arXiv subjects

Tom Oomen

Publications and source records attributed to Tom Oomen.

At least 19 recordsLinked to original sources

arXiv2026

Closed-loop Optimal Fault Detection for Uncertain Systems

Faults compromise the reliability and safety of complex engineering systems. The aim of this article is to address the problem of robust fault detection filter design for continuous-time linear time-invariant uncertain systems in open-loop or closed-loop configurations. The developed method offers a unified approach to handle parametric and dynamic uncertainties by solving a single Riccati equation, based on a worst-case disturbance and uncertainty model. This worst-case model is obtained by nonlinear optimization and application of the boundary Nevanlinna-Pick method. The efficacy of the proposed approach is demonstrated using an uncertain model of an experimental reticle stage used in the lithography industry. The results illustrate that an optimal compromise is achieved between sensitivity to faults and rejection of modelling uncertainties and disturbances on the other hand. This capability enables the clear differentiation between faults and undesired effects in residuals, thereby enhancing fault detection reliability, ultimately contributing to improved safety and performance of machines.

eess.SY↗

arXiv2026

Scaled Graph Bounding Techniques for Reset Systems

Reset systems can overcome fundamental limitations of linear time-invariant control. The recently introduced notion of scaled (relative) graphs provides a promising framework for developing graphical analysis and design tools for reset systems, in line with widely adopted loopshaping methods for linear systems. The aim of this paper is to derive techniques for over-bounding the scaled graph of reset systems, and obtain insights in their accuracy. We exploit connections between quadratic dissipativity and scaled graphs to recast the over-bounding problem as the search for piecewise quadratic storage functions. Using specific sampling techniques, we reveal a fundamental limitation of general scaled graph approximation methods that are based on quadratic dissipativity.

math.OC↗

arXiv2026

D-Optimized Sampling Design for System Identification

Traditional system identification with multisine inputs relies on uniform sampling and periodic excitation to preserve Fourier orthogonality and avoid spectral leakage, limiting its use in scenarios with irregular sampling or nonperiodic inputs. This work investigates continuous-time system identification under nonperiodic multisine excitation and nonuniform sampling. We develop a nonparametric frequency response function estimator suited to such conditions and design irregular sampling schemes that enhance the informativeness of measurements and reduce spectral leakage. The proposed sampling scheme improve the statistical accuracy of system identification in settings where periodic excitation is impractical.

eess.SY↗

arXiv2026

Nullspace-based Fault Diagnosis for Closed-Loop Mechatronic Systems with Application to Semiconductor Equipment

Fault detection and isolation (FDI) systems are critical for modern mechatronic production equipment, as their continuous operation is heavily dependent on the ability to detect and isolate faults in a timely and efficient manner. The aim of this paper is to address closed-loop aspects for linear systems and enable the application of well-known nullspace-based FDI synthesis conditions to mechatronic systems subject to actuator and sensor faults. These tailored FDI synthesis conditions are applied to a large-scale prototype wafer stage, showcasing the proposed approach through real experiments, thereby underlining the usefulness of the derived synthesis conditions for a wide range of production machines and scientific instruments.

eess.SY↗

arXiv2026

End-to-End ILC for Repetitive Untrackable Tasks: A Cooperative Game Perspective

An inherent assumption of perfect tracking in iterative learning control (ILC) is that there exists an ILC input such that the generated output can track the desired trajectory reference. This assumption may fail in practice, which gives rise to desired but untrackable tasks. This paper gives an end-to-end ILC design for repetitive untrackable tasks in closed-loop systems. The reference input is trial-to-trial updated together with the ILC feedforward input based on the measurement data. This two-player behavior of the closed-loop ILC system is investigated from a cooperative game perspective. A sufficient condition for the two-player end-to-end ILC to have a lower cost than the one-player norm optimal ILC (NOILC) is discovered. Finally, a numerical example is given to verify the effectiveness of the developed method.

eess.SY↗

arXiv2026

Scaled Relative Graphs and Dynamic Integral Quadratic Constraints: Connections and Computations for Nonlinear Systems

Scaled relative graphs (SRGs) enable graphical analysis and design of nonlinear systems. In this paper, we present a systematic approach for computing both soft and hard SRGs of nonlinear systems using dynamic integral quadratic constraints (IQCs). These constraints are exploited via application of the S-procedure to compute tractable SRG overbounds. In particular, we show that the multipliers associated with the IQCs define regions in the complex plane. Soft SRG computations are formulated through frequency-domain conditions, while hard SRGs are obtained via hard factorizations of multipliers and linear matrix inequalities. The overbounds are used to derive an SRG-based feedback stability result for Lur'e-type systems, providing a new graphical interpretation of classical IQC stability results with dynamic multipliers.

math.OC↗

arXiv2026

Structured identification of multivariable modal systems

Physically interpretable models are essential for next-generation industrial systems, as these representations enable effective control, support design validation, and provide a foundation for monitoring strategies. The aim of this paper is to develop a system identification framework for estimating modal models of complex multivariable mechanical systems from frequency response data. To achieve this, a two-step structured identification algorithm is presented, where an additive model is first estimated using a refined instrumental variable method and subsequently projected onto a modal form. The developed identification method provides accurate, physically-relevant, minimal-order models, for both generally-damped and proportionally damped modal systems. The effectiveness of the proposed method is demonstrated through experimental validation on a prototype wafer-stage system, which features a large number of spatially distributed actuators and sensors and exhibits complex flexible dynamics.

eess.SY↗

arXiv2025

Finite Sample MIMO System Identification with Multisine Excitation: Nonparametric, Direct, and Two-step Parametric Estimators

Multisine excitations are widely used for identifying multi-input multi-output systems due to their periodicity, data compression properties, and control over the input spectrum. Despite their popularity, the finite sample statistical properties of frequency-domain estimators under multisine excitation, for both nonparametric and parametric settings, remain insufficiently understood. This paper develops a finite-sample statistical framework for least-squares estimation of the frequency response function (FRF) and its implications for parametric modeling. First, we derive exact distributional and covariance properties of the FRF estimator, explicitly accounting for aliasing effects under slow sampling regimes, and establish conditions for unbiasedness, uncorrelatedness, and consistency across multiple experiments. Second, we show that the FRF estimate is a sufficient statistic for any parametric model under Gaussian noise, leading to an exact equivalence between optimal two stage frequency-domain methods and time-domain prediction error and maximum likelihood estimation. This equivalence is shown to yield finite-sample concentration bounds for parametric maximum likelihood estimators, enabling rigorous uncertainty quantification, and closed-form prediction error method estimators without iterative optimization. The theoretical results are demonstrated in a representative case study.

stat.ME↗

arXiv2025

Truncated Gaussian Noise Estimation in State-Space Models

Within Bayesian state estimation, considerable effort has been devoted to incorporating constraints into state estimation for process optimization, state monitoring, fault detection and control. Nonetheless, in the domain of state-space system identification, the prevalent practice entails constructing models under Gaussian noise assumptions, which can lead to inaccuracies when the noise follows bounded distributions. With the aim of generalizing the Gaussian noise assumption to potentially truncated densities, this paper introduces a method for estimating the noise parameters in a state-space model subject to truncated Gaussian noise. Our proposed data-driven approach is rooted in maximum likelihood principles combined with the Expectation-Maximization algorithm. The efficacy of the proposed approach is supported by a simulation example.

eess.SY↗

arXiv2025

Identification of additive multivariable continuous-time systems

Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main aim of this paper is to develop a parametric identification strategy that delivers accurate and physically relevant models of multivariable systems using time-domain data. The introduced approach adopts an additive model structure, providing a parsimonious and interpretable representation of many physical systems, and applies a refined instrumental variable-based estimation algorithm. The developed identification method enables the estimation of multivariable parametric additive models in continuous time and is applicable to both open- and closed-loop systems. The performance of the estimator is demonstrated through numerical simulations and experimentally validated on a flexible beam system.

eess.SP↗

arXiv2025

System Identification Beyond the Nyquist Frequency: A Kernel-Regularized Approach

Models that contain intersample behavior are important for control design of systems with slow-rate outputs. The aim of this paper is to develop a system identification technique for fast-rate models of systems where only slow-rate output measurements are available, e.g., vision-in-the-loop systems. In this paper, the intersample response is estimated by identifying fast-rate models through least-squares criteria, and the limitations of these models are determined. In addition, a method is developed that surpasses these limitations and is capable of estimating unique fast-rate models of arbitrary order by regularizing the least-squares estimate. The developed method utilizes fast-rate inputs and slow-rate outputs and identifies fast-rate models accurately in a single identification experiment. Finally, both simulation and experimental validation on a prototype wafer stage demonstrate the effectiveness of the framework.

eess.SY↗

arXiv2025

Performance Analysis of Multirate Systems: A Direct Frequency-Domain Identification Approach

Frequency-domain performance analysis of intersample behavior in sampled-data and multirate systems is challenging due to the lack of a frequency-separation principle, and systematic identification techniques are lacking. The aim of this \manuscript is to develop an efficient technique for identifying the full intersample performance in the frequency-domain for closed-loop multirate systems, in particular the Performance Frequency Gain (PFG). Through local modeling techniques, aliased frequency components are effectively disentangled when identifying the PFG, which is directly facilitated by frequency-lifting the multirate system to a multivariable time-invariant representation. The developed method accurately and directly identifies the PFG in a single identification experiment. Finally, the developed method is experimentally validated on a prototype motion system, showing accurate identification of frequency-domain representations for the multirate system, including the PFG.

eess.SY↗

arXiv2025

Statistically Optimal Structured Additive MIMO Continuous-time System Identification

Many applications in mechanical, acoustic, and electronic engineering require estimating complex dynamical models, often represented as additive multi-input multi-output (MIMO) transfer functions with structural constraints. This paper introduces a two-stage procedure for estimating structured additive MIMO models, where structural constraints are enforced through a weighted nonlinear least-squares projection of the parameter vector initially estimated using a recently developed refined instrumental variables algorithm. The proposed approach is shown to be consistent and asymptotically efficient in open-loop scenarios. In closed-loop settings, it remains consistent despite potential noise model misspecification and achieves minimum covariance among all instrumental variable estimators. Extensive simulations are performed to validate the theoretical findings, and to show the efficacy of the proposed approach.

eess.SY↗

arXiv2025

Parameter-Varying Feedforward Control: A Kernel-Based Learning Approach

The increasing demands for high accuracy in mechatronic systems necessitate the incorporation of parameter variations in feedforward control. The aim of this paper is to develop a data-driven approach for direct learning of parameter-varying feedforward control to increase tracking performance. The developed approach is based on kernel-regularized function estimation in conjunction with iterative learning to directly learn parameter-varying feedforward control from data. This approach enables high tracking performance for feedforward control of linear parameter-varying dynamics, providing flexibility to varying reference tasks. The developed framework is validated on a benchmark industrial experimental setup featuring a belt-driven carriage.

eess.SY↗

arXiv2025

Automatic Basis Function Selection in Iterative Learning Control: A Sparsity-Promoting Approach Applied to an Industrial Printer

Iterative learning control (ILC) techniques are capable of improving the tracking performance of control systems that repeatedly perform similar tasks by utilizing data from past iterations. The aim of this paper is to design a systematic approach for learning parameterized feedforward signals with limited complexity. The developed method involves an iterative learning control in conjunction with a data-driven sparse subset selection procedure for basis function selection. The ILC algorithm that employs sparse optimization is able to automatically select relevant basis functions and is validated on an industrial flatbed printer.

eess.SY↗

arXiv2025

Self-Calibrating Position Measurements: Applied to Imperfect Hall Sensors

Linear Hall sensors are a cost-effective alternative to optical encoders for measuring the rotor positions of actuators, with the main challenge being that they exhibit position-dependent inaccuracies resulting from manufacturing tolerances. This paper develops a data-driven calibration procedure for linear analog Hall sensors that enables accurate online estimates of the rotor angle without requiring expensive external encoders. The approach combines closed-loop data collection with nonlinear identification to obtain an accurate model of the sensor inaccuracies, which is subsequently used for online compensation. Simulation results show that when the flux density model structure is known, measurement errors are reduced to the sensor noise floor, and experiments on an industrial setup demonstrate a factor of 2.6 reduction in the root-mean-square measurement error. These results confirm that Hall sensor inaccuracies can be calibrated even when no external encoder is available, improving their practical applicability.

eess.SY↗

arXiv2025

Recursive Identification of Structured Systems: An Instrumental-Variable Approach Applied to Mechanical Systems

Online system identification algorithms are widely used for monitoring, diagnostics and control by continuously adapting to time-varying dynamics. Typically, these algorithms consider a model structure that lacks parsimony and offers limited physical interpretability. The objective of this paper is to develop a real-time parameter estimation algorithm aimed at identifying time-varying dynamics within an interpretable model structure. An additive model structure is adopted for this purpose, which offers enhanced parsimony and is shown to be particularly suitable for mechanical systems. The proposed approach integrates the recursive simplified refined instrumental variable method with block-coordinate descent to minimize an exponentially-weighted output error cost function. This novel recursive identification method delivers parametric continuous-time additive models and is applicable in both open-loop and closed-loop controlled systems. Its efficacy is shown using numerical simulations and is further validated using experimental data to detect the time-varying resonance dynamics of a flexible beam system. These results demonstrate the effectiveness of the proposed approach for online and interpretable estimation for advanced monitoring and control applications.

eess.SY↗

arXiv2025

Exploiting Structure in MIMO Scaled Graph Analysis

Scaled graphs offer a graphical tool for analysis of nonlinear feedback systems. Although recently substantial progress has been made in scaled graph analysis, at present their use in multivariable feedback systems is limited by conservatism. In this paper, we aim to reduce this conservatism by introducing multipliers and exploit system structure in the analysis with scaled graphs. In particular, we use weighted inner products to arrive at a weighted scaled graph and combine this with a commutation property to formulate a stability result for multivariable feedback systems. We present a method for computing the weighted scaled graph of Lur'e systems based on solving sets of linear matrix inequalities, and demonstrate a significant reduction in conservatism through an example.

eess.SY↗