### Linierisasi Model Sistem Ball and Beam dan Metode Kendali LQG Berbasis MATLAB-Simulink

https://doi.org/10.22146/juliet.v4i1.81744

Hanifah Suwardi(1), Anisa Septyaning Choir(2), Salima Nurrahma(3), Imroatul Hudati(4*)

(*) Corresponding Author

#### Abstract

Abstract – There are some unstable control systems, it can be an important problem in control, like systems in aerospace and flight. This can be studied simply in the ball and beam system. The ball and beam system uses an LQG (Linear Quadratic Gaussian) controller to determine the effect of stability and optimal system to reach the set point and the results of the slope angle on the beam at the set point. There is a combination of LQR with the element matrix parameters Q and R which can be searched using a trial and error technique with the condition that the Q matrix is a positive semidefinite while the R matrix is a positive definite matrix. As well as the use of gain Kalman filter as an estimator. Two experiments are given on the Q and R matrix elements which will be used in three distance/position displacement tests. The design of LQG on ball and beam systems is carried out in the MATLAB-Simulink software. Then the results of the angle of inclination of the beam (beam) obtained 14° to make the ball reach a set point of 10 cm, 17° for a set point of 20 cm, and 28° for a set point of 30 cm.

Keywords – ball and beam, angle, LQG, LQR, linearization

IntisariSistem kontrol yang tidak stabil menjadi sebuah masalah yang penting dalam pengontrolan, seperti sistem dalam aerospace dan penerbangan. Hal ini dapat dipelajari secara sederhana pada sistem ball and beam. Pada sistem ball and beam digunakan pengontrol LQG (linear quadratic gaussian) untuk mengetahui pengaruh stabilitas maupun optimalnya sistem mencapai set point serta hasil kemiringan sudut pada balok (beam) pada titik set point. Terdapat kombinasi LQR dengan parameter matriks elemen Q dan R yang dapat dicari menggunakan teknik  trial and error dengan syarat matriks Q ialah semidefinite positive sedangkan matriks R ialah matrik definit positif Serta penggunaan gain filter Kalman sebagai estimator. Dilakukan dua eksperimen pada elemen matriks Q dan R yang akan digunakan pada tiga pengujian perpindahan jarak/posisi. Rancangan LQG pada sistem ball dan beam dilakukan di software MATLAB-Simulink.  Diperoleh hasil sudut kemiringan beam sebesar 14° untuk membuat ball mencapai di posisi set point 10 cm, 17° untuk set point 20 cm, dan 28° untuk set point 30 cm.

Kata kunci ball and beam, sudut, LQG, LQR, linierisasi

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DOI: https://doi.org/10.22146/juliet.v4i1.81744

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