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Tom Oomen

Publications and source records attributed to Tom Oomen.

At least 37 records · Page 2Linked to original sources
arXiv2025

Tractable reformulations of DRO problems over structured optimal transport ambiguity sets

Structuring ambiguity sets in Wasserstein-based distributionally robust optimization (DRO) can improve their statistical properties when the uncertainty consists of multiple independent components. The aim of this paper is to solve stochastic optimization problems with unknown uncertainty when we only have access to a finite set of samples from it. Exploiting strong duality of DRO problems over structured ambiguity sets, we derive tractable reformulations for certain classes of DRO and uncertainty quantification problems. We also derive tractable reformulations for distributionally robust chance-constrained problems. As the complexity of the reformulations may grow exponentially with the number of independent uncertainty components, we employ clustering strategies to obtain informative estimators, which yield problems of manageable complexity. We demonstrate the effectiveness of the theoretical results in a numerical simulation example.

math.OC↗
arXiv2025

Lifted Frequency-Domain Identification of Closed-Loop Multirate Systems: Applied to Dual-Stage Actuator Hard Disk Drives

Frequency-domain representations are crucial for the design and performance evaluation of controllers in multirate systems, specifically to address intersample performance. The aim of this paper is to develop an effective frequency-domain system identification technique for closed-loop multirate systems using solely slow-rate output measurements. By indirect identification of multivariable time-invariant representations through lifting, in combination with local modeling techniques, the multirate system is effectively identified. The developed method is capable of accurate identification of closed-loop multirate systems within a single identification experiment, using fast-rate excitation and inputs, and slow-rate outputs. Finally, the developed framework is validated using a benchmark problem consisting of a multivariable dual-stage actuator from a hard disk drive, demonstrating its applicability and accuracy.

eess.SY↗
arXiv2025

GraFIT: A toolbox for fast and accurate frequency response identification in Gravitational Wave Detectors

Frequency response function (FRF) measurements are widely used in Gravitational Wave (GW) detectors, e.g., for the design of controllers, calibrating signals and diagnostic problems with system dynamics. The aim of this paper is to present GraFIT: a toolbox that enables fast, inexpensive, and accurate identification of FRF measurements for GW detectors compared to the commonly used approaches, including common spectral analysis techniques. The toolbox consists of a single function to estimate the frequency response function for both open-loop and closed-loop systems and for arbitrary input and output dimensions. The toolbox is validated on two experimental case studies of the Virgo detector, illustrating more than a factor 3 reduction in standard deviation of the estimate for the same measurement times, and comparable standard deviations with up to 10 times less data for the new method with respect to the currently implemented Spectral Analysis method.

gr-qc↗
arXiv2025

Compensating Hysteresis and Mechanical Misalignment in Piezo-Stepper Actuators

Piezo-stepper actuators enable accurate positioning through the sequential contraction and expansion of piezoelectric elements, generating a walking motion. The aim of this paper is to reduce velocity ripples caused by parasitic effects, due to hysteresis in the piezoelectric material and mechanical misalignments, through suitable feedforward control. The presented approach involves the integration of a rate-dependent hysteresis model with a position-dependent feedforward learning scheme to compensate for these effects. Experimental results show that this approach leads to a significant reduction in the velocity ripples, even when the target velocity is changed. These results enable the use of piezo-stepper actuators in applications requiring high positioning accuracy and stiffness over a long stroke, without requiring expensive position sensors for high-gain feedback.

eess.SY↗
arXiv2025

Local Rational Modeling for Identification Beyond the Nyquist Frequency: Applied to a Prototype Wafer Stage

Fast-rate models are essential for control design, specifically to address intersample behavior. The aim of this paper is to develop a frequency-domain non-parametric identification technique to estimate fast-rate models of systems that have relevant dynamics and allow for actuation above the Nyquist frequency of a slow-rate output. Examples of such systems include vision-in-the-loop systems. Through local rational models over multiple frequency bands, aliased components are effectively disentangled, particularly for lightly-damped systems. The developed technique accurately determines non-parametric fast-rate models of systems with slow-rate outputs, all within a single identification experiment. Finally, the effectiveness of the technique is demonstrated through experiments conducted on a prototype wafer stage used for semiconductor manufacturing.

eess.SY↗
arXiv2025

A Direct State-Space Realization of Discrete-Time Linear Parameter-Varying Input-Output Models

A minimal state-space (SS) realization of an identified linear parameter-varying (LPV) input-output (IO) model usually introduces dynamic and nonlinear dependency of the state-space coefficient functions, complicating stability analysis and controller synthesis. The aim of this paper is to introduce and analyze a direct SS realization of this IO model that avoids this nonlinear and dynamic dependency, at the cost of introducing a nonminimal state. It is shown that this direct SS realization 1) is reachable under a coprimeness condition on the coefficient functions of the IO model and a well-posedness condition on the model order, and 2) is never observable but that the unobservable directions converge to zero in a finite amount of steps, i.e., that the realization is reconstructible. The derived results are illustrated through numerical examples in both the LPV and LTI case.

eess.SY↗
arXiv2025

Feedback linearisation of mechanical systems using data-driven models

Linearising the dynamics of nonlinear mechanical systems is an important and open research area. A common approach is feedback linearisation, which is a nonlinear control method that transforms the input-output response of a nonlinear system into an equivalent linear one. The main problem with feedback linearisation is that it requires an accurate first-principles model of the system, which are typically hard to obtain. In this paper, we design an alternative control approach that exploits data-driven models to linearise the input-output response of nonlinear mechanical systems. Specifically, a model-based reference tracking architecture is developed for nonlinear feedback systems with output nonlinearities. The overall methodology shows a high degree of performance combined with significant robustness against imperfect modelling and extrapolation. These findings are demonstrated using large set of synthetic experiments conducted on a asymmetric Duffing oscillator and using an experimental prototype of a high-precision motion system.

eess.SY↗
arXiv2024

Sampling in Parametric and Nonparametric System Identification: Aliasing, Input Conditions, and Consistency

The sampling rate of input and output signals is known to play a critical role in the identification and control of dynamical systems. For slow-sampled continuous-time systems that do not satisfy the Nyquist-Shannon sampling condition for perfect signal reconstructability, careful consideration is required when identifying parametric and nonparametric models. In this letter, a comprehensive statistical analysis of estimators under slow sampling is performed. Necessary and sufficient conditions are obtained for unbiased estimates of the frequency response function beyond the Nyquist frequency, and it is shown that consistency of parametric estimators can be achieved even if input frequencies overlap after aliasing. Monte Carlo simulations confirm the theoretical properties.

eess.SY↗
arXiv2024

Identification of Additive Continuous-time Systems in Open and Closed loop

When identifying electrical, mechanical, or biological systems, parametric continuous-time identification methods can lead to interpretable and parsimonious models when the model structure aligns with the physical properties of the system. Traditional linear system identification may not consider the most parsimonious model when relying solely on unfactored transfer functions, which typically result from standard direct approaches. This paper presents a novel identification method that delivers additive models for both open and closed-loop setups. The estimators that are derived are shown to be generically consistent, and can admit the identification of marginally stable additive systems. Numerical simulations show the efficacy of the proposed approach, and its performance in identifying a modal representation of a flexible beam is verified using experimental data.

eess.SY↗
arXiv2024

Data-enabled Predictive Repetitive Control

Many systems are subject to periodic disturbances and exhibit repetitive behaviour. Model-based repetitive control employs knowledge of such periodicity to attenuate periodic disturbances and has seen a wide range of successful industrial implementations. The aim of this paper is to develop a data-driven repetitive control method. In the developed framework, linear periodically time-varying (LPTV) behaviour is lifted to linear time-invariant (LTI) behaviour. Periodic disturbance mitigation is enabled by developing an extension of Willems' fundamental lemma for systems with exogenous disturbances. The resulting Data-enabled Predictive Repetitive Control (DeePRC) technique accounts for periodic system behaviour to perform attenuation of a periodic disturbance. Simulations demonstrate the ability of DeePRC to effectively mitigate periodic disturbances in the presence of noise.

eess.SY↗
arXiv2024

Stable Inversion of Piecewise Affine Systems with Application to Feedforward and Iterative Learning Control

Model inversion is a fundamental technique in feedforward control. Unstable inverse models present a challenge in that useful feedforward control trajectories cannot be generated by directly propagating them. Stable inversion is a process for generating useful trajectories from unstable inverses by handling their stable and unstable modes separately. Piecewise affine (PWA) systems are a popular framework for modeling complicated dynamics. The primary contributions of this article are closed-form inverse formulas for a general class of PWA models, and stable inversion methods for these models. Both contributions leverage closed-form model representations to prove sufficient conditions for solution existence and uniqueness, and to develop solution computation methods. The result is implementable feedforward control synthesis from PWA models with either stable or unstable inverses. In practice, feedforward control alone may yield substantial tracking errors due to mismatch between the known system model and the unknowable complete system physics. Iterative learning control (ILC) is a technique for achieving robustness to model error in feedforward control. To demonstrate the primary contributions' validity and utility, this article also integrates PWA stable inversion with ILC in simulations based on a physical printhead positioning system.

eess.SY↗
arXiv2024

Statistical Analysis of Block Coordinate Descent Algorithms for Linear Continuous-time System Identification

Block coordinate descent is an optimization technique that is used for estimating multi-input single-output (MISO) continuous-time models, as well as single-input single output (SISO) models in additive form. Despite its widespread use in various optimization contexts, the statistical properties of block coordinate descent in continuous-time system identification have not been covered in the literature. The aim of this paper is to formally analyze the bias properties of the block coordinate descent approach for the identification of MISO and additive SISO systems. We characterize the asymptotic bias at each iteration, and provide sufficient conditions for the consistency of the estimator for each identification setting. The theoretical results are supported by simulation examples.

eess.SY↗
arXiv2024

Robust Commutation Design: Applied to Switched Reluctance Motors

Switched Reluctance Motors (SRMs) are cost-effective electric actuators that utilize magnetic reluctance to generate torque, with torque ripple arising from unaccounted manufacturing defects in the rotor tooth geometry. This paper aims to design a versatile, resource-efficient commutation function for accurate control of a range of SRMs, mitigating torque ripple despite manufacturing variations across SRMs and individual rotor teeth. The developed commutation function optimally distributes current between coils by leveraging the variance in the torque-current-angle model and is designed with few parameters for easy integration on affordable hardware. Monte Carlo simulations and experimental results show a tracking error reduction of up to 31% and 11%, respectively. The developed approach is beneficial for applications using a single driver for multiple systems and those constrained by memory or modeling effort, providing an economical solution for improved tracking performance and reduced acoustic noise.

eess.SY↗
arXiv2024

Unconstrained Parameterization of Stable LPV Input-Output Models: with Application to System Identification

Ensuring stability of discrete-time (DT) linear parameter-varying (LPV) input-output (IO) models estimated via system identification methods is a challenging problem as known stability constraints can only be numerically verified, e.g., through solving Linear Matrix Inequalities. In this paper, an unconstrained DT-LPV-IO parameterization is developed which gives a stable model for any choice of model parameters. To achieve this, it is shown that all quadratically stable DT-LPV-IO models can be generated by a mapping of transformed coefficient functions that are constrained to the unit ball, i.e., a small-gain condition. The unit ball is then reparameterized through a Cayley transformation, resulting in an unconstrained parameterization of all quadratically stable DT-LPV-IO models. As a special case, an unconstrained parameterization of all stable DT linear time-invariant transfer functions is obtained. Identification using the stable DT-LPV-IO model with neural network coefficient functions is demonstrated on a simulation example of a position-varying mass-damper-spring system.

eess.SY↗
arXiv2024

A Frequency-Domain Approach for Enhanced Performance and Task Flexibility in Finite-Time ILC

Iterative learning control (ILC) is capable of improving the tracking performance of repetitive control systems by utilizing data from past iterations. The aim of this paper is to achieve both task flexibility, which is often achieved by ILC with basis functions, and the performance of frequency-domain ILC, with an intuitive design procedure. The cost function of norm-optimal ILC is determined that recovers frequency-domain ILC, and consequently, the feedforward signal is parameterized in terms of basis functions and frequency-domain ILC. The resulting method has the performance and design procedure of frequency-domain ILC and the task flexibility of basis functions ILC, and are complimentary to each other. Validation on a benchmark example confirms the capabilities of the framework.

eess.SY↗
arXiv2024

Kernel-based identification using Lebesgue-sampled data

Sampling in control applications is increasingly done non-equidistantly in time. This includes applications in motion control, networked control, resource-aware control, and event-based control. Some of these applications, like the ones where displacement is tracked using incremental encoders, are driven by signals that are only measured when their values cross fixed thresholds in the amplitude domain. This paper introduces a non-parametric estimator of the impulse response and transfer function of continuous-time systems based on such amplitude-equidistant sampling strategy, known as Lebesgue sampling. To this end, kernel methods are developed to formulate an algorithm that adequately takes into account the bounded output uncertainty between the event timestamps, which ultimately leads to more accurate models and more efficient output sampling compared to the equidistantly-sampled kernel-based approach. The efficacy of our proposed method is demonstrated through a mass-spring damper example with encoder measurements and extensive Monte Carlo simulation studies on system benchmarks.

eess.SY↗
arXiv2024

Closed-loop Data-Enabled Predictive Control and its equivalence with Closed-loop Subspace Predictive Control

Factors like improved data availability and increasing system complexity have sparked interest in data-driven predictive control (DDPC) methods like Data-enabled Predictive Control (DeePC). However, closed-loop identification bias arises in the presence of noise, which reduces the effectiveness of obtained control policies. In this paper we propose Closed-loop Data-enabled Predictive Control (CL-DeePC), a framework that unifies different approaches to address this challenge. To this end, CL-DeePC incorporates instrumental variables (IVs) to synthesize and sequentially apply consistent single or multi-step-ahead predictors. Furthermore, a computationally efficient CL-DeePC implementation is developed that reveals an equivalence with Closed-loop Subspace Predictive Control (CL-SPC). Compared to DeePC, CL-DeePC simulations demonstrate superior reference tracking, with a sensitivity study finding a 48% lower susceptibility to noise-induced reference tracking performance degradation.

eess.SY↗