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Optimal-control theoretic methods for optimization and regulation of distributed parameter systems.

机译：用于优化和调节分布式参数系统的最优控制理论方法。

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摘要

Optimal control and optimization of distributed parameter systems are discussed in the context of a common control framework. The adjoint method of optimization and the traditional linear quadratic regulator implementation of optimal control both employ adjoint or costate variables in the determination of control variable progression. As well both theories benefit from a reduced order model approximation in their execution. This research aims to draw clear parallels between optimization and optimal control utilizing these similarities. Several applications are presented showing the use of adjoint/costate variables and reduced order models in optimization and optimal control problems.;The adjoint method for shape optimization is derived and implemented for the quasi-one-dimensional duct and two variations of a two-dimensional double ramp inlet. All applications are governed by the Euler equations. The quasi-one-dimensional duct is solved first to test the adjoint method and to verify the results against an analytical solution. The method is then adapted to solve the shape optimization of the double ramp inlet. A finite volume solver is tested on the flow equations and then implemented for the corresponding adjoint equations. The gradient of the cost function with respect to the shape parameters is derived based on the computed adjoint variables.;The same inlet shape optimization problem is then solved using a reduced order model. The basis functions in the reduced order model are computed using the method of snapshots form of proper orthogonal decomposition. The corresponding weights are derived using an optimization in the design parameter space to match the reduced order model to the original snapshots. A continuous map of these weights in terms of the design variables is obtained via a response surface approximations and artificial neural networks. This map is then utilized in an optimization problem to determine the optimal inlet shape. As in the adjoint method of optimization, the methodology for a reduced order model is validated using the quasi-one-dimensional duct. The reduced order model is tested for efficiency and accuracy by performing an inverse optimization to match the pressure along the duct to a desired pressure profile. The method is then extended to generate a reduced order model for the two dimensional double ramp inlet. In this case, we optimize the inlet shape to minimize the mass weighted total pressure loss. The optimal control problem addressed is a two-dimensional channel flow governed by the Burgers equation. An obstacle in the flow is utilized for the implementation of boundary control to influence the flow. The Burgers equation is written in the abstract Cauchy form to allow for the implementation of linear control routines.;The Riccati and Chandrasekhar equations are used to solve for the optimal control input to influence a region downstream of the obstacle. The results of both the controlled and uncontrolled scenarios are presented, and the Riccati and Chandrasekhar methods of gain calculation are compared. Reduced order modelling of the channel flow is performed using proper orthogonal decomposition and standard projection techniques. The reduced order model is then used for feedback control of the system in both set point and time-varying tracking problems.
机译：在通用控制框架的背景下讨论了分布式参数系统的最优控制和优化。优化的伴随方法和最优控制的传统线性二次调节器实现均在确定控制变量级数时采用伴随变量或代价变量。同样，这两种理论都受益于其执行过程中降阶模型的近似。本研究旨在利用这些相似性在优化和最优控制之间找到明确的相似之处。提出了几个应用程序，它们显示了伴随/共变量和降阶模型在优化和最优控制问题中的使用。;为准一维管道和二维的两个变体推导并实现了形状优化的伴随方法双斜坡入口。所有应用程序都由Euler方程控制。首先解决准一维管道问题，以测试伴随方法并针对解析解验证结果。该方法然后适于解决双斜坡入口的形状优化。在流动方程上测试了有限体积求解器，然后将其用于相应的伴随方程。根据计算出的伴随变量得出成本函数相对于形状参数的梯度。;然后使用降阶模型来解决相同的入口形状优化问题。使用适当的正交分解的快照形式的方法来计算降阶模型中的基函数。使用设计参数空间中的优化将对应的权重导出，以将降阶模型与原始快照匹配。这些权重在设计变量方面的连续映射是通过响应面近似和人工神经网络获得的。然后将此图用于优化问题中，以确定最佳的入口形状。与优化的伴随方法一样，使用准一维导管来验证降阶模型的方法。通过执行逆向优化以使沿管道的压力与所需压力曲线相匹配，来测试降阶模型的效率和准确性。然后扩展该方法以为二维双斜坡入口生成降阶模型。在这种情况下，我们将优化入口形状，以使质量加权总压力损失最小。解决的最佳控制问题是由Burgers方程控制的二维通道流。流程中的障碍物用于实施边界控制以影响流程。 Burgers方程以抽象的Cauchy形式编写，以允许执行线性控制例程。Riccati和Chandrasekhar方程用于求解影响障碍物下游区域的最佳控制输入。给出了受控场景和非受控场景的结果，并比较了Riccati和Chandrasekhar增益计算方法。使用适当的正交分解和标准投影技术执行通道流的降阶建模。然后将降阶模型用于设定点跟踪和时变跟踪问题中的系统反馈控制。

著录项

  • 作者

    Goss, Jennifer Dawn.;

  • 作者单位

    The University of Texas at Arlington.;

  • 授予单位 The University of Texas at Arlington.;
  • 学科 Engineering Aerospace.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 175 p.
  • 总页数 175
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 航空、航天技术的研究与探索;
  • 关键词

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