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首页> 外文会议>American Control Conference, 2009. ACC '09 >Model predictive control of nonlinear stochastic PDEs: Application to a sputtering process
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Model predictive control of nonlinear stochastic PDEs: Application to a sputtering process

机译：非线性随机PDE的模型预测控制：在溅射过程中的应用

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In this work, we develop a method for model predictive control of nonlinear stochastic partial differential equations (PDEs) to regulate the state variance, which physically represents the roughness of a surface in a thin film growth process, to a desired level. We initially formulate a nonlinear stochastic PDE into a system of infinite nonlinear stochastic ordinary differential equations (ODEs) by using Galerkin's method. A finite-dimensional approximation is then derived that captures the dominant mode contribution to the state variance. A model predictive control problem is formulated based on the finite-dimensional approximation so that the future state variance can be predicted in a computationally efficient way. The control action is computed by minimizing an objective function including penalty on the discrepancy between the predicted state variance and a reference trajectory, and a terminal penalty. An analysis of the closed-loop nonlinear infinite-dimensional system is performed to characterize the closed-loop performance enforced by the model predictive controller. The model predictive controller is initially applied to the stochastic Kuramoto-Sivashinsky equation (KSE), a fourth-order nonlinear stochastic PDE. Simulation results demonstrate that the proposed predictive controller can successfully drive the norm of the state variance of the stochastic KSE to a desired level in the presence of significant model parameter uncertainties. In addition, we consider the problem of surface roughness regulation in a one-dimensional ion-sputtering process. The predictive controller is applied to the kinetic Monte Carlo model of the sputtering process to successfully regulate the expected surface roughness to a desired level.
机译：在这项工作中，我们开发了一种用于非线性随机偏微分方程（PDE）的模型预测控制的方法，以将状态变化（其物理表示薄膜生长过程中的表面粗糙度）调节到所需水平。我们最初使用Galerkin方法将非线性随机PDE公式化为无限非线性随机常微分方程（ODE）系统。然后得出一个有限维近似值，该近似值捕获了主模对状态方差的贡献。基于有限维逼近来制定模型预测控制问题，以便可以以计算有效的方式预测未来状态方差。通过使目标函数最小化来计算控制动作，该目标函数包括对预测状态方差与参考轨迹之间的差异的惩罚以及最终惩罚。对闭环非线性无限维系统进行了分析，以表征模型预测控制器强制执行的闭环性能。最初将模型预测控制器应用于随机Kuramoto-Sivashinsky方程（KSE），它是四阶非线性随机PDE。仿真结果表明，在存在明显的模型参数不确定性的情况下，所提出的预测控制器可以成功地将随机KSE的状态方差范数驱动至所需水平。另外，我们考虑一维离子溅射过程中表面粗糙度调节的问题。将预测控制器应用于溅射过程的动力学蒙特卡洛模型，以将预期的表面粗糙度成功地调节到所需的水平。

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