Proportional integral derivative controller design using Legendre orthogonal functions

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• 作者：Reza Moradi ; Mohammad Tabatabaei
• 关键词：Key wordsPID controllers ; orthogonal functions ; legendre functions ; moment matching ; PI controller ; PD controller
• 刊名：Journal of Central South University
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：23
• 期：10
• 页码：2616-2629
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Engineering, general; Metallic Materials;
• 出版者：Central South University
• ISSN：2227-5223
• 卷排序：23

文摘

The Legendre orthogonal functions are employed to design the family of PID controllers for a variety of plants. In the proposed method, the PID controller and the plant model are represented with their corresponding Legendre series. Matching the first three terms of the Legendre series of the loop gain with the desired one gives the PID controller parameters. The closed loop system stability conditions in terms of the Legendre basis function pole (λ) for a wide range of systems including the first order, second order, double integrator, first order plus dead time, and first order unstable plants are obtained. For first order and double integrator plants, the closed loop system stability is preserved for all values of λ and for the other plants, an appropriate range in terms of λ is obtained. The optimum value of λ to attain a minimum integral square error performance index in the presence of the control signal constraints is achieved. The numerical simulations demonstrate the benefits of the Legendre based PID controller.