Frequency Response Function Identification of LPV Systems: a Global Approach with Application to Mechanical Systems

Rozario, Robin de; Oomen, Tom

doi:10.1016/j.ifacol.2018.09.099

Cited by 6 publications

(5 citation statements)

References 19 publications

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“…5) Identification Approach: To identify the modal system model defined by (9), (11) and parameterized by (14) from the identified FRFG s (s k ), the following steps are followed. 1) Define weighting filters W (k) as in (18). 2) Perform i SK iterations of the SK algorithm using the mechanical LMFD model with constraints as defined in Section IV-A3.…”

Section: A Methodsmentioning

confidence: 99%

“…In the gain-scheduling control approach [12]- [14], nonlinear systems are controlled by exploiting scheduling variables to switch between LTI controllers. For position-dependent mechanical systems, the relative positioning between individual components can be effectively used as scheduling variables in this approach [15]- [18]. The Linear Parameter-Varying (LPV) control framework formalizes the gain-scheduling method by ensuring stability and performance through a rigorous mathematical approach that strongly relies on accurate system models, [19]- [22].…”

Section: Fixed Worldmentioning

confidence: 99%

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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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Section: A Methodsmentioning

confidence: 99%

Section: Fixed Worldmentioning

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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“…This corollary states that the Nyquist curve lies below a line in the complex plane with slope α and provides a sufficient condition for the closed-loop in Figure 1 to be locally stable for each operating point p. Note that these stability concepts give no guarantees for stability of the closed-loop behavior in Figure 2 for varying p. For that the available information in the frozen FRFs is insufficient and concepts like the global FRF forms presented in [19], [20] might provide stability concepts in the future, but currently theoretical tools are missing for global stability analysis purely on frequency domain data. However, if the scheduling variation is sufficiently slow, stability can be guaranteed in the global sense based on purely local conditions as motivated in [23], however there is no exact characterization of how slow that scheduling variation needs to be.…”

Section: Stabilitymentioning

confidence: 99%

“…In the identification literature, recent developments have been made towards nonparametric modeling through FRF identification of LPV systems. These developments follow the paths of local identification in [17], [18] and more recently also a global approach to FRF identification of LPV systems has been developed [19]. For an overview of FRF representations of LPV systems see [20].…”

Section: Introductionmentioning

confidence: 99%

Towards Data-Driven LPV Controller Synthesis Based on Frequency Response Functions

Bloemers

Tóth

Oomen

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…The pragmatic approach to obtain (6) is to identify the FRF around different operating points using a local input/output data set, avoiding the need to explicitly find the state-space representation. The FRF can be obtained using a wealth of existing and well-understood techniques [21], [13], or more recent approaches focusing on LPV FRF identification [22], [23].…”

Section: Description Of the Systemmentioning

confidence: 99%

Frequency-Domain Data-Driven Position-Dependent Controller Synthesis for Cartesian Robots

Schuchert

Karimi

2023

IEEE Trans. Contr. Syst. Technol.

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Cartesian robots have position-dependent dynamics that must be taken into account for highperformance applications. Traditional methods design Linear Time-Invariant (LTI) controllers that are robustly stable with respect to position variations, but result in reduced performance. Advanced methods require Linear Parameter Varying (LPV) models and LPV controller design methods that are not well-established in the industry. On the other hand, the classical model-based gain-scheduled technique involves parametric identification, high-performance controller design for each position, interpolation of the controller parameters, and real-time controller validation, making it time-consuming and costly. Our approach uses frequency response at different operating points to design an LPV controller using a convex optimization algorithm based on second-order cone programming. The approach is applied to an industrial 3-axis Cartesian robot, showing significant improvements over state-of-the-art control design strategies. Data acquisition and controller design can be performed automatically, reducing significantly the engineering costs for controller synthesis.

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Frequency Response Function Identification of LPV Systems: a Global Approach with Application to Mechanical Systems

Cited by 6 publications

References 19 publications

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

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

Towards Data-Driven LPV Controller Synthesis Based on Frequency Response Functions

Frequency-Domain Data-Driven Position-Dependent Controller Synthesis for Cartesian Robots

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