CRT PID Control / Robotics

How It Works

Traditional PID: ONE control signal u(t) = Kp*e + Ki*integral(e) + Kd*de/dt.
CRT PID: DECOMPOSE the control signal into 5 independent channels.

ARCHITECTURE:
  1. Plant output y(t) -> error e(t) = setpoint - y(t)
  2. Quantize error: e_q = round(e * scale) mod 970200
  3. CRT decompose: e_q -> (e mod 8, e mod 9, e mod 25, e mod 49, e mod 11)
  4. Each channel runs its OWN PID controller independently:
     u_i = Kp_i * e_i + Ki_i * sum(e_i) + Kd_i * (e_i - prev_e_i)
  5. CRT reconstruct: u = CRT(u_0, u_1, u_2, u_3, u_4)
  6. De-quantize and apply to plant

WHY CRT WINS:
  - 5 INDEPENDENT control loops = fault tolerance by structure
  - If channel i fails, remaining 4 channels still control (graceful degradation)
  - L=11 channel = FREE actuator integrity check
  - Each channel has different dynamic range (8,9,25,49,11) = multi-scale control
  - Block-diagonal: no cross-channel interference in Jacobian
  - Patent-free: PID is old, CRT decomposition makes it algebraically robust

1. Plant Simulation

Plant type: First-order (1/(s+1)) Second-order (1/(s^2+s+1)) Unstable (1/(s-0.5)) With delay (e^(-0.5s)/(s+1)) Setpoint:

Standard PID CRT PID Compare Both Reset

2. Channel Decomposition View

Watch each CRT channel's independent PID action:

3. Fault Tolerance

Kill a channel and watch the system adapt:

Kill Z/8 Kill Z/9 Kill Z/25 Kill Z/49 Kill Z/11 Kill 2 channels All healthy

4. L=11 Actuator Integrity

Inject Actuator Fault + Detect

5. Multi-Scale Resolution

Show Channel Resolutions