Design and Implementation of LQR PI Controller for Second-order Time Delay Process

Harshavardhana Reddy K, Sachin Sharma, Avagaddi Prasad, Shivarama Krishna K
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Abstract

In this paper, an optimal PI Controller has been designed using continuous Linear Quadratic Regulator (LQR) theory for the application of first order plus time delay (FOPTD) systems. In general, time delays can limit and deteriorate the achievable system performance and induce stability. To achieve the optimal performance, the LQR PI controller is designed, the selection of weight matrices Q plays a key role in the design in order to minimize settling time, peak overshoot and Integral Absolute Error (IAE). So, selection of Q matrices is proposed using Lyapunov Function incorporated with the state feedback gain matrix. In this, Lyapunov function gives the stability of the system and the state feedback gain matrix gives optimal PI Controller gains. The proposed
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二阶时滞过程LQR PI控制器的设计与实现
本文利用连续线性二次型调节器(LQR)理论,设计了一种用于一阶加时滞系统的最优PI控制器。通常,时间延迟会限制和降低系统的可实现性能,并导致系统的稳定性。为了达到最优的性能,设计了LQR PI控制器,权重矩阵Q的选择是设计的关键,以最小化稳定时间、峰值超调和积分绝对误差(IAE)。因此,提出了结合状态反馈增益矩阵的李雅普诺夫函数来选择Q矩阵。其中,李雅普诺夫函数给出了系统的稳定性,状态反馈增益矩阵给出了最优PI控制器增益。被提议的
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