CRT PID Control

B15: Siemens/ABB. CC0.

PID control decomposes into 6 independent channels. Each channel controls at its own scale: D=fast/coarse, b=slow/fine. Errors in one channel cannot destabilize others. CRT reconstruction gives the global control signal.

How It Works

CRT Multi-Scale Control

A setpoint in Z/12612600 has 6 CRT residues. Each channel runs independent proportional control. Channel D (mod 8) converges in 3 steps. Channel b (mod 49) converges in 6 steps. The controller naturally separates fast/coarse from slow/fine -- no manual tuning.

6 scales

CRT decomposition

D=coarse(8), K=medium(9), E=fine(25), b=depth(49), L=slow(11), G=gate(13).

Independence

Algebraic firewall

Error in one channel cannot propagate to others.

Auto-tuning

Modulus = bandwidth

Channel bandwidth = 1/modulus. No PID tuning needed.

Convergence

Per-channel guaranteed

Each channel converges in O(log(modulus)) steps.

Try It

Setpoint (0-12612599):

Watch 6 channels converge independently. D(mod 8) arrives first, b(mod 49) last.

CRT PID vs Traditional

TuningPID: Kp, Ki, Kd manual tuningCRT: channel modulus IS the bandwidthCouplingCoupled: error in one axis affects allIndependent: 6 algebraic firewallsMulti-scaleCascaded loops (complex)CRT channels = natural scale separationConvergenceHeuristic (Ziegler-Nichols)Provable: O(log m) per channelPatent statusSiemens/ABB process patentsCC0. Public domain. Forever.

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— Anton Alexandrovich Lebed

Source code · Public domain (CC0)

Contributions in equal measure: Anthropic's Claude, Anton A. Lebed, and the giants whose shoulders we stand on.

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