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A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach
European Journal of Control ( IF 3.4 ) Pub Date : 2021-06-30 , DOI: 10.1016/j.ejcon.2021.06.003
Mehmet Nur Alpaslan Parlakci , Elbrous M. Jafarov

This paper deals with the new formulated problem of designing a robust delay-dependent guaranteed optimal cost proportional-integral-derivative (PID) multivariable output feedback controller for linear uncertain time delay systems with nonlinear parameter perturbations using a linear matrix inequalities (LMI) approach. Several less conservative delay-dependent stability conditions are formulated for the time-delay system under consideration in terms of LMIs. Based on an augmented form of Lyapunov-Krasovskii functionals, the free weighting matrices and Wirtinger inequality techniques are employed to obtain improved performance. An optimal guaranteed cost PID controller which minimizes the upper bound of cost function is provided. The main advantage of the proposed approach is to decouple the input and the output gain matrices allowing to synthesize the controller gain matrices through a strict LMI technique. The synthesis conditions are thus formulated in LMI form which avoids the use of any iterative approach to resolve the feasibility problem. Two numerical examples selected from the literature are presented to illustrate the effectiveness of the developed methodology. The numerical results indicate that the proposed method performs efficiently in comparison to the approaches from the existing literature.



中文翻译:

用于时变延迟系统的鲁棒延迟相关保证成本 PID 多变量输出反馈控制器设计:LMI 优化方法

本文涉及使用线性矩阵不等式 (LMI) 方法为具有非线性参数扰动的线性不确定时间延迟系统设计稳健的延迟相关保证最优成本比例积分微分 (PID) 多变量输出反馈控制器的新问题。几个不太保守的延迟相关稳定性条件被公式化用于考虑 LMI 的时延系统。基于 Lyapunov-Krasovskii 泛函的增强形式,采用自由加权矩阵和 Wirtinger 不等式技术来获得改进的性能。提供了一种最小化成本函数上限的最优保证成本PID控制器。所提出方法的主要优点是解耦输入和输出增益矩阵,允许通过严格的 LMI 技术合成控制器增益矩阵。因此,合成条件以 LMI 形式制定,避免使用任何迭代方法来解决可行性问题。提出了从文献中选择的两个数值例子来说明所开发方法的有效性。数值结果表明,与现有文献中的方法相比,所提出的方法执行效率高。提出了从文献中选择的两个数值例子来说明所开发方法的有效性。数值结果表明,与现有文献中的方法相比,所提出的方法执行效率高。提出了从文献中选择的两个数值例子来说明所开发方法的有效性。数值结果表明,与现有文献中的方法相比,所提出的方法执行效率高。

更新日期:2021-07-22
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