3D打印螺杆挤出机的时变和状态相关输入延迟补偿砰砰控制
Time- and State-Dependent Input Delay-Compensated Bang-Bang Control of a Screw Extruder for 3D Printing
摘要：
提出了一种基于延迟补偿的砰砰控制设计方法，用于螺杆挤出机3D打印过程中喷嘴输出流量的控制。所提出的应用程序具有很大的潜力，超越了最常用的工艺，如熔融沉积成型（FDM）和基于注射器的挤出（SBE），提高了构建速度。在部分和完全填充区域（PFZ和FFZ）中的螺杆挤出机的几何分解允许通过与常微分方程（ODE）耦合的1D双曲偏微分方程（PDE）来描述挤出机腔室中的材料对流。通过特征线法求解双曲型偏微分方程，将耦合偏微分方程-常微分方程系统转化为一个非线性状态相关输入时滞系统。上述延迟系统被扩展到非等温的情况下，考虑到周期性波动作用于材料的对流速度，这代表了由于温度变化在挤出机腔室中的粘度变化的影响，导致一个非线性系统的输入延迟，同时取决于状态和时间变量。在设计的分段指数反馈控制器下，证明了非线性无时滞对象的全局指数稳定性。通过将标称分段指数反馈控制器与非线性预测器反馈相结合，实现了对挤出机模型的时间和状态相关输入延迟的补偿。在Bang-Bang预测器反馈控制律下的闭环系统的全局渐近稳定性（GAS）是建立在满足与挤出机设计和材料特性以及材料输送速度变化的幅度和频率相关的某些条件时，这些条件易于验证。
英文摘要：
A delay-compensated Bang-Bang control design methodology for the control of the nozzle output flow rate of screw-extruder-based 3D printing processes is developed. The presented application has a great potential to move beyond the most commonly used processes such as Fused Deposition Modeling (FDM) and Syringe Based Extrusion (SBE), improving the build speed. A geometrical decomposition of the screw extruder in a partially and a fully filled regions (PFZ and FFZ) allows to describe the material convection in the extruder chamber by a 1D hyperbolic Partial Differential Equation (PDE) coupled with an Ordinary Differential Equation (ODE). After solving the hyperbolic PDE by the Method of Characteristics (MC), the coupled PDE-ODE's system is transformed into a nonlinear state-dependent input delay system. The aforementioned delay system is extended to the nonisothermal case with the consideration of periodic fluctuations acting on the material's convection speed, which represent the effect of viscosity variations 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 (GES) 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- and state-dependent input delay of the extruder model is achieved. Global Asymptotic Stability (GAS) of the closed-loop system under the Bang-Bang predictor feedback control law is established when certain conditions, which are easy to verify, 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.
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