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Fuzzy singularly perturbed modeling and composite controller design for nonlinear multiple time-scale systems with time-delay

机译：具有时滞的非线性多时标系统的模糊奇异摄动建模和复合控制器设计

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摘要

This paper investigates the problems of modeling and robust controller design for nonlinear multiple time-scale systems (MTSSs) with time-delay. An uncertain standard discrete-time fuzzy singularly perturbed model (FSPM) with time-delay is firstly constructed to estimate the considered system. Based on a matrix spectral norm approach, robust composite controllers with or without time-delay are designed respectively. They are composed by a slow-state-variables feedback controller and an output integrator. The controller's gains are obtained by solving a set of s-independent linear matrix inequalities (LMIs) such that the ill-conditioned problems caused by s can be easily avoided. The designed control laws not only can stabilize resulting closed-loop systems but also can overcome external disturbances. Finally, simulation results for CE 150 helicopter system illustrate the effectiveness of the proposed approaches. In contrast to the existing results, the proposed methods have the following advantages: ⅰ) They have better practical value since parameter uncertainty, external disturbances and the problem that the state variables are not fully measurable are considered. ⅱ) A high accurate control performance can be achieved. ⅲ) External disturbances can be effectively reduced.
机译：本文研究了具有时滞的非线性多时标系统（MTSS）的建模和鲁棒控制器设计问题。首先构造了带有时滞的不确定标准离散时间模糊奇摄动模型（FSPM）来估计所考虑的系统。基于矩阵谱范数方法，分别设计了具有或不具有时间延迟的鲁棒复合控制器。它们由一个慢状态变量反馈控制器和一个输出积分器组成。控制器的增益是通过求解一组独立于s的线性矩阵不等式（LMI）来获得的，从而可以轻松避免由s引起的不良条件问题。设计的控制定律不仅可以稳定最终的闭环系统，而且可以克服外部干扰。最后，CE 150直升机系统的仿真结果说明了所提出方法的有效性。与现有结果相比，所提出的方法具有以下优点：ⅰ）由于考虑了参数不确定性，外部干扰以及状态变量不能完全测量的问题，因此具有较好的实用价值。 ⅱ）可以实现高精度的控制性能。 ⅲ）可以有效减少外部干扰。

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