Noorma Yulia Megawati
Jurusan Matematika, FMIPA, UGM, Yogyakarta

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Pemodelan Sistem Kendali PIDpada Quadcopterdengan Metode Euler Lagrange Andi Dharmawan; Yohana Yulya Simanungkalit; Noorma Yulia Megawati
IJEIS (Indonesian Journal of Electronics and Instrumentation Systems) Vol 4, No 1 (2014): April
Publisher : IndoCEISS in colaboration with Universitas Gadjah Mada, Indonesia.

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (520.462 KB) | DOI: 10.22146/ijeis.4218

Abstract

Penelitian ini bertujuan untuk membuat dan menghasilkan dasar-dasar pemodelan dari sistem kendali sebuah quadcopter dengan metode PID. Manfaat yang diharapkan dari penelitian ini adalah agar menjadi dasar pembelajaran ataupun sebagai acuan untuk melakukan penelitian sebagai proses pengembangan dari sistem.Parameter-parameter yang digunakan pada pemodelan ini yaitu massa, panjang lengan, radius, torsi motor, dan kecepatan motor. Beberapa asumsi yang diterapkan dalam melakukan pemodelan dari quadcopter ini yaitu, struktur dari quadcopter dianggap kaku, struktur dari quadcopter dianggap simetris, titik berat beban quadcopter diasumsikan berada tepat di tengah (pusat massa) quadcopter, dan efek getaran masing-masing propeller dianggap tidak terjadi. Pengontrol yang dianalisis pada penelitian ini terdapat 4 pengontrol yaitu proporsional kontroller, proporsional Integral kontroller, proporsional Derivatif kontroller, serta proporsional  Integral dan Derivatif kontroller. Pengujian dilakukan sesuai dengan analisis menggunakan matlab untuk mengetahui respon dari masing-masing sistem.Hasil dari penelitian ini yaitu pemodelan dapat digunakan untuk memprediksi kontrol yang digunakan dan memprediksi konstanta-konstanta dari masing-masing pengontrol. Jika sistem sangat ideal, cukup digunakan pengontrol berupa PD kontrol.  Kata Kunci—Pemodelan, Euler Lagrange, Quadcopter, PID, Kendali This study aims to create and produce the basics of modeling a Quadcopter control system with PID method. The expected benefits of the research is to be the basis of learning or as a reference for conducting research as a process of development of the system.The parameters used in this modeling is the mass, arm length, radius, torque motors, and motor speed. Some assumptions are applied in these modeling ie, the structure of the Quadcopter considered rigid, the structure of the Quadcopter considered symmetric, gravity load Quadcopter assumed to be right in the middle (center of mass) Quadcopter, and vibration effects of each propeller is considered not happen.The controller was analyzed in this study there are proportional controllers, Proportional Integral controller, proportional derivative controller, also proportional Integral and Derivative controller. Tests carried out in accordance with the analysis using matlab to determine the response of each system.Results from this research that modeling can be used to predict and control that is used to predict the constants of each controller. If the system is ideal, just use the controller in the form of PD control.  Keyword—Modelling, Euler Lagrange, Quadcopter, PID, Control
A Mathematical Model of Human-to-Human Transmission of Monkeypox with Reinfection Rahayu, Eka Widia; Megawati, Noorma Yulia
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40140

Abstract

Monkeypox is a zoonotic disease caused by the monkeypox virus and remains a public health concern due to its potential for sustained human-to-human transmission. This study analyzes the transmission dynamics of monkeypox by developing a deterministic compartmental model that explicitly incorporates reinfection arising from waning immunity. The model is analyzed by deriving the basic reproduction number and determining the disease-free and endemic equilibrium points, whose local and global stability properties are rigorously investigated. A sensitivity analysis is conducted to identify key parameters driving transmission dynamics. Motivated by these results, an optimal control problem is formulated in which vaccination is implemented as a time-dependent control, and the optimal strategy is characterized using Pontryagin’s Minimum Principle. Numerical simulations reveal that even low reinfection rates can sustain endemic transmission in the absence of control, while appropriately timed vaccination strategies significantly reduce infection levels and prevent long-term persistence.