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This paper aims to develop a new data-driven \cal H\infty norm estimation algorithm for model-error modeling of multivariable systems. An iterative approach is presented that requires significantly a fewer prior assumptions on the true system, hence it provides stronger guarantees in a robust control design. The iterative estimation algorithm is embedded in a robust control design framework with a judiciously selected uncertainty structure to facilitate high control performance. The approach is experimentally implemented on an industrial active vibration isolation system. [ABSTRACT FROM PUBLISHER]

The standard assumption that a measurement signal is available at each sample in iterative learning control (ILC) is not always justified, e.g., when exploiting time-stamped data from incremental encoders or in systems with data dropouts. The aim of this paper is to develop a computationally tractable ILC framework that is capable of exploiting intermittent data while maintaining favourable properties, including monotonic convergence. A controllability and observability analysis of the intermittent ILC framework leads to appropriate monotonic convergence conditions which allow for missing data. These conditions lead to a new explicit ILC controller design independent of the sampling instances, which is reminiscent of gradient-descent ILC. The approach is demonstrated on both an intuitive example and a practically relevant example which exploits time-varying timestamped data from an incremental encoder. [ABSTRACT FROM AUTHOR]

Iterative learning control (ILC) yields perfect output‐tracking performance at sampling instances for systems that perform repetitive tasks. The aim of this article is to develop a framework for a state‐tracking ILC that mitigates oscillatory intersample behavior, which is often encountered in output tracking ILC. As a framework for the analysis, the stability of the iterative domain including the robustness filter and the asymptotic signal is formulated. In addition, as a framework for the design, the design method using frequency response data to reduce the modeling effort, the learning filter design based on inversion, and the specific design procedure of the robustness filter are presented. The designed method is successfully applied to a motion system and it is shown that the presented state‐tracking ILC provides better intersample behavior than the standard output‐tracking ILC. [ABSTRACT FROM AUTHOR]

Abstract: Many iterative approaches in the field of system identification for control have been developed. Although successful implementations have been reported, a solid analysis with respect to the convergence of these iterations has not been established. The aim of this paper is to present a thorough analysis of a specific iterative algorithm that involves nonparametric -norm estimation. The pursued methodology involves a novel frequency domain approach that addresses both additive stochastic disturbances and input normalization. The results of the convergence analysis are twofold: (1) the presence of additive disturbances introduces a bias in the estimation procedure, and (2) the iterative procedure can be interpreted as experiment design for -norm estimation, revealing the value of iterations and limits of accuracy in terms of the Fisher information matrix. The results are confirmed by means of a simulation example. [Copyright &y& Elsevier]

The performance of algorithms in system identification and control, depends on their implementation in finite-precision arithmetic. The aim of this paper is to develop a unified approach for numerically reliable system identification that combines the numerical advantages of data-dependent orthogonal polynomials and the discrete-time δ -domain parametrization. In this paper, earlier results for discrete orthogonal polynomials on the real-line and the unit-circle are generalized to obtain an approach for the construction of orthogonal polynomials on generalized circles in the complex plane. This enables the formulation of a unified framework for the numerically reliable identification of systems expressed in the δ -domain, as well as in the traditional Laplace and Z -domains. An example is presented which shows the significant numerical advantages of the δ -domain approach for the identification of fast-sampled systems. [ABSTRACT FROM AUTHOR]

Iterative learning control (ILC) and repetitive control (RC) can lead to high performance by attenuating repeating disturbances perfectly, yet these approaches may amplify non-repeating disturbances. The aim of this paper is to achieve both perfect, fast attenuation of repeating disturbances and limited amplification of non-repeating disturbances. This is achieved by including a deadzone nonlinearity in the learning filter, which distinguishes disturbances based on their different amplitudes to apply different learning gains. Convergence conditions for nonlinear ILC and RC are developed, which are used in combination with system measurements in a comprehensive design procedure. Experimental implementation demonstrates fast learning and small errors. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. • Novel control method that linearises input–output dynamics of mechanical systems. • Nonlinear data-driven state-space models are used; linear part is preserved. • Nonlinear distortion analysis quantifies efficacy over frequency range of interest. • Simulations and experiments show high performance and robustness properties. [ABSTRACT FROM AUTHOR]

This article develops a novel framework for iterative learning control (ILC) design of discrete‐time systems with non‐uniform trial lengths by using the method of alternating projections. In contrast to existing results for the non‐uniform trial length problem, this article uses the Hilbert space setting and hence the linear discrete‐time system dynamics with non‐uniform trial lengths can be represented by multiple affine subspaces (or linear varieties). Motivated by the successive projection design between two closed convex sets, the considered ILC problem can be transformed into alternating projections between multiple sets, then the Hilbert space setting is used to establish key systems theoretic properties. Moreover, an optimal ILC design is developed for systems with non‐uniform trial lengths, which is also extended to the case of input constraints. A numerical case study is given to illustrate the applicability of the new design. [ABSTRACT FROM AUTHOR]

Model-based control design requires a careful specification of performance and robustness requirements. In typical norm-based control designs, performance and robustness requirements are specified in a scalar optimization criterion, even for complex multivariable systems. This paper aims to develop a novel approach for the formulation of this optimization criterion for multivariable motion systems that exhibit spatio-temporal deformations. To achieve this, characteristics of the underlying system are exploited to design multivariable weighting functions. In contrast to pre-existing approaches, which typically lead to diagonal weighting functions, the proposed approach enables the design of non-diagonal weighting functions. Extensive experimental results confirm that the proposed procedure can significantly improve the performance of an industrial motion system compared to earlier approaches. [ABSTRACT FROM AUTHOR]

Repetitive control enables the exact compensation of periodic disturbances if the internal model is appropriately selected. The aim of this paper is to develop a novel synthesis technique for repetitive control (RC) based on a new more general internal model. By employing a Gaussian process internal model, asymptotic rejection is obtained for a wide range of disturbances through an appropriate selection of a kernel. The implementation is a simple linear time-invariant (LTI) filter that is automatically synthesized through this kernel. The result is a user-friendly design approach based on a limited number of intuitive design variables, such as smoothness and periodicity. The approach naturally extends to reject multi-period and non-periodic disturbances, exiting approaches are recovered as special cases, and a case study shows that it outperforms traditional RC in both convergence speed and steady-state error. [ABSTRACT FROM AUTHOR]

This paper presents a framework for the derivation of a noise budget and the subsequent utilization in the optimization of the control design, using the laser frequency stabilization loop in the Virgo interferometer, which is a complex nested feedback system, as an experimental case study. First, the system dynamics and noise sources are modeled and experimentally verified to produce the noise budget, after which an optimization problem using the H 2 norm is formulated and tailored to the specific design requirements for the detector. The structure of the synthesized controller is then used to produce an improved control design. Experimental verification of the developed controller on the Virgo interferometer shows roughly a factor 3 reduction in root-mean-square error, illustrating the effectiveness of the presented method. [ABSTRACT FROM AUTHOR]

The increasing complexity of next-generation mechatronic systems leads to different types of periodic disturbances, which require dedicated repetitive control strategies to attenuate. The aim of this paper is to develop a new repetitive control strategy to completely attenuate a periodic disturbance and a user-defined number of relevant higher harmonics with limited memory usage. To this end, a multirate repetitive controller is developed, which combines a buffer at a reduced sampling rate with learning and robustness filters at the original sampling rate of the system. This leads to a linear periodic time-varying system, for which convergence conditions are developed. The method is implemented on an industrial print-belt system, demonstrating that it can match the performance of traditional repetitive control while significantly reducing the memory usage. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Next-generation deformable mirrors are envisaged to exhibit low-frequency flexible dynamics and to contain a large number of spatially distributed actuators due to increasingly stringent performance requirements. The increasingly complex system characteristics necessitate identifying the flexible dynamic behavior for design validation and next-generation control. The aim of this paper is to develop a unified approach for the identification of mechanical systems with a large number of spatially distributed actuators and a limited number of sensors. A frequency domain-based approach using local modeling techniques is developed. The modal modeling framework is employed to analyze the design and create outputs that were not measured. The proposed approach is applied to an experimental deformable mirror case study that illustrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Actuators that require commutation algorithms, such as the switched reluctance motor (SRM) considered in this paper and employed in the coarse pointing assembly (CPA) for free-space optical communication, often have torque-ripple disturbances that are periodic in the commutation-angle domain that deteriorate the positioning performance. The aim of this paper is to model the torque ripple as a Gaussian Process (GP) in the commutation-angle domain and consequently compensate for it at arbitrary velocity. The approach employs repetitive control (RC) at a constant velocity. A spatial GP with a periodic kernel is trained using data that is obtained from the RC step resulting in a static non-linear function for compensation at arbitrary velocity. Stability conditions are provided for both steps. The approach is successfully applied to a CPA prototype to improve the tracking performance for laser communication, where the torque ripple is compensated at arbitrary velocity. [ABSTRACT FROM AUTHOR]

Piezo stepper actuators are very promising for nanopositioning systems due to their high resolution, high stiffness, fast response, and the ability to position a mover over an infinite stroke by means of motion reminiscent of walking. The aim of this paper is to enhance the waveforms for actuating piezo steppers, by actively compensating for repetitive disturbances that are introduced by the walking behavior. A compensation method is developed to compensate for disturbances in the stepping domain, since disturbances may vary in the time domain if the velocity changes. The results from this procedure are exploited to determine an optimal waveform for the working range of the actuator. A significant improvement in performance is achieved after applying this waveform to a piezo stepper actuator. [ABSTRACT FROM AUTHOR]