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Tom Oomen

Publications and source records attributed to Tom Oomen.

At least 55 records · Page 3Linked to original sources
arXiv2023

Structured ambiguity sets for distributionally robust optimization

Distributionally robust optimization (DRO) incorporates robustness against uncertainty in the specification of probabilistic models. This paper focuses on mitigating the curse of dimensionality in data-driven DRO problems with optimal transport ambiguity sets. By exploiting independence across lower-dimensional components of the uncertainty, we construct structured ambiguity sets that exhibit a faster shrinkage as the number of collected samples increases. This narrows down the plausible models of the data-generating distribution and mitigates the conservativeness that the decisions of DRO problems over such ambiguity sets may face. We establish statistical guarantees for these structured ambiguity sets and provide dual reformulations of their associated DRO problems for a wide range of objective functions. The benefits of the approach are demonstrated in a numerical example.

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arXiv2023

Nonlinear Bayesian Identification for Motor Commutation: Applied to Switched Reluctance Motors

Switched Reluctance Motors (SRMs) enable power-efficient actuation with mechanically simple designs. This paper aims to identify the nonlinear relationship between torque, rotor angle, and currents, to design commutation functions that minimize torque ripple in SRMs. This is achieved by conducting specific closed-loop experiments using purposely imperfect commutation functions and identifying the nonlinear dynamics via Bayesian estimation. A simulation example shows that the presented method is robust to position-dependent disturbances, and experiments suggest that the identification method enables the design of commutation functions that significantly increase performance. The developed approach enables accurate identification of the torque-current-angle relationship in SRMs, without the need for torque sensors, an accurate linear model, or an accurate model of position-dependent disturbances, making it easy to implement in production.

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arXiv2023

Direct Learning for Parameter-Varying Feedforward Control: A Neural-Network Approach

The performance of a feedforward controller is primarily determined by the extent to which it can capture the relevant dynamics of a system. The aim of this paper is to develop an input-output linear parameter-varying (LPV) feedforward parameterization and a corresponding data-driven estimation method in which the dependency of the coefficients on the scheduling signal are learned by a neural network. The use of a neural network enables the parameterization to compensate a wide class of constant relative degree LPV systems. Efficient optimization of the neural-network-based controller is achieved through a Levenberg-Marquardt approach with analytic gradients and a pseudolinear approach generalizing Sanathanan-Koerner to the LPV case. The performance of the developed feedforward learning method is validated in a simulation study of an LPV system showing excellent performance.

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arXiv2023

Beyond Nyquist in Frequency Response Function Identification: Applied to Slow-Sampled Systems

Fast-sampled models are essential for control design, e.g., to address intersample behavior. The aim of this paper is to develop a non-parametric identification technique for fast-sampled models of systems that have relevant dynamics and actuation above the Nyquist frequency of the sensor, such as vision-in-the-loop systems. The developed method assumes smoothness of the frequency response function, which allows to disentangle aliased components through local models over multiple frequency bands. The method identifies fast-sampled models of slowly-sampled systems accurately in a single identification experiment. Finally, an experimental example demonstrates the effectiveness of the technique.

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arXiv2023

Direct Shaping of Minimum and Maximum Singular Values: An $\mathcal{H}_{-}/\mathcal{H}_{\infty}$ Synthesis Approach for Fault Detection Filters

The performance of fault detection filters relies on a high sensitivity to faults and a low sensitivity to disturbances. The aim of this paper is to develop an approach to directly shape these sensitivities, expressed in terms of minimum and maximum singular values. The developed method offers an alternative solution to the $\mathcal{H}_{-}/\mathcal{H}_{\infty}$ synthesis problem, building upon traditional multiobjective synthesis results. The result is an optimal filter synthesized via iterative convex optimization and the approach is particularly useful for fault diagnosis as illustrated by a numerical example.

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arXiv2023

A Kernel-Based Identification Approach to LPV Feedforward: With Application to Motion Systems

The increasing demands for motion control result in a situation where Linear Parameter-Varying (LPV) dynamics have to be taken into account. Inverse-model feedforward control for LPV motion systems is challenging, since the inverse of an LPV system is often dynamically dependent on the scheduling sequence. The aim of this paper is to develop an identification approach that directly identifies dynamically scheduled feedforward controllers for LPV motion systems from data. In this paper, the feedforward controller is parameterized in basis functions, similar to, e.g., mass-acceleration feedforward, and is identified by a kernel-based approach such that the parameter dependency for LPV motion systems is addressed. The resulting feedforward includes dynamic dependence and is learned accurately. The developed framework is validated on an example.

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arXiv2023

Cascaded Calibration of Mechatronic Systems via Bayesian Inference

Sensors in high-precision mechatronic systems require accurate calibration, which is achieved using test beds that, in turn, require even more accurate calibration. The aim of this paper is to develop a cascaded calibration method for position sensors of mechatronic systems while taking into account the variance of the calibration model of the test bed. The developed calibration method employs Gaussian Process regression to obtain a model of the position-dependent sensor inaccuracies by combining prior knowledge of the sensor with data using Bayesian inference. Monte Carlo simulations show that the developed calibration approach leads to significantly higher calibration accuracy when compared to alternative regression techniques, especially when the number of available calibration points is limited. The results indicate that more accurate calibration of position sensors is possible with fewer resources.

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arXiv2023

Identifying Lebesgue-sampled Continuous-time Impulse Response Models: A Kernel-based Approach

Control applications are increasingly sampled non-equidistantly in time, including in motion control, networked control, resource-aware control, and event-triggered control. Some of these applications use measurement devices that sample equidistantly in the amplitude domain. The aim of this paper is to develop a non-parametric estimator of the impulse response of continuous-time systems based on such sampling strategy, known as Lebesgue-sampling. To this end, kernel methods are developed to formulate an algorithm that adequately takes into account the output intersample behavior, which ultimately leads to more accurate models and more efficient output sampling compared to the standard approach. The efficacy of this method is demonstrated through a mass-spring damper case study.

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arXiv2023

Learning for Precision Motion of an Interventional X-ray System: Add-on Physics-Guided Neural Network Feedforward Control

Tracking performance of physical-model-based feedforward control for interventional X-ray systems is limited by hard-to-model parasitic nonlinear dynamics, such as cable forces and nonlinear friction. In this paper, these nonlinear dynamics are compensated using a physics-guided neural network (PGNN), consisting of a physical model, embedding prior knowledge of the dynamics, in parallel with a neural network to learn hard-to-model dynamics. To ensure that the neural network learns only unmodelled effects, the neural network output in the subspace spanned by the physical model is regularized via an orthogonal projection-based approach, resulting in complementary physical model and neural network contributions. The PGNN feedforward controller reduces the tracking error of an interventional X-ray system by a factor of 5 compared to an optimally tuned physical model, successfully compensating the unmodeled parasitic dynamics.

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arXiv2022

Unifying Model-Based and Neural Network Feedforward: Physics-Guided Neural Networks with Linear Autoregressive Dynamics

Unknown nonlinear dynamics often limit the tracking performance of feedforward control. The aim of this paper is to develop a feedforward control framework that can compensate these unknown nonlinear dynamics using universal function approximators. The feedforward controller is parametrized as a parallel combination of a physics-based model and a neural network, where both share the same linear autoregressive (AR) dynamics. This parametrization allows for efficient output-error optimization through Sanathanan-Koerner (SK) iterations. Within each SK-iteration, the output of the neural network is penalized in the subspace of the physics-based model through orthogonal projection-based regularization, such that the neural network captures only the unmodelled dynamics, resulting in interpretable models.

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arXiv2022

Feedforward Control in the Presence of Input Nonlinearities: A Learning-based Approach

Advanced feedforward control methods enable mechatronic systems to perform varying motion tasks with extreme accuracy and throughput. The aim of this paper is to develop a data-driven feedforward controller that addresses input nonlinearities, which are common in typical applications such as semiconductor back-end equipment. The developed method consists of parametric inverse-model feedforward that is optimized for tracking error reduction by exploiting ideas from iterative learning control. Results on a simulated set-up indicate improved performance over existing identification methods for systems with nonlinearities at the input.

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arXiv2022

Optimal Commutation for Switched Reluctance Motors using Gaussian Process Regression

Switched reluctance motors are appealing because they are inexpensive in both construction and maintenance. The aim of this paper is to develop a commutation function that linearizes the nonlinear motor dynamics in such a way that the torque ripple is reduced. To this end, a convex optimization problem is posed that directly penalizes torque ripple in between samples, as well as power consumption, and Gaussian Process regression is used to obtain a continuous commutation function. The resulting function is fundamentally different from conventional commutation functions, and closed-loop simulations show significant reduction of the error. The results offer a new perspective on suitable commutation functions for accurate control of reluctance motors.

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arXiv2022

Automated MIMO Motion Feedforward Control: Efficient Learning through Data-Driven Gradients via Adjoint Experiments and Stochastic Approximation

Parameterized feedforward control is at the basis of many successful control applications with varying references. The aim of this paper is to develop an efficient data-driven approach to learn the feedforward parameters for MIMO systems. To this end, a cost criterion is minimized using a stochastic gradient descent algorithm, in which both the search direction and step size are determined through system experiments. In particular, the search direction is chosen as an unbiased estimate of the gradient which is obtained from a single experiment, regardless of the size of the MIMO system. The approach is illustrated using a simulation example, in which it is shown to be superior to a deterministic method in terms of convergence speed and thus experimental cost.

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arXiv2022

Cross-Coupled Iterative Learning Control for Complex Systems: A Monotonically Convergent and Computationally Efficient Approach

Cross-coupled iterative learning control (ILC) can achieve high performance for manufacturing applications in which tracking a contour is essential for the quality of a product. The aim of this paper is to develop a framework for norm-optimal cross-coupled ILC that enables the use of exact contour errors that are calculated offline, and iteration- and time-varying weights. Conditions for the monotonic convergence of this iteration-varying ILC algorithm are developed. In addition, a resource-efficient implementation is proposed in which the ILC update law is reframed as a linear quadratic tracking problem, reducing the computational load significantly. The approach is illustrated on a simulation example.

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arXiv2022

Data-enabled predictive control with instrumental variables: the direct equivalence with subspace predictive control

Direct data-driven control has attracted substantial interest since it enables optimization-based control without the need for a parametric model. This paper presents a new Instrumental Variable~(IV) approach to Data-enabled Predictive Control (DeePC) that results in favorable noise mitigation properties, and demonstrates the direct equivalence between DeePC and Subspace Predictive Control (SPC). The methodology relies on the derivation of the characteristic equation in DeePC along the lines of subspace identification algorithms. A particular choice of IVs is presented that is uncorrelated with future noise, but at the same time highly correlated with the data matrix. A simulation study demonstrates the improved performance of the proposed algorithm in the presence of process and measurement noise.

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arXiv2022

Frequency Domain Identification of Multirate Systems: A Lifted Local Polynomial Modeling Approach

Frequency-domain representations of multirate systems are essential for controller design and performance evaluation of multirate systems and sampled-data control. The aim of this paper is to develop a time-efficient closed-loop identification approach for multirate systems in the frequency-domain. The developed method utilizes local polynomial modeling for lifted representations of LPTV systems, which enables direct identification of closed-loop multirate systems in a single identification experiment. Unlike LTI identification techniques, the developed method does not suffer from bias due to ignored LPTV dynamics. The developed approach is demonstrated on a multirate example, resulting in accurate and fast identification in the frequency domain.

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arXiv2022

Neural Network Training Using Closed-Loop Data: Hazards and an Instrumental Variable (IVNN) Solution

An increasing trend in the use of neural networks in control systems is being observed. The aim of this paper is to reveal that the straightforward application of learning neural network feedforward controllers with closed-loop data may introduce parameter inconsistency that degrades control performance, and to provide a solution. The proposed method employs instrumental variables to ensure consistent parameter estimates. A nonlinear system example reveals that the developed instrumental variable neural network (IVNN) approach asymptotically recovers the optimal solution, while pre-existing approaches are shown to lead to inconsistent estimates.

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