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Frequency Domain Auto-tuning of Structured LPV Controllers for High-Precision Motion Control

Yorick Broens, Hans Butler, Roland Tóth

TL;DR

This work tackles the challenge of achieving high-precision motion control for MIMO systems with position-dependent dynamics by introducing a frequency-domain auto-tuning framework for structured LPV controllers that relies solely on FRFs. The approach features a modular controller parameterization combining a low-frequency LTI block and a high-frequency LPV block with an LFR-based interconnection, together with a novel extended Nyquist stability test and a CT-preserving discretization. An optimization pipeline combines PSO and gradient-based refinement to minimize a weighted H-infinity-like objective while enforcing stability, and uses sophisticated performance shaping via piecewise-affine frequency filters. Experimental validation on a moving-magnet planar actuator demonstrates that the LPV controller achieves a substantial improvement (43% reduction in Ry tracking error) over a robust design, underscoring the method’s practical impact for high-precision motion systems.

Abstract

Motion systems are a vital part of many industrial processes. However, meeting the increasingly stringent demands of these systems, especially concerning precision and throughput, requires novel control design methods that can go beyond the capabilities of traditional solutions. Traditional control methods often struggle with the complexity and position-dependent effects inherent in modern motion systems, leading to compromises in performance and a laborious task of controller design. This paper addresses these challenges by introducing a novel structured feedback control auto-tuning approach for multiple-input multiple-output (MIMO) motion systems. By leveraging frequency response function (FRF) estimates and the linear-parameter-varying (LPV) control framework, the proposed approach automates the controller design, while providing local stability and performance guarantees. Key innovations include norm-based magnitude optimization of the sensitivity functions, an automated stability check through a novel extended factorized Nyquist criterion, a modular structured MIMO LPV controller parameterization, and a controller discretization approach which preserves the continuous-time (CT) controller parameterization. The proposed approach is validated through experiments using a state-of-the-art moving-magnet planar actuator prototype.

Frequency Domain Auto-tuning of Structured LPV Controllers for High-Precision Motion Control

TL;DR

This work tackles the challenge of achieving high-precision motion control for MIMO systems with position-dependent dynamics by introducing a frequency-domain auto-tuning framework for structured LPV controllers that relies solely on FRFs. The approach features a modular controller parameterization combining a low-frequency LTI block and a high-frequency LPV block with an LFR-based interconnection, together with a novel extended Nyquist stability test and a CT-preserving discretization. An optimization pipeline combines PSO and gradient-based refinement to minimize a weighted H-infinity-like objective while enforcing stability, and uses sophisticated performance shaping via piecewise-affine frequency filters. Experimental validation on a moving-magnet planar actuator demonstrates that the LPV controller achieves a substantial improvement (43% reduction in Ry tracking error) over a robust design, underscoring the method’s practical impact for high-precision motion systems.

Abstract

Motion systems are a vital part of many industrial processes. However, meeting the increasingly stringent demands of these systems, especially concerning precision and throughput, requires novel control design methods that can go beyond the capabilities of traditional solutions. Traditional control methods often struggle with the complexity and position-dependent effects inherent in modern motion systems, leading to compromises in performance and a laborious task of controller design. This paper addresses these challenges by introducing a novel structured feedback control auto-tuning approach for multiple-input multiple-output (MIMO) motion systems. By leveraging frequency response function (FRF) estimates and the linear-parameter-varying (LPV) control framework, the proposed approach automates the controller design, while providing local stability and performance guarantees. Key innovations include norm-based magnitude optimization of the sensitivity functions, an automated stability check through a novel extended factorized Nyquist criterion, a modular structured MIMO LPV controller parameterization, and a controller discretization approach which preserves the continuous-time (CT) controller parameterization. The proposed approach is validated through experiments using a state-of-the-art moving-magnet planar actuator prototype.
Paper Structure (17 sections, 26 equations, 4 figures)

This paper contains 17 sections, 26 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Background
  4. Problem Statement
  5. Controller Parameterization
  6. Low-frequency LTI controller design
  7. High-frequency LPV controller design
  8. Controller interconnection
  9. Auto-tuning
  10. Stability Analysis
  11. Performance Shaping
  12. Solving the optimization problem
  13. Controller implementation
  14. Experimental Validation
  15. MMPA Prototype System
  16. ...and 2 more sections

Figures (4)

  • Figure 1: Set of local FRFs of a high-precision moving-magnet planar actuator prototype, illustrating the high-frequency position dependent flexible dynamics for the RB decoupled transfer in $R_y$-direction.
  • Figure 2: Closed-loop motion control interconnection, where $\mathcal{K}$ is partitioned into a low-frequency LTI controller and a high-frequency LPV controller.
  • Figure 3: Photograph of a moving-magnet planar actuator system prototype.
  • Figure 4: Position tracking error in $R_y$ direction during the constant velocity interval of the motion profile with: (-) Robust controller, (-) LPV controller.