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.

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.

Robust fault detection is crucial for ensuring the reliability and safety of complex engineering systems. However, distinguishing faults from disturbances and model uncertainty which are inherently present in any practical system remains remains a challenging task. This paper addresses the robust fault detection filter design problem for continuous-time linear time-invariant uncertain systems operating in open or closed-loop configurations. The proposed framework offers a unified approach to handle both parametric and dynamic uncertainties by solving a single Riccati equation, based on a worst-case disturbance and uncertainty scenario. The efficacy of the proposed approach is demonstrated on a numerical multivariable double mass-spring-damper system. The results illustrate that an optimal compromise is achieved between fault sensitivity and rejection of modelling uncertainties and disturbances. This capability enables the clear differentiation between faults and undesired effects in the residuals, thereby enhancing fault detection reliability, ultimately contributing to improved safety and performance.

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.

Increasing performance requirements in high-precision mechatronic systems lead to a situation where both multivariable and sampled-data implementation aspects need to be addressed. The aim of this paper is to develop a design framework for a multi-input multi-output feedforward controller to improve continuous-time tracking performance through learning. The sampled-data feedforward controller is designed with physically interpretable tuning parameters using a multirate zero-order-hold differentiator. The developed approach enables interaction compensation for multi-input multi-output systems and the feedforward controller parameters are updated through learning. The performance improvement is experimentally validated in a multi-input multi-output motion system compared to the conventional feedforward controllers.

Accurately modeling nonlinearities is becoming increasingly important for mechanical systems, particularly in the context of system design, model-based control and monitoring systems for fault diagnosis. In the nonlinear modeling process, a pivotal phase involves pinpointing the physical locations and quantifying the magnitude of nonlinearities. This paper introduces a data-driven approach for nonlinearity location and quantification by analyzing nonparametric frequency response functions. To achieve this objective, measurement locations in mechanical systems are interpreted as nodes arranged in a dynamic network, and linearization techniques are employed on the frequency response functions formed from node to node. The efficacy of the proposed approach and the concept of nonlinearity localization and quantification are illustrated by numerical simulations and experiments on a flexible beam setup.

Multivariable parametric models are essential for optimizing the performance of high-tech systems. The main objective of this paper is to develop an identification strategy that provides accurate parametric models for complex multivariable systems. To achieve this, an additive model structure is adopted, offering advantages over traditional black-box model structures when considering physical systems. The introduced method minimizes a weighted least-squares criterion and uses a refined instrumental variable method to solve the estimation problem, achieving local optimality upon convergence. Experimental validation is conducted on a prototype wafer-stage system, featuring a large number of spatially distributed actuators and sensors and exhibiting complex flexible dynamic behavior, to demonstrate 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.

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.

Cross-coupled iterative learning control (ILC) can improve the contour tracking performance of manufacturing systems significantly. This paper aims to develop a framework for norm-optimal cross-coupled ILC that enables intuitive tuning of time- and iteration-varying weights of the exact contour error and its tangential counterpart. This leads to an iteration-varying ILC algorithm for which convergence conditions are developed. In addition, a resource-efficient implementation is developed that reduces the computational load significantly and enables the use of long reference signals. The approach is experimentally validated on an industrial flatbed printer.

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 letter 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.

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 H_-/H_∞ 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.

The condition of mechatronic production equipment slowly deteriorates over time, increasing the risk of failure and associated unscheduled downtime. A key indicator for an increased risk for failures is the shifting of resonances. The aim of this paper is to track the shifting resonances of the equipment online and during normal operation. This paper contributes to real-time parametric fault diagnosis by applying and comparing parameter estimators in this new context, highly relevant for next-generation mechatronic systems. The proposed fault diagnosis systems consist of recursive least squares algorithms and the effectiveness is illustrated on an overactuated and oversensed flexible beam setup, allowing to artificially manipulate its effective resonances in a controlled manner.

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.