Time- and state-dependent input delay-compensated bang–bang control of a screw extruder for 3D printing
Open accessAbstract
Summary In this paper, a delay‐compensated bang‐bang control design methodology for the control of the nozzle output flow rate of screw extruder‐based three‐dimensional printing processes is developed. A geometrical decomposition of the screw extruder in a partially and a fully filled regions allows to describe the material convection in the extruder chamber by a one‐dimensional hyperbolic partial differential equation (PDE) coupled with an ordinary differential equation. After solving the hyperbolic PDE by the method of characteristics, the coupled PDE–ordinary differential equation's system is transformed into a nonlinear state‐dependent input delay system. The aforementioned delay system is extended to the non‐isothermal case with the consideration of periodic fluctuations acting on the material's convection speed, which represent the process variabilities due to temperature changes in the extruder chamber, resulting to a nonlinear system with an input delay that simultaneously depends on the state and the time variable. Global exponential stability of the nonlinear delay‐free plant is established under a piecewise exponential feedback controller that is designed. By combining the nominal, piecewise exponential feedback controller with nonlinear predictor feedback, the compensation of the time‐dependent and state‐dependent input delay of the extruder model is achieved. Global asymptotic stability of the closed‐loop system under the bang‐bang predictor feedback control law is established when certain conditions related to the extruder design and the material properties, as well as to the magnitude and frequency of the materials transport speed variations, are satisfied. Simulations results are presented to illustrate the effectiveness of the proposed control design. Copyright © 2017 John Wiley & Sons, Ltd.
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System (1)-(3) is no longer equivalent to the classical time-delay system in [5,6,14-17].
“Equation (31) indicates that system (1)-(3) is no longer equivalent to the following classical time-delay system in [5,6,14-17]”
From Multi-layer predictor feedback design for nonlinear integro-differential equations with state-dependent input delays (2026) · cites this paper as [15]
Using φ(t) avoids the density-based transformation employed in prior work and feeds the predicted flux directly into (75).
“By using the ϕ ( t ) , we avoid the density-based transformation employed in prior work (e.g. [9,15,23], and instead feed the predicted flux directly into (75).”
From Multi-layer predictor feedback design for nonlinear integro-differential equations with state-dependent input delays (2026) · cites this paper as [15]
The citation is attached to the claim that prior work employed a density-based transformation. Sections 2.2.3–2.2.4 use density in the extruder’s mass-balance and flow-rate equations, but the passages found do not describe a density-based transformation. Section 5.1 defines φ(t) as an input-delay relation, not as evidence for that attributed prior-work method. (LLM, conf=0.72)
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- Authors
- Diagne, M., Bekiaris‐Liberis, N., & Krstic, M.
- Affiliations
- University of Michigan (US)
- Department of Production Engineering and Management Technical University of Crete Chania 73100 Greece
- Department of Mechanical and Aerospace Engineering University of California San Diego 92093 CA USA
- Corresponding author
- Diagne, Mamadou
- ORCID
- Diagne, Mamadou
- Venue
- International Journal of Robust and Nonlinear Control
- Publisher
- Wiley
- Published
- 2017-02-21
- Volume
- 27
- Issue
- 17
- Pages
- 3727-3757
- ISSN
- 1049-8923 (ISSN-L)
- 1099-1239
- OpenAlex
- W2590817262
- Cited by
- 21
- References
- 59
- Citations by year
- 2026: 3 · 2025: 1 · 2024: 3 · 2023: 1 · 2021: 1 · 2020: 4 · 2019: 4 · 2018: 4
- FWCI
- 2.06
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- International Journal of Robust and Nonlinear Control (publishedVersion)
- Deep Blue (University of Michigan) (submittedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Controllability of Differential Equations
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Design
- Keywords
- screw extruder, 3D printing, bang-bang control, input delay compensation, hyperbolic equations, method of characteristics, global exponential stability, global asymptotic stability
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