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Robust Linear Quadratic Optimal Control of Cementitious Material Extrusion

Mandana Mohammadi Looey, Amrita Basak, Satadru Dey

Abstract

Extrusion-based 3D printing of cementitious materials enables fabrication of complex structures, however it is highly sensitive to disturbances, material property variations, and process uncertainties that decrease flow stability and dimensional fidelity. To address these challenges, this study proposes a robust linear quadratic optimal control framework for regulating material extrusion in cementitious direct ink writing systems. The printer is modeled using two coupled subsystems: an actuation system representing nozzle flow dynamics and a printing system describing the printed strand flow on the build plate. A hybrid control architecture combining sliding mode control for disturbance rejection with linear quadratic optimal feedback for energy-efficient tracking is developed to ensure robustness and optimality. In simulation case studies, the control architecture guarantees acceptable convergence of nozzle and strand flow tracking errors under bounded disturbances.

Robust Linear Quadratic Optimal Control of Cementitious Material Extrusion

Abstract

Extrusion-based 3D printing of cementitious materials enables fabrication of complex structures, however it is highly sensitive to disturbances, material property variations, and process uncertainties that decrease flow stability and dimensional fidelity. To address these challenges, this study proposes a robust linear quadratic optimal control framework for regulating material extrusion in cementitious direct ink writing systems. The printer is modeled using two coupled subsystems: an actuation system representing nozzle flow dynamics and a printing system describing the printed strand flow on the build plate. A hybrid control architecture combining sliding mode control for disturbance rejection with linear quadratic optimal feedback for energy-efficient tracking is developed to ensure robustness and optimality. In simulation case studies, the control architecture guarantees acceptable convergence of nozzle and strand flow tracking errors under bounded disturbances.
Paper Structure (10 sections, 2 theorems, 18 equations, 6 figures)

This paper contains 10 sections, 2 theorems, 18 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Robust Optimal Control of Extrusion-based Printer
  3. System Setup
  4. Mathematical Representation of Extrusion
  5. Optimality and Robustness in Extrusion
  6. Robust Linear Quadratic Optimal Control Framework
  7. Proposed Robust Optimal Control Architecture
  8. Design and Analysis of the Robust Optimal Controller
  9. Results and Discussion
  10. Conclusions

Key Result

Proposition 1

Consider the nozzle flow dynamics given by ss-1, the nozzle flow control law con-lw-1, the existence of a non-zero disturbance with the bound bnd, and the reference trajectory $x_{1_r}$ with the bounds bnd-2. Then, as desired by the robustness criterion rob-3, the reference nozzle flow velocity trac

Figures (6)

  • Figure 1: Schematic and system-level abstraction of extrusion-based 3D printer.
  • Figure 2: Proposed robust optimal control architecture.
  • Figure 3: Reference velocity tracking for the actuation system under disturbance injection.
  • Figure 4: Reference velocity tracking for printing system with optimal only controller.
  • Figure 5: Reference velocity tracking for printing system with optimal and sliding mode (SM) controller.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Remark 1
  • Proposition 1: Robustness of nozzle flow dynamics
  • proof
  • Proposition 2: Optimality and robustness of strand flow dynamics
  • proof