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首页> 外文学位 >Vibrational and adaptive control of a class of distributed parameter systems described by parabolic partial differential equations.
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Vibrational and adaptive control of a class of distributed parameter systems described by parabolic partial differential equations.

机译：抛物线偏微分方程描述的一类分布参数系统的振动和自适应控制。

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摘要

Two nonclassical control techniques, vibrational control and direct model reference adaptive control, for a class of distributed parameter systems described by parabolic partial differential equations (PDE's) are discussed.;Vibrational control is an open loop control technique which proposes a utilization of zero mean parametric excitation to a dynamical system to achieve desired control objectives. The vibrational control problem consists of establishing the existence of parametric vibrations which stabilize an unstable system, and in synthesizing these parametric vibrations. The transient behavior analysis for a vibrationally controlled system is also included in the vibrational control problem. Stability criteria for linear oscillatory parabolic PDE's are discussed first. Vibrational control for nonlinear parabolic PDE's is considered for nonlinearities that give rise to two classes of vibrations; vector additive, and linear multiplicative. Since vibrational control strategy requires no on-line measurements, vibrational stabilization is a powerful alternative in situations when feedback and/or feedforward are difficult or impossible to apply due to the restrictions on sensing and actuation.;The second half of this work addresses direct adaptive control for parabolic PDE's with constant or spatially-varying coefficients. It is assumed that the distributed measurement and the distributed control are both possible. The adaptation laws are obtained by the Lyapunov redesign method. It is shown that the concept of persistency of excitation in infinite dimensional adaptive systems needs to be investigated in relation to time variable, spatial variable, and boundary conditions. It is demonstrated that even a constant input signal is sufficiently rich in the sense that it guarantees the convergence of parameter errors to zero. Averaging theorems for two-time scale systems which involve a finite dimensional slow system and an infinite dimensional fast system are developed. The exponential stability of the adaptive algorithm, which is critical in finite dimensional adaptive control in terms of tolerating disturbances and unmodeled dynamics, is shown by applying averaging.;In both vibrational control and direct adaptive control, averaging methods are being used for stability analysis. In vibrational control, which utilizes a qualitative change of global behavior of attractors caused by oscillations, the stability properties of the nonautonomous system is deduced from the stability properties of the averaged autonomous system. In adaptive control the whole closed loop system becomes time-varying by continuous modification of the control laws, and the stability of the closed loop is concluded from the exponential stability of the averaged system. Examples and computer simulations are provided to support the theory in both cases.
机译：讨论了由抛物线偏微分方程（PDE's）描述的一类分布参数系统的两种非经典控制技术：振动控制和直接模型参考自适应控制。振动控制是一种开环控制技术，提出了利用零均值参数的方法激励动力系统以实现所需的控制目标。振动控制问题包括建立稳定不稳定系统的参数振动的存在，以及合成这些参数振动。振动控制系统的瞬态行为分析也包括在振动控制问题中。首先讨论线性振荡抛物线PDE的稳定性准则。非线性抛物线PDE的振动控制被认为是引起两类振动的非线性。向量加法和线性乘法。由于振动控制策略不需要在线测量，因此在由于感应和驱动的限制而难以或无法应用反馈和/或前馈的情况下，振动稳定是一种有力的选择。控制具有恒定或空间变化系数的抛物线PDE。假设分布式测量和分布式控制都是可能的。适应律是通过Lyapunov重新设计方法获得的。结果表明，在无限维自适应系统中，励磁持续性的概念需要针对时间变量，空间变量和边界条件进行研究。事实证明，即使恒定的输入信号在保证参数误差收敛到零的意义上也足够丰富。建立了包含有限维慢系统和无限维快速系统的两尺度系统的平均定理。自适应算法的指数稳定性在有限维自适应控制中对于容忍干扰和非建模动力学至关重要，它通过应用平均来显示。在振动控制和直接自适应控制中，均值方法都用于稳定性分析。在振动控制中，利用了振动引起的吸引子的整体性能的质变，从平均自治系统的稳定性推导了非自治系统的稳定性。在自适应控制中，整个闭环系统通过不断修改控制律而变得时变，并且闭环的稳定性由平均系统的指数稳定性得出。提供示例和计算机模拟以支持这两种情况下的理论。

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  • 作者

    Hong, Keum Shik.;

  • 作者单位

    University of Illinois at Urbana-Champaign.;

  • 授予单位 University of Illinois at Urbana-Champaign.;
  • 学科 Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 1991
  • 页码 130 p.
  • 总页数 130
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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