Control Loop Fundamentals

The feedback basics - error, gain, stability, and bandwidth - that underlie every plasma control loop.

The feedback loop

A control loop measures an output, compares it to a reference to form an error, and drives an actuator to reduce that error. Formally, for a plant with transfer function G(s) and controller C(s), the closed-loop response is C(s)G(s) / (1 + C(s)G(s)). Everything about performance and stability follows from that denominator, the return difference 1 + C(s)G(s).

Stability margins

A loop is stable if its open-loop response C(s)G(s) does not encircle the point -1 in the complex plane (the Nyquist criterion). How far it stays from -1 defines the gain and phase margins - how much extra gain or delay the loop tolerates before oscillating. Plasma loops are designed for generous margins because the plant model is uncertain and the plasma is changing.

Bandwidth and speed

Loop bandwidth is roughly how fast the loop can correct errors. It must exceed the growth rate of whatever instability the loop fights - vertical modes need high bandwidth, slow shape drift needs less - but it is bounded above by sensor noise, actuator limits, and time delay. Pushing bandwidth past those limits amplifies noise and can destabilize the loop.

The cost of delay

Every millisecond of delay - sampling, computation, actuator response - subtracts phase margin and caps achievable bandwidth. This is why the fast layers are engineered for minimal, deterministic latency. A pure time delay of T seconds costs phase linearly with frequency, and no controller can fully undo it.

Feedforward complements feedback

Feedback corrects error after it appears; feedforward acts on known future demands before error appears. Plasma control uses both: precomputed scenario waveforms as feedforward, feedback trimming the residual. Good feedforward reduces the burden on feedback and lets loops run with safer, lower gain.