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Contouring Error Bounded Control for Biaxial Switched Linear Systems

Meng Yuan, Ye Wang, Chris Manzie, Zhezhuang Xu, Tianyou Chai

TL;DR

The paper tackles contouring control for biaxial switched linear systems with position-dependent flexibility, where the switching signal is unknown but minimum dwell-times are available. It develops an MPC-based controller that guarantees state, input, and contouring-error constraints for any admissible switch by computing switch control invariant sets and handling non-compact feasible sets through polygonal approximations. Key contributions include offline construction of switch CI sets, proofs of recursive feasibility and practical stability, and a synthesis framework for linear and circular contours; validated on a high-fidelity dual-drive laser machine, achieving contouring errors within the prescribed bound. This work enables precise, high-throughput biaxial contouring in industrial machines with structural flexibility, contributing to improved product quality and process reliability.

Abstract

Biaxial motion control systems are used extensively in manufacturing and printing industries. To improve throughput and reduce machine cost, lightweight materials are being proposed in structural components but may result in higher flexibility in the machine links. This flexibility is often position dependent and compromises precision of the end effector of the machine. To address the need for improved contouring accuracy in industrial machines with position-dependent structural flexibility, this paper introduces a novel contouring error-bounded control algorithm for biaxial switched linear systems. The proposed algorithm utilizes model predictive control to guarantee the satisfaction of state, input, and contouring error constraints for any admissible mode switching. In this paper, the switching signal remains unknown to the controller, although information about the minimum time the system is expected to stay in a specific mode is considered to be available. The proposed algorithm has the property of recursive feasibility and ensures the stability of the closed-loop system. The effectiveness of the proposed method is demonstrated by applying it to a high-fidelity simulation of a dual-drive industrial laser machine. The results show that the contouring error is successfully bounded within the given tolerance.

Contouring Error Bounded Control for Biaxial Switched Linear Systems

TL;DR

The paper tackles contouring control for biaxial switched linear systems with position-dependent flexibility, where the switching signal is unknown but minimum dwell-times are available. It develops an MPC-based controller that guarantees state, input, and contouring-error constraints for any admissible switch by computing switch control invariant sets and handling non-compact feasible sets through polygonal approximations. Key contributions include offline construction of switch CI sets, proofs of recursive feasibility and practical stability, and a synthesis framework for linear and circular contours; validated on a high-fidelity dual-drive laser machine, achieving contouring errors within the prescribed bound. This work enables precise, high-throughput biaxial contouring in industrial machines with structural flexibility, contributing to improved product quality and process reliability.

Abstract

Biaxial motion control systems are used extensively in manufacturing and printing industries. To improve throughput and reduce machine cost, lightweight materials are being proposed in structural components but may result in higher flexibility in the machine links. This flexibility is often position dependent and compromises precision of the end effector of the machine. To address the need for improved contouring accuracy in industrial machines with position-dependent structural flexibility, this paper introduces a novel contouring error-bounded control algorithm for biaxial switched linear systems. The proposed algorithm utilizes model predictive control to guarantee the satisfaction of state, input, and contouring error constraints for any admissible mode switching. In this paper, the switching signal remains unknown to the controller, although information about the minimum time the system is expected to stay in a specific mode is considered to be available. The proposed algorithm has the property of recursive feasibility and ensures the stability of the closed-loop system. The effectiveness of the proposed method is demonstrated by applying it to a high-fidelity simulation of a dual-drive industrial laser machine. The results show that the contouring error is successfully bounded within the given tolerance.
Paper Structure (14 sections, 2 theorems, 21 equations, 7 figures, 3 algorithms)

This paper contains 14 sections, 2 theorems, 21 equations, 7 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem statement
  3. Switched linear system
  4. Bounded contouring error
  5. Switched Model Predictive Controller for Bounded Contouring Error
  6. Computation of switch control invariant set
  7. Model Predictive Controller Formulation
  8. Closed-loop properties
  9. Synthesis for the proposed MPC
  10. Feasible sets for biaxial applications
  11. Linear contour
  12. Circular contour
  13. Simulation results
  14. Conclusion

Key Result

Theorem 1

Consider Assumptions ass:stab_obs-ass:P_matrix hold. Given a feasible initial state $\mathbf{x}(0)$, the closed-loop system of eq:switched_system with the MPC controller eq:MPC_problem is recursively feasible for time-varying reference signal $\mathbf{r}(k), \; k \in \mathbb{N}$.

Figures (7)

  • Figure 1: Industrial dual drive machine: (a) photo of industrial laser machine from our partner ANCA Motion; (b) schematic diagram of dual drive machine (top view).
  • Figure 2: Contouring errors and tracking errors.
  • Figure 3: Feasible sets with respect to circular contour: (a) non-compact set $\mathcal{S}_{c}$ (grey shaded area) and desired contour (dot line); (b) approximated sets with partitioned polygons (blue shaded area).
  • Figure 4: Reference: (a) time-dependent trajectory in X and Y-axis; (b) contour.
  • Figure 5: Feasible sets for bounded contouring error.
  • ...and 2 more figures

Theorems & Definitions (8)

  • Remark 1
  • Definition 1: Control Invariant Set
  • Definition 2: Backward Reachable Set
  • Definition 3: Switch Control Invariant Sets
  • Theorem 1: Recursive Feasibility
  • proof
  • Theorem 2: Closed-loop Stability
  • proof