KENDALI OPTIMAL MENGGUNAKAN LINEAR QUADRATIC REGULATOR PADA SISTEM 3D OVERHEAD CRANE

Ratna Nur Aini Mutmainnah, Dr. Solikhatun, M.Si.

2019 | Skripsi | S1 MATEMATIKA

Pada skripsi ini, sistem 3D Overhead Crane dipandang sebagai sistem nonlinear dan merupakan sistem Multi-Input-Multi-Output (MIMO). Linearisasi dilakukan untuk mendapatkan pendekatan linear dari sistem 3D Overhead Crane, sehingga kendali sistem linear dapat diterapkan. Pengendali linear dirancang untuk memindahkan muatan ke posisi tujuan pada ruang tiga dimensi. Masukan sistem yakni gaya penggerak girder, gaya penggerak troli, dan gaya angkat muatan pada sistem hoist digunakan untuk menggerakkan lima variabel keadaan (state variable) meliputi perpindahan girder, perpindahan troli, perpindahan muatan di sepanjang tali baja, dan dua sudut osilasi muatan. Sistem 3D Overhead Crane didekomposisi menjadi subsistem actuated dan subsistem unactuated. Kendali sistem 3D Overhead Crane ditentukan dari gabungan kendali umpan balik dari kedua subsistem. Berdasarkan simulasi numerik yang dilakukan, diperoleh bahwa kendali sistem 3D Overhead Crane berhasil menstabilkan seluruh variabel keadaan.

In this study, the 3D Overhead Crane system is considered a nonlinear and Multi-Input-Multi-Output (MIMO) system. Linearization is carried out to find the linear approximation from the original system. The linear controller is designed to drive the payload to the desired position in the three-dimensional space. Given three control inputs consisting of force applied to the girder, trolley, and for the hoisting system to drive five states composed of girder displacement, trolley displacement, payload hoisting displacement, and two components of swing angles. The 3D Overhead Crane system is divided into actuated subsystem and unactuated subsystem. The control law of the 3D Overhead Crane system is obtained from combining the feedback controller for both subsystems. Based on the numerical simulation results, it can be shown that the control law can stabilize all states of the 3D Overhead Crane system.

Kata Kunci : Sistem underactuated, overhead crane, linearisasi umpan balik, kendali optimal, linear quadratic regulator