Well‐posedness and exact controllability of the mass balance equations for an extrusion process

Shang, Peipei; Wang, Zhiqiang

doi:10.1002/mma.3719

Cited by 5 publications

(2 citation statements)

References 34 publications

(50 reference statements)

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“…A predictive controller is designed in , which, in fact, is the inspiration for the present paper. We mention that the exact controllability and the well‐posedness of the bizone model – are also treated in .…”

Section: Control Of the Delay‐free System With A ‘Bang‐bang’ Control Lawmentioning

confidence: 99%

“…In the present article, a generic and dynamical model of a homogeneous melt SE process derived from mass and momentum balance laws [22][23][24][25][26][27][28][29][30] is used for the design of a delay-compensated bang-bang controller that permits a fast and accurate control of the flow at the nozzle output. The model consists of a one-dimensional partial differential equation (PDE) that is defined on a timevarying spatial domain whose dynamics obeys to an ordinary differential equation (ODE).…”

Section: Introductionmentioning

confidence: 99%

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Time‐ and State‐Dependent Input Delay‐Compensated Bang‐Bang Control of a Screw Extruder for 3D Printing

Bekiaris-Liberis

Krstić

2017

Intl J Robust & Nonlinear

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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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Section: Control Of the Delay‐free System With A ‘Bang‐bang’ Control Lawmentioning

confidence: 99%