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Reduced-order robust adaptive controller design and convergence analysis for uncertain SISO linear systems with noisy output measurements .

机译：具有噪声输出测量的不确定SISO线性系统的降阶鲁棒自适应控制器设计和收敛分析。

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摘要

In this research, we study the reduced-order robust adaptive control design problem for a class of uncertain SISO linear systems, that are subject to system and measurement noise. Two controller order reduction methodologies are obtained with different level of simplification as compared to the full-order design. The key technique for these two order-reduction methodologies both lies in the modification of a particular step of the backstepping design in the controller design part. The first order-reduction methodology reduces the controller structure by n - 1 or n - 2 integrators, depending on the eigen-structure of a particular feedback matrix. The second order-reduction methodology simplifies controller structure by n integrators, the trade-off for this order reduction is that the worst-case estimate for the expanded state vector has to be chosen as a suboptimal choice, rather than the optimal choice. It is shown that the resulting reduced-order adaptive controllers preserve the strong robustness properties of the full-order adaptive controller in disturbance attenuation, boundedness of closed-loop signals, and output tracking. Simulation results corroborate our theoretical findings.;Furthermore, convergence analysis is investigated for the reduced-order adaptive control system achieved using the first order-reduction design methodology. We explore the conditions under which various closed-loop signals converge. We rigorously prove that, whenever the exogenous disturbance inputs is of finite energy and bounded, and the reference trajectory and its derivatives up to rth order are bounded, r being the relative degree of the transfer function of the true system, then a set of closed-loop signals are of finite energy and converge to zero; the system states and their estimates exhibit asymptotic behaviors with certain formats. If the rth order time derivative of the reference trajectory is uniformly continuous, then the rth order noiseless derivative of the output asymptotically tracks the rth order derivative of the reference trajectory. With an additional persistency of excitation condition, the parameter estimates converge to their true values and the state estimates asymptotically track the true state. Two simulation examples are included to illustrate the convergence analysis results.
机译：在这项研究中，我们研究了一类不确定的SISO线性系统的降阶鲁棒自适应控制设计问题，该系统受系统噪声和测量噪声的影响。与全订单设计相比，获得了两种具有不同简化程度的控制器降阶方法。这两种降阶方法的关键技术都在于修改控制器设计部分中反推设计的特定步骤。一阶降阶方法根据特定反馈矩阵的本征结构，将控制器结构减少n-1或n-2积分器。第二种降阶方法论通过n个积分器简化了控制器的结构，这种降阶的权衡是必须选择扩展状态向量的最坏情况估计作为次优选择，而不是最优选择。结果表明，所得的降阶自适应控制器在干扰衰减，闭环信号的有界性和输出跟踪方面保留了全阶自适应控制器的强大鲁棒性。仿真结果证实了我们的理论发现。此外，对使用一阶降阶设计方法实现的降阶自适应控制系统的收敛性分析进行了研究。我们探索了各种闭环信号收敛的条件。我们严格证明，每当外源扰动输入具有有限能量且有界时，参考轨迹及其导数一直到第r阶都有界，r是真实系统传递函数的相对程度，则是一个封闭的集合回路信号具有有限的能量，并收敛到零；系统状态及其估计以某些格式表现出渐近行为。如果参考轨迹的r阶时间导数是一致连续的，则输出的r阶无噪声导数将渐近地跟踪参考轨迹的r阶导数。在激发条件具有额外的持久性的情况下，参数估计收敛到其真实值，并且状态估计渐近地跟踪真实状态。包括两个仿真示例以说明收敛性分析结果。

著录项

  • 作者

    Zhao, Qingrong.;

  • 作者单位

    University of Cincinnati.;

  • 授予单位 University of Cincinnati.;
  • 学科 Engineering Electronics and Electrical.
  • 学位 Ph.D.
  • 年度 2007
  • 页码 226 p.
  • 总页数 226
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 无线电电子学、电信技术;
  • 关键词

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