Probe-Conditioned Memory for Actuator-Deadband-Aware Koopman MPC in Industrial Sealing

Technical Summary: Probe-Conditioned Memory for Actuator-Deadband-Aware Koopman MPC in Industrial Sealing

Problem Statement
Industrial sealing and dispensing processes often reuse hardware (pressure chains, nozzles, vision interfaces) across different product recipes. While static pressure-to-width calibration is typically accurate for nominal recipes, narrow-width recipes expose a critical nonlinearity: actuator deadband. In proportional pneumatic valves, a "dead zone" exists where command positions yield little to no flow. Consequently, a calibrated static pressure setpoint may remain theoretically correct, but small corrective moves are absorbed by the deadband, preventing the actual delivered pressure from changing until a history-dependent threshold is crossed.

The core challenge is commissioning: the setup and retuning interval immediately following a recipe change. During this phase, target data is scarce, and the static bead map is insufficient because it ignores the actuator's delivery state (hysteresis, deadband, and pressure loss). Existing methods—such as static inverse control, adaptive PI, or online recursive-least-squares (RLS) identification—either ignore the delivered-pressure loss or require extensive target data to rediscover actuator behavior that may already be present in historical records. The paper identifies a missing capability: a mechanism to combine static calibration with a short actuator probe to retrieve relevant historical context before feedback control begins.

Methodology
The proposed solution is the Actuator-Deadband-Aware Koopman Model Predictive Controller (AK-MPC), initialized from Probe-Conditioned Memory (PCM).

1. Probe-Conditioned Memory (PCM):

   • PCM acts as a repository of historical operating cases. Each record ($C_i$) stores a tuple including the product recipe, quality reference, static pressure root, material descriptors, and crucially, an actuator descriptor ($z_a$).
   • The actuator descriptor is inferred from a fixed 16-action probe sequence executed at the start of a new commissioning run. This probe estimates the deadband ($d$), delivered-pressure gain ($g$), lag ($\ell$), and hysteresis ($h$).
   • Upon a new recipe change, the system performs a retrieval query using a weighted distance metric between the new target's static and dynamic descriptors and the stored library. The closest historical context provides a "warm start" for the predictor and controller.

2. Actuator-Deadband-Aware Koopman MPC:

   • Prediction: The controller utilizes a Koopman lifting framework with a finite dictionary to create a compact nonlinear predictor. The predictor is initialized with the retrieved context ($\Theta_K, S, \pi$).
   • Local Correction: During the short commissioning run, the controller applies a low-rank, online correction to the retrieved predictor based on the transition buffer, adapting to specific target drifts without rewriting the entire model.
   • Feasibility Filtering: A hard constraint layer ensures pressure and input bounds are respected. A "tube" filter manages width prediction errors; if the predicted error exceeds a threshold, the system falls back to a bounded pressure-root or static inverse adaptive-PI strategy.
   • Workflow: The process involves executing the probe, retrieving the best-matching historical context, initializing the MPC, and running a receding-horizon control loop that updates local corrections while preserving the retrieved actuator terms.

Key Contributions

• Definition of PCM: The paper formalizes Probe-Conditioned Memory as a record linking pressure setpoints to probe-inferred actuator behaviors, enabling the reuse of historical actuator states (deadband, gain, hysteresis) rather than just model checkpoints.
• Theoretical Analysis: The authors provide propositions and theorems demonstrating that:
  • A static pressure root is insufficient in deadband regimes (Proposition 1).
  • Probe-estimation errors are bounded under specific excitation conditions (Lemma 1).
  • The retrieved PCM bounds the initial predictor mismatch (Theorem 1).
  • The finite-horizon tracking cost degradation is bounded by the prediction tube error (Theorem 2).
• Control Architecture: The integration of a constrained Koopman predictor with online low-rank correction and a feasibility filter specifically tailored for actuator deadband.

Results
The method was evaluated on a calibrated digital twin of a physical gluing cell, focusing on a 1.00 mm narrow-width benchmark where delivered-pressure loss is significant. The study compared AK-MPC against several baselines: static inverse pressure MPC, static inverse adaptive PI, online RLS-ARX-MPC, and a probe-fitted ARX-MPC (which uses the probe but no memory).

• Tracking Accuracy: AK-MPC achieved a Mean Absolute Error (MAE) of 0.0487 mm over 60 paired cases.
  • This significantly outperformed the best dynamic baseline (Online RLS-ARX-MPC at 0.2492 mm) and the static baselines (approx. 0.25–0.27 mm).
  • The probe-fitted ARX-MPC, which lacks memory retrieval, performed the worst (0.3956 mm).
• Ablation Studies:
  • Removing PCM (AK-MPC without PCM) increased the error to 0.0655 mm, isolating the specific contribution of memory retrieval.
  • Freezing online updates (Frozen-PCM) resulted in an error of 0.1158 mm, highlighting the necessity of online adaptation.
• Safety and Efficiency: AK-MPC maintained zero pressure or input violations and demonstrated lower total variation in actuator actions compared to baselines. The 95th percentile runtime was 13.7 ms on a standard workstation.

Significance and Claims
The paper claims that the primary value of this approach lies in fast commissioning for low-width recipes where actuator deadband is active. The significance is not a general transfer-learning claim, but a specific mechanism: historical runs are most useful when they carry pressure-delivery information (deadband, gain, hysteresis) that a short target probe can verify and refine.

The authors emphasize that the large performance gap between AK-MPC and classical baselines is a result of the full workflow (constrained prediction + online correction + feasibility filtering), while the isolated gain from PCM (approx. 0.0168 mm improvement over the no-memory variant) demonstrates that retrieving actuator-specific states provides critical information before sufficient target data is available. The results are validated on a calibrated digital twin, with a single physical-cell trace provided as a deployment sanity check rather than a statistical benchmark.