Factors like growing 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). Time marching simulations of DeePC and CL-DeePC are conducted using Hankel matrices of past data that are updated at every time step to induce potentially troublesome closed-loop correlations between inputs and noise. 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.

Data-driven estimation of system norms is essential for analyzing, verifying, and designing control systems. Existing data-based methods often do not capture the inter-grid and transient behavior of the system, leading to inaccurate and unreliable system norm estimations. This paper presents a unified approach for accurate and reliable estimation of the H₂ and H_∞ norm with a limited amount of data. The key step is to exploit local parametric models that explicitly incorporate the inter-grid and transient dynamics. The system norm is estimated through the computation of local system norms of the local parametric models within their the local frequency interval. Simulation and experimental results illustrate the effectiveness of the proposed method.

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.

Fast-rate models are essential for control design, specifically to address intersample behavior. The aim of this article is to develop a frequency-domain nonparametric 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 nonparametric 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.

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.

The kernel-based inverse system identification framework enables accurate identification of systems with non-minimum phase dynamics, greatly expanding the potential of non-causal system identification approaches. The existing kernel-based inverse system identification method performs the estimation assuming noisy input data, while in practice noise is typically present only in the output measurements. To address this impracticality, we propose a Bayesian identification method that employs the Expectation-Maximization algorithm and the Markov chain Monte Carlo method to enable direct identification of the inverse system using the available data. Through numerical simulations, we found that the proposed method allows for an accurate estimation of inverse models, and outperforms an indirect approach in both model fit and variance. The proposed method can be used to develop enhanced data-driven feedforward control methods that allow for flexible design while incorporating design specifications.

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 output measurements 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.

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 paper 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.

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.

Safe deployment of neural networks to classify time series in safety-critical applications relies on the ability of the classifier to detect data that does not originate from the same distribution as the training data. The aim of this paper is to propose a framework for detecting whether time series data is sampled from a different distribution than the training data, known as the problem of out-of-distribution (OOD) detection. We propose a novel distance-based OOD method for time series data using a hierarchical clustering method together with dynamic time-warping to measure the difference between a new data instance and the training set. The method is evaluated in the context of mechanical ventilation, a safety critical application, using both simulated and clinical datasets. Results of the mechanical ventilation use case demonstrate that the proposed approach effectively detects out-of-distribution data and improves classification performance in diverse settings.

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.

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.

Iterative learning control (ILC) is typically applied in practice combined with a feedback controller for time-domain stability. In this closed-loop design with actuator constraints, existing constrained ILC designs suffer from determining the exact input constraint on the ILC controller. This issue brings in an important gap between the existing constrained ILC designs and their real-world applications. This paper gives a systematic consideration of the input constraint problem in the closed-loop ILC design with actuator saturation. A constraint-aware ILC is developed to autonomously determine the constraint on the feedforward controller. The convergence of the constrained ILC process is proved under the framework of alternating projection. Finally, the effectiveness of the developed method is verified on a numerical simulation.

Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main aim of this letter 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.