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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., Comment: Extended report

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., Comment: 16 pages, 6 figures

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., Comment: 6 pages, 2 figures

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.

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., Comment: DOIs for code and data are available in paper

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., Comment: 6 pages, 7 figures. Final version

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., Comment: Accepted for presentation at the European Control Conference, Stockholm, 2024

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., Comment: 14 pages, 6 figures

A direct data-driven iterative algorithm is developed to accurately estimate the $H_\infty$ norm of a linear time-invariant system from continuous operation, i.e., without resetting the system. The main technical step involves a reversed-circulant matrix that can be evaluated in a model-free setting by performing experiments on the real system., Comment: 7 pages, 4 figures

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.

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., Comment: 6 pages, 6 figures

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., Comment: Final author version, accepted for publication at 62nd IEEE Conference on Decision and Control, Singapore, 2023

In this paper, we propose a novel $K$-nearest neighbor resampling procedure for estimating the performance of a policy from historical data containing realized episodes of a decision process generated under a different policy. We provide statistical consistency results under weak conditions. In particular, we avoid the common assumption of identically and independently distributed transitions and rewards. Instead, our analysis allows for the sampling of entire episodes, as is common practice in most applications. To establish the consistency in this setting, we generalize Stone's Theorem, a well-known result in nonparametric statistics on local averaging, to include episodic data and the counterfactual estimation underlying off-policy evaluation (OPE). By focusing on feedback policies that depend deterministically on the current state in environments with continuous state-action spaces and system-inherent stochasticity effected by chosen actions, and relying on trajectory simulation similar to Monte Carlo methods, the proposed method is particularly well suited for stochastic control environments. Compared to other OPE methods, our algorithm does not require optimization, can be efficiently implemented via tree-based nearest neighbor search and parallelization, and does not explicitly assume a parametric model for the environment's dynamics. Numerical experiments demonstrate the effectiveness of the algorithm compared to existing baselines in a variety of stochastic control settings, including a linear quadratic regulator, trade execution in limit order books, and online stochastic bin packing.

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.

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.

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., Comment: 6 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:2303.06045

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., Comment: 6 pages, accepted for 22nd IFAC World Congress

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., Comment: Included conference information in banner of paper

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., Comment: Final author version

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., Comment: 16 pages, 8 figures

Amperometry is a commonly used electrochemical method for studying the process of exocytosis in real-time. Given the high precision of recording that amperometry procedures offer, the volume of data generated can span over several hundreds of megabytes to a few gigabytes and therefore necessitates systematic and reproducible methods for analysis. Though the spike characteristics of amperometry traces in the time domain hold information about the dynamics of exocytosis, these biochemical signals are, more often than not, characterized by time-varying signal properties. Such signals with time-variant properties may occur at different frequencies and therefore analyzing them in the frequency domain may provide statistical validation for observations already established in the time domain. This necessitates the use of time-variant, frequency-selective signal processing methods as well, which can adeptly quantify the dominant or mean frequencies in the signal. The Fast Fourier Transform (FFT) is a well-established computational tool that is commonly used to find the frequency components of a signal buried in noise. In this work, we outline a method for spike-based frequency analysis of amperometry traces using FFT that also provides statistical validation of observations on spike characteristics in the time domain. We demonstrate the method by utilizing simulated signals and by subsequently testing it on diverse amperometry datasets generated from different experiments with various chemical stimulations. To our knowledge, this is the first fully automated open-source tool available dedicated to the analysis of spikes extracted from amperometry signals in the frequency domain., Comment: 34 pages, 16 figures

Elucidating exocytosis processes provide insights into cellular neurotransmission mechanisms, and may have potential in neurodegenerative diseases research. Amperometry is an established electrochemical method for the detection of neurotransmitters released from and stored inside cells. An important aspect of the amperometry method is the sub-millisecond temporal resolution of the current recordings which leads to several hundreds of gigabytes of high-quality data. In this study, we present a universal method for the classification with respect to diverse amperometric datasets using data-driven approaches in computational science. We demonstrate a very high prediction accuracy (greater than or equal to 95%). This includes an end-to-end systematic machine learning workflow for amperometric time series datasets consisting of pre-processing; feature extraction; model identification; training and testing; followed by feature importance evaluation - all implemented. We tested the method on heterogeneous amperometric time series datasets generated using different experimental approaches, chemical stimulations, electrode types, and varying recording times. We identified a certain overarching set of common features across these datasets which enables accurate predictions. Further, we showed that information relevant for the classification of amperometric traces are neither in the spiky segments alone, nor can it be retrieved from just the temporal structure of spikes. In fact, the transients between spikes and the trace baselines carry essential information for a successful classification, thereby strongly demonstrating that an effective feature representation of amperometric time series requires the full time series. To our knowledge, this is one of the first studies that propose a scheme for machine learning, and in particular, supervised learning on full amperometry time series data., Comment: 56 pages, 11 figures

Feedforward for motion systems is getting increasingly more important to achieve performance requirements. This leads to a situation where position-dependent effects cannot be neglected anymore., Comment: 3 page abstract; to appear in euspen Special Interest Group Meeting on Precision Motion Systems & Control

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., Comment: Accepted for presentation at the 2022 Conference on Decision and Control (CDC)

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., Comment: 6 pages, 8 figures, to be presented at Modeling Estimation and Control Conference 2022 in Jersey City, NJ, to be published in IFAC-PapersOnLine

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., Comment: 6 pages, 11 figures

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., Comment: paper submitted to the CDC

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., Comment: To appear in Conference on Decision and Control 2022

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., Comment: To appear in Modeling, Estimation and Control Conference (MECC) 2022

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., Comment: To appear in IEEE 61st Conference on Decision and Control, Cancun, Mexico, 2022, uploaded to arXiv 31-08-2022