Mappingmodel

CD Mapping & Control

Paper Machine Cross-Direction Control

PRBS Identification • Adaptive Shrinkage • MPC Control

Stec Corporation

System Architecture

• Two-process architecture over ZeroMQ REQ/REP
• automap4.py: REP controller (binds port 5555)
• PRBS identification, MPC control, mapping
• modeldriver.py: REQ simulator (connects)
• Paper machine simulation, scan generation
• Key principle: automap4 discovers everything
• Transport delay, gain, response width
• modeldriver keeps its secrets (like real machine)
• Message schema identical for sim/live machine

Mapping Matrix G[i,j]

• N_act × N_box matrix (96 × 500 default)
• Each row = actuator response profile
• Row sum = 1.0 (area-normalised)
• Process gain recovered separately:

gain = √(2π) × σ

• Negative gain for dilution actuators

(opening valve decreases basis weight)

• Initial mapping: fallback S-curve + Gaussians

G[i,j] = response of actuator i at databox j

PRBS Identification

• Pseudo-Random Binary Sequence
• Values: {-1, 0, +1}
• Probabilities: P(-1)=0.25, P(0)=0.5, P(+1)=0.25
• Sequence length: 511 per actuator
• All 96 zones excited simultaneously
• Amplitude: 3% of full stroke (configurable 1-20%)
• Uncorrelated excitation across actuators
• Learning rate α = 0.05 (PRBS)

u(t) = clamp(50 + A × PRBS(t), 0, 100)

Cross-Correlation & Response Extraction

• Transport delay D scans (initially 2, auto-estimated)
• Profile change: Δy(t) = y_CD(t) - y_CD(t-D-1)
• Response window: ±35 databoxes around centre
• Sign correction: PROCESS_GAIN_SIGN × sign(PRBS_i)
• Gaussian filter: σ = 1.5 databoxes
• Normalise to sum = 1
• Window positioned at hardcoded S-curve centre

(prevents divergence feedback loop)

r_i = sign(PRBS_i) × Δy[c_i - W : c_i + W]

EWMA Update Rules

• Exponential Weighted Moving Average:

G_i[window] = (1-α) × G_i[window] + α × response

• Two learning rates:
• α = 0.05 for PRBS identification
• α = 0.20 for control-time refinement
• Row re-normalised after each update
• Quality metric: Q_i = min(1.0, count_i / 5.0)
• Progress: P = (ΣQ_i + N_unlearned × 0.5) / N_act

G_i ← (1 - α) · G_i + α · r_i / Σ(r_i)

Shrinkage Model (S-Curve)

• Non-linear edge shrinkage from angled jet trajectory
• 3rd-order polynomial: s(x) = C₃x³ + C₁x
• Initial coefficients: C₃ = -0.4, C₁ = 0.95
• Normalised actuator position: x = i/(N_act-1) - 0.5
• Expected centre: c_i = 250 + s(x) × 460
• Polynomial fitted from learned response centres
• Fallback S-curve used for window positioning

(NOT learned model — prevents divergence)

s(x) = -0.4x³ + 0.95x

Transport Delay Auto-Estimation

• Cross-correlate actuator moves with profile changes
• Uses act_history (actual positions, not PRBS {-1,0,1})
• For each actuator with ≥3 bumps:
• Weighted centre: c = Σ(x × row) / Σ(row)
• Extract profile time series at centre
• Cross-correlate: corr = correlate(Δmeas, Δact)
• Average correlation across actuators
• Peak lag = transport delay in scans
• Updates every 5 scans during PRBS

delay = argmax(corr(Δact, Δmeas))

Coordinate System & Normalisation

• Raw profiles: absolute databox coordinates [0, 499]
• Sheet wander shifts edges → different raw positions
• Normalise to sheet coordinate frame:

x_norm = linspace(left_edge, right_edge, N_box)

profile_norm = interp(x_norm, raw_profile)

• Raw-to-normalised index conversion:

norm_idx = (raw_pos - left) / (right - left) × 499

• Critical fix: edge zones now learn correctly

(previously missed responses by 40+ databoxes)

MPC Supervisory Control

• SLSQP optimiser (Sequential Least Squares)
• Objective: J = Q·Σ(error²) + R·Σ(Δu²) + S·Σ(bending²)
• Q = 1.0 (target tracking)
• R = 4.0 (move suppression)
• S = 8.0 (bending penalty)
• Constraints: |Δu| ≤ 10%, |Δu_adj| ≤ 25%
• Control interval: transport_delay + 1 scan
• Process gain: √(2π) × σ (converts normalised to raw)

J = Q·||y + G·Δu - y_tgt||² + R·||Δu||² + S·||D²u||²

Wander Detection & Feed-Forward

• EWMA-smoothed edge positions (α = 0.02)
• Wander = (left + right)/2 - 250.0 databoxes
• FFT frequency estimation (Hann-windowed rFFT)
• 200-scan history
• Dominant frequency in cycles/scan
• Confidence: (peak/background - 1) / 9 × 100%
• Green if confidence ≥ 90% threshold
• Feed-forward: project 1 scan ahead
• Compensate before wander appears in profile

Stale Scan Protection

• Monitor time between consecutive scans
• If gap > 40s (configurable):
• skip_mapping = True
• Hold last setpoints (PRBS frozen)
• Log: 'SKIP: Xs gap exceeds max Ys'
• Automatic resume when fresh scans arrive
• Tested via modeldriver standardisation:
• Interval: 90 min (configurable)
• Duration: 30 s (configurable)

Setpoint Ownership & Bumpless Transfer

• automap4 owns setpoints
• Initialised from actuator positions at init

(first_after_init=True in setpoint_poll)

• Priority: stale > PRBS > control > idle > manual
• _last_setpoints cached for mid-scan polls
• modeldriver snaps positions immediately
• Simulator transport delay handles timing
• Manual bump: exclude zones from PRBS

prbs_vals[manual_mask] = 0

CSV Tuning Log

• Record button (Ctrl+R) starts/stops logging
• Core: scan_number, timestamp, mode, progress
• Wander: wander_db, freq, confidence, edge_mode
• Controller: horizon, R, S, Q, max_delta_u

estimated_gain, width, tau, tc

• Truth (SIM only): centre_err, width_est vs true
• View > CSV Report: printable HTML summary
• Enables offline tuning analysis

Key Parameter Relationships

• Process gain: √(2π) × σ
• Transport delay: cross-correlation peak lag
• Control interval: delay + (0 or 1 scan)
• MPC horizon: max(3, delay + 1)
• Progress: (Σquality + unlearned×0.5) / N_act
• Wander confidence: (peak/bg - 1)/9 × 100%
• Shrinkage: y = -0.4x³ + 0.95x
• Response window: ±35 databoxes
• EWMA: α=0.05 (PRBS), α=0.20 (control)

PaperMachineSimulator Constants

• N_act = 96, N_box = 500 (defaults)
• FOOTPRINT_STD_DEV = 4.5 databoxes
• S-curve: C₃ = -0.4, C₁ = 0.95
• WANDER_AMPLITUDE = 6.0 databoxes
• machine_speed = 1.5 m/s
• L = 40.0 m (transport distance)
• NOISE_STD_DEV = 0.8
• Negative gain: -exp() footprint
• These are modelstdcom.py's secrets!

Field Report Example

This is the auto report generated during the PRBS phase.