Robust LPV Modeling of Precision Motion Systems Via Edge-Theorem Verification
Yazan Al-Rawashdeh, Mohammad Al Janaideh
AI summary
Problem
Precision motion systems exhibit position-dependent dynamics and nonlinearities that complicate accurate modeling and control. Existing LPV identification methods often suffer from state alignment issues, lack robust stability guarantees, and rely on complex time-domain experiments.
Approach
The method fits local transfer functions at grid points, converts them to controllable canonical state-space forms for consistent interpolation, and verifies global stability by checking edge polynomials of the convex hull via the Edge Theorem.
Key results
- Modular frequency-domain LPV modeling workflow
- Guaranteed state alignment through fixed-order canonical realizations
- Efficient global stability verification via finite Edge Theorem checks
- Experimental validation on a precision XY scanner with strong simulation-experiment agreement
Why it matters
Enables control engineers and robotics researchers to reliably design robust LPV controllers directly from accessible frequency-response data for precision motion applications.
Abstract
This work proposes a systematic workflow for con- structing grid-based Linear Parameter-Varying (LPV) models from frequency response data. Transfer functions are estimated at multiple scheduling-parameter grid points, fitted with a fixed model order, and transformed into controllable canoni- cal realizations to ensure structural consistency. These vertex models are interpolated into an LPV state-space representation, while robust stability is verified using the Edge Theorem, which reduces the problem to checking edge polynomials of the convex hull. The novelty of the approach lies in integrating frequency-domain identification, canonical-form embedding, and polytope-based robust stability analysis into a unified LPV framework. Unlike conventional methods that rely on time-domain experiments or subspace techniques, the proposed method exploits experimentally accessible frequency-response data and avoids coordinate mismatches during interpolation. Validation on a precision motion system demonstrates both theoretical soundness and practical applicability, confirming the workflow as a reliable pathway from frequency-domain data to robust LPV control design.