کنفرانس مهندسی برق ایران

صفحه اصلی / سی و یکمین کنفرانس بین المللی مهندسی برق

Modeling and optimal control of the vibration model of constrained buildings based on fractional order singular theory using orthogonal polynomials

نویسندگان :

Vahid Safari Dehnavi¹ Masoud Shafiee²

1- دانشگاه صنعتی امیرکبیر 2- دانشگاه صنعتی امیرکبیر

کلمات کلیدی :

fractional-order singular system،finite modes،infinite modes،orthogonal polynomials

چکیده :

This paper introduces the analytical and numerical solution methods, optimal control and application of finite-mode fractional-order singular systems in modeling practical systems. In singular systems, algebraic and differential equations exist simultaneously; By solving these equations simultaneously can obtain the desired solution by considering the constraints. In this paper, there are only finite modes in the system. The aim is to control fractional order singular systems without using operational matrices by using optimal control and virtual calculus of variations. After, using orthogonal polynomials, we achieved a formulation to find the answer to the problem. This problem was solved using Legendre, Chebyshev, and Jacobi orthogonal polynomials. In this paper, an example of fractional-order singular systems is examined. The vibration model of two constrained buildings is modeled using the fractional order singular system. The aim is to control the vibration of the constrained buildings against shocks and earthquakes. Finally, a comparison was made between different orthogonal polynomials and the number of the polynomial of these functions.