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Application of Pontryagin’s Minimum Principle in Optimum Time of Missile Manoeuvring Cahyaningtias, Sari; Subchan, Subchan
CAUCHY Vol 4, No 3 (2016): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (695.528 KB) | DOI: 10.18860/ca.v4i3.3534

Abstract

Missile is a guided weapon and designed to protect outermost island from a thread of other country. It, commonly, is used as self defense. This research presented surface-to-surface missile in final dive manoeuvre for fixed target. Furthermore, it was proposed manoeuvring based on unmanned aerial vehicle (UAV), autopilot system, which needs accuration and minimum both time and thrust of missile while attacking object. This paper introduced pontryagin’s Minimum Principle, which is useable to solve the problem. The numerical solution showed that trajectory of the missile is split it up in three sub-intervals; flight, climbing, and diving. The numerical simulation showed that the missile must climb in order to satisfy the final dive condition and the optimum time of a missile depend on initial condition of the altitude and the terminal velocity
Trajectory Shaping of Surface-to-Surface Missile with Terminal Impact Angle Constraint Subchan, Subchan
Makara Journal of Technology Vol 11, No 2 (2007)
Publisher : Directorate of Research and Community Services, Universitas Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (126.04 KB) | DOI: 10.7454/mst.v11i2.129

Abstract

This paper presents trajectory shaping of a surface-to-surface missile attacking a fixed with terminal impact angle constraint. The missile must hit the target from above, subject to the missile dynamics and path constraints. The problem is reinterpreted using optimal control theory resulting in the formulation of minimum integrated altitude. The formulation entails nonlinear, two-dimensional missile flight dynamics, boundary conditions and path constraints. The generic shape of optimal trajectory is: level flight, climbing, diving; this combination of the three flight phases is called the bunt manoeuvre. The numerical solution of optimal control problem is solved by a direct collocation method. The computational results is used to reveal the structure of optimal solution which is composed of several arcs, each of which can be identified by the corresponding manoeuvre executed and constraints active.
THE MISSILE GUIDANCE ESTIMATION USING EXTENDED KALMAN FILTER-UNKNOWN INPUT-WITHOUT DIRECT FEEDTHROUGH (EKF-UI-WDF) METHOD Subchan, Subchan; Asfihani, Tahiyatul
Journal of the Indonesian Mathematical Society Volume 19 Number 1 (April 2013)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.19.1.124.1-14

Abstract

This paper consider the estimation of the optimal missile guidance which the objective is to minimize the interception time and the energy expen-diture. The proposed Extended Kalman Filter-Unknown Input-Without Direct Feedthrough (EKF-UI-WDF) approach is to estimate the optimal missile guidance and the target acceleration as unknown input to the missile-target interception model. Unknown input is any type of signals without prior information from agiven state model or a measurement. The computational for the EKF-UI-WDF method and optimal missile guidance show the closest range to the missile-target is smaller than using the EKF. However the Mean Squared Error (MSE) of estimating the optimal missile guidance using EKF method is smaller than using EKF-UI-WDF method.DOI : http://dx.doi.org/10.22342/jims.19.1.124.1-14
Minimum-Energy Control of Two-Link Manipulator withPure State Constraints Subchan, Subchan
Limits: Journal of Mathematics and Its Applications Vol 2, No 1 (2005)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (98.344 KB) | DOI: 10.12962/j1829605X.v2i1.1360

Abstract

This paper presents an analysis and numerical solutions of the minimum-energy control of two-link robot manipulator. The minimum-energy control point-to-point trajectory is investigated subject to control constraints and state constraints on the angular velocities. The numerical solutions are solved by transforming the original problem into a nonlinear programming problem. The mathematical analysis of the optimal control problems is done based on the numerical results using an indirect method. The necessary conditions can be stated as a multi-point boundary value problems.
Desain Rute Jaringan Moda Bus Kota di Balikpapan sebagai Antisipasi Kemacetan di Balikpapan Winarni, Winarni; Pratiwi, Evina Rahmatya; Subchan, Subchan
Specta Journal Vol 2 No 3 (2018): SPECTA Journal of Technology
Publisher : Specta Journal

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (620.873 KB) | DOI: 10.0610/specta.v2i3.39

Abstract

Abstract. Public transport facilities are fundamental needs as population growth and society mobility increases. Nowadays, Balikpapan is one of the cities growing quite rapidly, including the level of society mobility. If it is not anticipated, this could lead Balikpapan becomes a crowded city such as Jakarta, Surabaya, Bandung and others. One of public transportation in Balikpapan is angkot which has capacity only about 10 passengers. Others are taxi and online transportation such as Gojek, Go-Car, and Grab. These are not yet the appropriate solution for public transportation services for all levels of society.  Thus, it needs to be developed the integrated mass public transportation system in Balikpapan and become an alternative solution to the problems. One of the public demands in using public transportation service is passengers can reach any location from anywhere (strongly connected). Therefore, it is necessary to design the route of mass public transport system such as city busway.  In this paper it is called Trans Balikpapan Busway. In this paper, we use graph concept to design Trans Balikpapan Busway route. The result is the design of Transbalikpapan Busway route. It is ilustrated by a directed graph. The matrix that represents the graph has unique eigen value, so that the graph is strongly connected. It connects all districts in Balikpapan with places that people ussually visit such as schools/campuses, shops, malls, hospitals, terminals, air port, harbour, institutions, companies, recreation destinations, etc. Abstrak. Fasilitas transportasi umum merupakan kebutuhan vital seiring pertumbuhan penduduk dan mobilitas masyarakat meningkat. Saat ini, Balikpapan adalah salah satu kota yang berkembang cukup pesat, termasuk tingkat mobilitas masyarakat. Jika tidak diantisipasi, ini dapat menyebabkan Balikpapan menjadi kota yang padat seperti Jakarta, Surabaya, Bandung dan lain-lain. Salah satu angkutan umum di Balikpapan adalah angkutan kota yang kapasitasnya hanya sekitar 10 penumpang. Angkutan umum lainnya adalah taksi argo dan transportasi online seperti Gojek, Go-Car, dan Grab. Itu pun belum menjadi solusi yang tepat untuk layanan transportasi umum bagi semua lapisan masyakat. Dengan demikian, perlu dikembangkan sistem transportasi umum massal terpadu di Balikpapan dan menjadi solusi alternatif untuk masalah tersebut. Salah satu tuntutan masyarakat dalam menggunakan layanan angkutan umum adalah penumpang dapat mencapai suatu lokasi dari mana saja (strongly connected). Oleh karena itu, perlu dirancang rute sistem transportasi umum massal seperti moda bus kota. Dalam hal ini dinamakan Trans Balikpapan Busway. Dalam paper ini, digunakan konsep graf untuk merancang rute Trans Balikpapan Busway. Hasil penelitian ini adalah desain rute Transbalikpapan Busway. Jaringan Transbalikpapan Busway diilustrasikan dalam graf berarah. Matriks yang mewakili graf tersebut memiliki nilai eigen yang tunggal/unik, sehingga dapat disimpulkan graf tersebut strongly connected. Jaringan Transbalikpapan Busway menghubungkan semua kecamatan di Balikpapan beserta tempat-tempat yang biasa dikunjungi oleh masyarakat seperti sekolah/kampus, pasar, mall, rumah sakit, terminal, bandara, pelabuhan, instansi, perusahaan, tujuan rekreasi dan lain-lain.
Estimasi Gerak Menyelam ITSUNUSA AUV dengan Metode Ensemble Kalman Filter Square Root (EnKF-SR) Herlambang, Teguh; Subchan, Subchan; Nurhadi, Hendro
Prosiding Seminar Nasional Sains dan Teknologi Terapan 2019: Menuju Penerapan Teknologi Terbarukan pada Industri 4.0: Perubahan Industri dan Transformasi P
Publisher : Institut Teknologi Adhi Tama Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (371.327 KB)

Abstract

Autonomous Underwater Vehicle (AUV) merupakan salah satu jenis robot bawah air yang relatif flexibel untuk peralatan sistem pertahanan bawah laut dan eksplorasi sumber daya alam di bawah laut. AUV terdiri dari gerak translasi dan rotasi yan tergabung dalam 6 Degree of Freedom (DOF). Pengendalian AUV dibagi menjadi dua yaitu kendali kecepatan dan kendali agar mengikuti lintasan yang diinginkan. Kendali AUV agar mengikuti trajectory yang diinginkan ini biasa disebut dengan system navigasi atau Estimasi trajectory. Pada penelitian ini dikembangkan sistem navigasi untuk gerak menyelam dengan model 3-DOF yaitu gerak surge, heave dan pitch dengan metode Ensemble Kalman Filter Square Root (EnKF-SR). Hasil simulasi menunjukkan bahwa metode EnKF-SR dapat digunakan sebagai sistem system navigasi 3-DOF dengan menghasilkan error estimasi gerak menyelam untuk surge, heave dan pitch memiliki error yang cukup kecil yaitu 0.02 m/s untuk gerak translasi dan 0.005 rad/s untuk gerak rotasi. Sedangkan error posisi menyelam hanya 0.03 meter atau 3 cm dari lintasan yang ditentukan
Desain Rute Jaringan Moda Bus Kota di Balikpapan sebagai Antisipasi Kemacetan di Balikpapan Winarni, Winarni; Pratiwi, Evina Rahmatya; Subchan, Subchan
SPECTA Journal of Technology Vol 2 No 3 (2018): SPECTA Journal of Technology
Publisher : LPPM ITK

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (620.873 KB) | DOI: 10.35718/specta.v2i3.39

Abstract

Abstract. Public transport facilities are fundamental needs as population growth and society mobility increases. Nowadays, Balikpapan is one of the cities growing quite rapidly, including the level of society mobility. If it is not anticipated, this could lead Balikpapan becomes a crowded city such as Jakarta, Surabaya, Bandung and others. One of public transportation in Balikpapan is angkot which has capacity only about 10 passengers. Others are taxi and online transportation such as Gojek, Go-Car, and Grab. These are not yet the appropriate solution for public transportation services for all levels of society.  Thus, it needs to be developed the integrated mass public transportation system in Balikpapan and become an alternative solution to the problems. One of the public demands in using public transportation service is passengers can reach any location from anywhere (strongly connected). Therefore, it is necessary to design the route of mass public transport system such as city busway.  In this paper it is called Trans Balikpapan Busway. In this paper, we use graph concept to design Trans Balikpapan Busway route. The result is the design of Transbalikpapan Busway route. It is ilustrated by a directed graph. The matrix that represents the graph has unique eigen value, so that the graph is strongly connected. It connects all districts in Balikpapan with places that people ussually visit such as schools/campuses, shops, malls, hospitals, terminals, air port, harbour, institutions, companies, recreation destinations, etc. Abstrak. Fasilitas transportasi umum merupakan kebutuhan vital seiring pertumbuhan penduduk dan mobilitas masyarakat meningkat. Saat ini, Balikpapan adalah salah satu kota yang berkembang cukup pesat, termasuk tingkat mobilitas masyarakat. Jika tidak diantisipasi, ini dapat menyebabkan Balikpapan menjadi kota yang padat seperti Jakarta, Surabaya, Bandung dan lain-lain. Salah satu angkutan umum di Balikpapan adalah angkutan kota yang kapasitasnya hanya sekitar 10 penumpang. Angkutan umum lainnya adalah taksi argo dan transportasi online seperti Gojek, Go-Car, dan Grab. Itu pun belum menjadi solusi yang tepat untuk layanan transportasi umum bagi semua lapisan masyakat. Dengan demikian, perlu dikembangkan sistem transportasi umum massal terpadu di Balikpapan dan menjadi solusi alternatif untuk masalah tersebut. Salah satu tuntutan masyarakat dalam menggunakan layanan angkutan umum adalah penumpang dapat mencapai suatu lokasi dari mana saja (strongly connected). Oleh karena itu, perlu dirancang rute sistem transportasi umum massal seperti moda bus kota. Dalam hal ini dinamakan Trans Balikpapan Busway. Dalam paper ini, digunakan konsep graf untuk merancang rute Trans Balikpapan Busway. Hasil penelitian ini adalah desain rute Transbalikpapan Busway. Jaringan Transbalikpapan Busway diilustrasikan dalam graf berarah. Matriks yang mewakili graf tersebut memiliki nilai eigen yang tunggal/unik, sehingga dapat disimpulkan graf tersebut strongly connected. Jaringan Transbalikpapan Busway menghubungkan semua kecamatan di Balikpapan beserta tempat-tempat yang biasa dikunjungi oleh masyarakat seperti sekolah/kampus, pasar, mall, rumah sakit, terminal, bandara, pelabuhan, instansi, perusahaan, tujuan rekreasi dan lain-lain.
Analisis Kestabilan Model Penyebaran Penyakit Toxoplasmosis pada Populasi Manusia dan Kucing Utami, Febrina Tedjo; Dewanti, Retno Wahyu; Subchan, Subchan
SPECTA Journal of Technology Vol 1 No 3 (2017): SPECTA Journal of Technology
Publisher : LPPM ITK

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35718/specta.v1i3.85

Abstract

This final project studies the contruction and analyzes the stability of Toxoplasmosis epidemic model. Using a compartment model, Toxoplasmosis epidemic model classified into human population and cat population. The human population is divided into three subpopulations such as susceptible human, infected human, and recovered human. The cat population is divided into two subpopulations such as susceptible cat and infected cat. Stability analysis performed on two equilibrium models of disease free equilibrium and endemic equilibrium point. Stability analysis result showed that cat infected spread, natural birthd rate of cat population, natural death rate of cat population, and the probability of cat natality in the form of basic reproductive number (R0) is value that affect human population and cat population changed spread. When R0<1 the population will be free of disease and when R0>1 the disease will be spread. Model of the simulation is numerically analyzed by Runge Kutta 4th Order methods.
Kendali Optimal Model Diversifikasi Beras dan Non-beras dengan Target Akhir Konsumsi Dewanti, Retno Wahyu; Subchan, Subchan
SPECTA Journal of Technology Vol 1 No 3 (2017): SPECTA Journal of Technology
Publisher : LPPM ITK

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35718/specta.v1i3.88

Abstract

Dalam Peraturan Presiden (Perpres) No. 22 Tahun 2009 disebutkan bahwa dua sasaran dari upaya diversifikasi pangan masyarakat Indonesia meliputi perbaikan pola konsumsi pangan yang beragam, bergizi, dan seimbang serta mengurangi konsumsi beras per kapita sebesar 1,5% per tahun. Upaya tersebut dilakukanuntuk menghindari ketergantungan pada satu jenis pangan pokok yaitu beras. Disisi lain ketersediaan pangan lokal merupakan alternatif terbaik sebagai pengganti beras karena lebih mudah dijangkau secara sik maupun ekonomi, seperti jagung, singkong, ubi jalar, sagu, gembili, yang biasa dikenal dengan istilah non-beras. Pada jurnal ini dibahas permasalahan kendali optimal model diversifikasi beras dan non-beras dengan penerapan target akhir konsumsi. Target akhir konsumsi adalah tingkat konsumsi beras dan non-beras yang diharapkan oleh pemerintah pada tahun yang sudah ditentukan. Model dinamik yang digunakan untuk mengintepretasikan adalah Model Lotka-Volterra. Persentase tingkat konsumsi beras dan non-beras dijadikan sebagai variabel pengendali yang bertujuan untuk meminimumkan biaya. Metode penyelesaian yang digunakan adalah Prinsip Minimum Pontryagin. Berdasarkan hasil simulasi ditunjukkan bahwa konsumsi beras menurun secara optimal sedangkan konsumsi non-beras meningkat, sehingga biaya yang dikeluarkan minimum.
Estimasi Kelajuan dan Volume Kendaraan Berdasarkan Model Makroskopik Arus Lalu Lintas Jalan Tol dengan Metode Extended Kalman Filter Prihatiningsih, Febriana; Pancahayani, Sigit; Subchan, Subchan
SPECTA Journal of Technology Vol 2 No 2 (2018): SPECTA Journal of Technology
Publisher : LPPM ITK

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35718/specta.v2i2.105

Abstract

In this thesis, the analysis of vehicles' determination of speed and volume in the traffic flow will be discussed by approach time. The analyzation of vehicles' speed and volume done by estimated on macroscopic term of traffic flow in the traffic jam with Extended Kalman Filter (EKF) method. The term of macroscopic views with measured the traffic variable by density the flow rate the flow rate of vehicle and also the vehicle speed's average. In the estimating process, forward difference scheme is implemented to the model and error are measured by Root Mean Square Error. The result showed that the estimation the average of the vehicle?s relative speed in a segment decreased when its volume of vehicle is increased and vice versa.