and the whole schedule is tested across the operating range in simulation. Abrupt gain changes are avoided in favor of continuous interpolation.

In the Kronos program

The Hyperion breeder's fast loops, above all vertical stabilization, are gain-scheduled across the discharge because the vertical instability growth rate changes with elongation and current as the plasma evolves. The schedules are tuned against the machine's reduced models and verified across the full operating range in the flight simulator ahead of first plasma.