Closed-Loop Sensitivity Identification for Large-Scale Cross-Directional Systems with Ill-Conditioned Response Matrices

Core Concepts

A method for estimating the closed-loop sensitivity of large-scale cross-directional systems with ill-conditioned response matrices by introducing a reference signal and leveraging the modal transformation.

Abstract

The paper proposes a method for estimating the closed-loop sensitivity of large-scale cross-directional (CD) systems, which are characterized by ill-conditioned response matrices. Such systems are common in applications like synchrotron electron beam stabilization, papermaking, steel rolling, and battery manufacturing.
Key highlights:

The authors introduce an output reference signal to estimate the complementary sensitivity in closed-loop, overcoming the inability to measure the disturbance spectrum in real-time.
By decoupling the MIMO system into sets of SISO systems using the modal transformation, the reference signal is designed mode-by-mode to accommodate the system's strong directionality.
Lower bounds on the reference amplitude are derived to achieve a predefined estimation error bound in the presence of disturbances and measurement noise.
The method enables performance estimation of ill-conditioned CD systems in closed-loop and provides a signal for fault detection.
Simulation results using real-world disturbance data from the Diamond synchrotron facility demonstrate the efficacy of the proposed approach.
The authors address the key challenge of estimating the closed-loop sensitivity for large-scale, ill-conditioned CD systems, which is crucial for ensuring the theoretical performance specifications are met. Their modal-based approach with a designed reference signal allows SISO system identification techniques to be leveraged, making the method suitable for practical implementation on complex systems.

Stats

The system has a response matrix R with condition number κ(R) ranging from 103 to 104.
The maximum and minimum singular values of R are σmax = 195 and σmin = 0.02, respectively.
The input and output constraints are |ui(t)| ≤ 5 A and |yi(t)| ≤ 150 μm.
The actuator dynamics are g(s) = a/(s + a)e^(-τ_d s) with a = 2π × 700 rad/s and time delay τ_d = 900 μs.
The IMC filter dynamics are λ(s) = λ̄/(s + λ̄)e^(-τ_d s) with λ̄ = 2π × 176 rad/s.

Quotes

"Due to the inability to measure the disturbance spectrum in real-time, the closed-loop sensitivity of the FOFB cannot be evaluated, making it difficult to compare FOFB algorithms and detect faults."
"By decoupling the system into sets of single-input, single-output (SISO) systems, we design the reference mode-by-mode to accommodate the system's strong directionality."
"Our approach not only enables performance estimation of ill-conditioned CD systems in closed-loop but also provides a signal for fault detection."

Key Insights Distilled From

Closed-Loop Sensitivity Identification for Cross-Directional Systems

by Callum Umana... at arxiv.org 05-03-2024

https://arxiv.org/pdf/2405.01094.pdf

Deeper Inquiries

How could the proposed method be extended to handle model uncertainty and plant-model mismatch in the closed-loop sensitivity estimation

To address model uncertainty and plant-model mismatch in closed-loop sensitivity estimation, the proposed method could be extended by incorporating robust control techniques. Robust control methods, such as H-infinity control or mu-synthesis, can help account for uncertainties in the system model and variations between the actual plant and the nominal model used for control design. By formulating the sensitivity estimation problem within a robust control framework, the algorithm can be enhanced to provide sensitivity estimates that are more resilient to model inaccuracies and uncertainties. Additionally, techniques like adaptive control or model predictive control (MPC) could be integrated to continuously update the model parameters based on real-time data, improving the accuracy of the sensitivity estimates in the presence of plant-model mismatch.

What alternative approaches could be explored to relax the conservative bounds on the reference signal amplitude and improve the signal-to-noise ratio for higher-order modes

To relax the conservative bounds on the reference signal amplitude and enhance the signal-to-noise ratio for higher-order modes, alternative approaches could be explored. One approach could involve optimizing the reference signal design using advanced signal processing techniques. For instance, instead of using a constant amplitude chirp signal, adaptive signal shaping algorithms could be employed to dynamically adjust the reference signal amplitude based on the system's response characteristics. By adaptively modulating the reference signal amplitude, the algorithm can ensure that the input constraints are met while maximizing the signal strength for accurate sensitivity estimation.
Furthermore, exploring advanced filtering and denoising methods can help improve the signal-to-noise ratio for higher-order modes. Techniques such as wavelet denoising, Kalman filtering, or spectral analysis combined with noise reduction algorithms can effectively enhance the quality of the data used for sensitivity estimation. By preprocessing the data to reduce noise and artifacts, the algorithm can achieve more reliable sensitivity estimates, especially for modes with low signal-to-noise ratios.

How could the closed-loop sensitivity estimates be incorporated into a comprehensive fault detection and diagnosis framework for large-scale cross-directional systems

Incorporating the closed-loop sensitivity estimates into a comprehensive fault detection and diagnosis framework for large-scale cross-directional systems can provide valuable insights for system monitoring and maintenance. One approach to integrating sensitivity estimates into fault detection is to establish baseline sensitivity profiles for the system under normal operating conditions. Deviations from these baseline profiles can indicate potential faults or anomalies in the system.
By continuously monitoring the sensitivity estimates in real-time, anomaly detection algorithms, such as statistical process control or machine learning-based anomaly detection, can be employed to flag any abnormal behavior in the system. The sensitivity estimates can serve as key indicators of system health, with significant changes or discrepancies triggering alarms for further investigation.
Moreover, the sensitivity estimates can be utilized in fault diagnosis by correlating specific patterns in the sensitivity profiles with known fault signatures. By establishing a database of sensitivity patterns associated with different types of faults, a diagnostic system can automatically identify and classify faults based on the observed deviations in the sensitivity estimates. This proactive approach to fault detection and diagnosis can help improve system reliability, reduce downtime, and facilitate timely maintenance interventions.