Identification of High-Tech Motion Systems: An Active Vibration Isolation Benchmark

Voorhoeve, Robbert; Rietschoten, Annemiek van; Geerardyn, Egon; Oomen, Tom

doi:10.1016/j.ifacol.2015.12.303

Cited by 20 publications

(14 citation statements)

References 21 publications

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“…Furthermore, an experimental example and comparison with pre-existing approaches is presented in [39]. Finally, recent experiments [40] have shown good results on a 100 th order model.…”

Section: Discussionmentioning

confidence: 99%

Bi-Orthonormal Polynomial Basis Function Framework With Applications in System Identification

Herpen

Bosgra

Oomen

2016

IEEE Trans. Automat. Contr.

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Abstract-Numerical aspects are of central importance in identification and control. Many computations in these fields involve approximations using polynomial or rational functions that are obtained using orthogonal or oblique projections. The aim of this paper is to develop a new and general theoretical framework to solve a large class of relevant problems. The proposed method is built on the introduction of bi-orthonormal polynomials with respect to a data-dependent bi-linear form. This bi-linear form generalises the conventional inner product and allows for asymmetric and indefinite problems. The proposed approach is shown to lead to optimal numerical conditioning (κ = 1) in a recent frequency-domain instrumental variable system identification algorithm. In comparison, it is shown that these recent algorithms exhibit extremely poor numerical properties when solved using traditional approaches. I. INTRODUCTIONApplications of system identification and control often involve numerical computations. The accuracy of these computations determines the quality of the resulting model or controller. This has led to considerable research to develop numerically reliable algorithms, see, e.g., [38] and [8], [4] for a general overview. Many computations involve weighted least-squares type problems for systems that are parametrized in terms of (vector) polynomials or rational forms, where orthogonal or oblique projections play a central role.In the field of system identification, weighted nonlinear least-squares criteria are particularly common, see [29]. Established identification algorithms include [26], the SK-iteration [34], and the Gauss-Newton iteration [1], which (iteratively) compute the least-squares solution to a linear systems of equations, for polynomial models or rational parametrizations. Although conceptually straightforward, the associated numerical conditioning is often extremely poor, as is evidenced by the developments in [1 , a fundamentally different solution strategy is pursued. The strategy is based upon the construction of orthogonal polynomials with respect to a data-dependent inner product, which directly provides the solution to the approximation problem in terms of polynomials. Essentially, this yields optimal conditioning of the associated linear system of equations, i.e., κ = 1.Besides developments in view of reliable algorithms that involve least-squares type solutions, recently, more general

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“…Furthermore, an experimental example and comparison with pre-existing approaches is presented in [39]. Finally, recent experiments [40] have shown good results on a 100 th order model.…”

Section: Discussionmentioning

confidence: 99%

Bi-Orthonormal Polynomial Basis Function Framework With Applications in System Identification

Herpen

Bosgra

Oomen

2016

IEEE Trans. Automat. Contr.

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“…Many related challenges, e.g., for specific application areas, have not been addressed in the present paper, including (4) (113)- (116) . In addition, numerical aspects are highly challenging for complex systems, in control (117) , system identification (79)- (82) , and learning (95) . In addition, resource-efficient approaches for ILC based on sparse optimization are investigated in (118) .…”

Section: Discussionmentioning

confidence: 99%

Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems

Oomen

2018

IEEJ Journal IA

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100

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Manufacturing equipment and scientific instruments, including wafer scanners, printers, microscopes, and medical imaging scanners, require accurate and fast motions. An increase in such requirements necessitates enhanced control performance. The aim of this paper is to identify several challenges for advanced motion control originating from these increasing accuracy, speed, and cost requirements. For instance, flexible mechanics must be explicitly addressed through overactuation, oversensing, inferential control, and position-dependent control. This in turn requires suitable models of appropriate complexity. One of the main advantages of such motion systems is the fact that experimenting and collecting large amounts of accurate data is inexpensive, paving the way for identifying and learning of models and controllers from experimental data. Several ongoing developments are outlined that constitute part of an overall framework for control, identification, and learning of complex motion systems. In turn, this may pave the way for new mechatronic design principles, leading to fast lightweight machines where spatio-temporal flexible mechanics are explicitly compensated through advanced motion control.

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“…1) Non-Parametric Identification: The non-parametric frequency response function for the wafer-stage system is estimated using the robust multisine approach as explained in, e.g., [49,Section 3.7], [45]. The rigid-body motions of the system need to be controlled for stable operation, therefore all experiments are performed in a closed-loop configuration.…”

Section: A Methodsmentioning

confidence: 99%

Identifying Position-Dependent Mechanical Systems: A Modal Approach Applied to a Flexible Wafer Stage

Voorhoeve

Rozario

Aangenent

et al. 2021

IEEE Trans. Contr. Syst. Technol.

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Increasingly stringent performance requirements for motion control necessitate the use of increasingly detailed models of the system behavior. Motion systems inherently move, therefore, spatio-temporal models of the flexible dynamics are essential. In this paper, a two-step approach for the identification of the spatio-temporal behavior of mechanical systems is developed and applied to a prototype industrial wafer stage with a lightweight design for fast and highly accurate positioning. The proposed approach exploits a modal modeling framework and combines recently developed powerful linear time invariant (LTI) identification tools with a spline-based mode-shape interpolation approach to estimate the spatial system behavior. The experimental results for the wafer stage application confirm the suitability of the proposed approach for the identification of complex positiondependent mechanical systems, and show the pivotal role of the obtained models for improved motion control performance.

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Identification of High-Tech Motion Systems: An Active Vibration Isolation Benchmark

Cited by 20 publications

References 21 publications

Bi-Orthonormal Polynomial Basis Function Framework With Applications in System Identification

Bi-Orthonormal Polynomial Basis Function Framework With Applications in System Identification

Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems

Identifying Position-Dependent Mechanical Systems: A Modal Approach Applied to a Flexible Wafer Stage

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