Tambah subbab tentang LQR dan revisi minor. Next step adalah tambah sub bab didalem "todo"
a2nr
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@ -116,7 +116,7 @@ bernilai kecil, dan dalam persamaan~\eqref{eq:dyn_motor} nilai induktansi dapat
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Penjabaran dinamika robot bisa diubah dalam bentuk \textit{state-space}
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\begin{align}
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\dot{x}(t) & = A_rx(t) + B_ru(t) + Ksgn(x(t)) \label{eq:ss1} \\
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\dot{x}(t) & = A_rx(t) + B_ru(t) + ksgn(x(t)) \label{eq:ss1} \\
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y(t) & = Cx(t) \label{eq:ss2}
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\end{align}
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dimana vektor \textit{state} adalah $x(t) = \begin{bmatrix} x_p & y_p & \theta & \dot{x}_r & \dot{y}_r & \dot{\theta}_r \end{bmatrix}^T$, dan
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@ -140,9 +140,7 @@ sistem robot
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\frac{l.K_t}{R_a.r}.\frac{-1}{M} & \frac{l.K_t}{R_a.r}.\frac{\cos(60^\circ)}{M} & \frac{l.K_t}{R_a.r}.\frac{\cos(60^\circ)}{M} \\
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\frac{l.K_t}{R_a.r}.\frac{b}{I} & \frac{l.K_t}{R_a.r}.\frac{b}{I} & \frac{l.K_t}{R_a.r}.\frac{b}{I} \\
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\end{bmatrix},
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%% \end{align*}
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%% \begin{align*}
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K = \begin{bmatrix}
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k = \begin{bmatrix}
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0 & 0 & 0 & 0 & 0 & 0 & \\
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0 & 0 & 0 & 0 & 0 & 0 & \\
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0 & 0 & 0 & 0 & 0 & 0 & \\
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@ -12,9 +12,8 @@ bidan kendali multi-robot, khususnya dalam kendali formasi.
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\caption{Kerangka Penelitian}
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\label{fig:kerangka_pen}
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\end{figure}
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\todo{
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Pada Gambar diberi kotak yang didalamnya menunjjukan fokus penelitian lalu diberi legend
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}
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\section{Definisi Permasalahan Kendali Formasi}
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Kendali formasi adalah kendali multi-agent untuk mencapai suatu formasi yang diinginkan.
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@ -26,33 +25,27 @@ Pembagian kategori tersebut berdasarkan kemampuan sensor yang digunakan dan
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penggunaan komunikasi dalam metodenya.
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Dari ketiga kategori tersebut, kendali formati berbasis jarak sangat dibutuhkan pembahasan
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mengenai penerapan metode tersebut pada agent yang nyata.
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\textit{Simple model, Model real,} dan \textit{Real} dapat dikatakan sebuah tahap pengemabangan.
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\kutip{OH2015424} menyatakan bahwa mayoritas dari hasil penelitian yang menggunakan pendekatan ini (\textit{distance-based}) berfokus pada model agent dengan integrator-tunggal di suatu bidang datar.
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Gagasan agent \textit{simple model} tersebut memiliki manfaat ketika menginvestigasi karakteristik kendali secara mendasar, model agent yang lebih relistik (\textit{Model real}) perlu untuk dipelajari lebih lanjut untuk menambah kepraktisan pada metode kendali multi-agent berdasarkan jarak.
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Dengan bertambahnya kepraktisan pada metode tersebut diharapkan dapat diterapkan dalam agent secara \textit{Real}.
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Pada penelitian oleh \kutip{Rozenheck2015}, kendali formasi berdasarkan jarak dikendalikan
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menggunakan kendali PI dan menghasilkan pergerakan yang baik.
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Dalam penelitian ini akan difokuskan pada kendali formasi berbasis jarak
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dengan mengembangkan kendali PI yang telah dilakukan sebelumnya beserta menggunakan
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model nyata.
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\todo{
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Diperlukan penjelasan mengenai simple model itu bagaiman,
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contohnya pada penjelasan jurnal kebanyakan analisis menggunakan model orde satu yang sangat
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sederhana
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lalu menggunakan model real untuk mendesain kendali
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dan model real adalah penerapan dari model real.
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}
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Dapat diperhatikan pada persamaan~\eqref{eq:modelorde1} bahwa peneliti menggunakan \textit{Simple model} untuk mengembangkan kendali multi-robotnya.
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Maka, penelitian ini akan difokuskan pada kendali formasi berbasis jarak
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kendali PI yang telah dilakukan sebelumnya dengan menggunakan model nyata.
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\section{Permasalah dan Solusi}
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Pada kerangka kendali-PI pada persamaan~\eqref{eq:ss-formasi}, state yang digunakan membutuhkan
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koordinat relatif dari tetangganya. Akan tetapi pada batasan penelitian ini, sensor yang digunakan
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hanya memberikan jarak terhadap tetangganya. Secara pendekatan, digunakan koordinat polar dan diubah
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ke koordinat kartesian. Akan tetapi koordinat polar membutuhkan sudut antara agent dan tetangganya.
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Dapat diperhatikan pada persamaan~\eqref{eq:ss-formasi}, state yang digunakan membutuhkan koordinat relatif dari tetangganya.
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Akan tetapi pada batasan penelitian ini, sensor yang digunakan hanya memberikan jarak terhadap tetangganya.
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Sedangkan koordinat relatif tersebut berupa kartesian.
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Koordinat kartesian dapat diubah ke bentuk koordinat polar, atau sebaliknya.
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Akan tetapi koordinat polar membutuhkan sudut antara agent dan tetangganya.
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Oleh karena itu dibutuhkan algoritma khusus untuk menutup permasalahan tersebut.
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Untuk mengembangkan algoritma tersebut, dapat menggunakan hukum \textit{cosinus} segitiga
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untuk menentukan sudutnya.
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Algoritma \textit{cosinus} tersebut hanya berlaku apabila tetangga tidak melakukan pergerakan dan
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akan dijalankan algoritma tersebut ketika inisialisasi.
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Ketika tetangga melakukan pergerakan, tetangga mengirimkan informasi percepatan koordinatnya pada agent.
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Kegunaannya adalah sebagai referensi perubahan koordinat terhadap tetangga.
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Sehingga harapanya adalah kerangka kendali-PI dapat digunakan menggunakan sensor yang hanya mendeteksi jarak saja.
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Untuk mengembangkan algoritma tersebut, dapat menggunakan hukum \textit{cosinus} segitiga untuk menentukan sudutnya.
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Dengan memanfaatkan komunikasi antar robot, maka robot dapat mengirimkan informasi state kecepatan kepada tetangganya.
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Sehingga informasi tersebut dapat digunakan untuk memantau koordinat relatif terhadap tetangganya.
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Akan tetapi state kecepatan tersebut membutuhkan nilai inisialisasi.
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Nilai inisialisasi ini akan diperoleh menggunakan algoritma \textit{cosinus}.
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Sehingga, harapanya adalah kendali multi-robot menggunakan kendali PI dapat digunakan sesuai batasan penelitian.
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@ -1,7 +1,7 @@
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k1,k2,k3,k4,k5,k6
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-0,-82.81000000000003,6.900833333333332,-0,-9.670003622750881,1.028166847804211
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-0,-82.81000000000003,6.900833333333335,-0,-0,-0
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-71.71556368738936,41.40500000000002,6.900833333333334,-0,-0,-0
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350
BAB4/bab4.tex
350
BAB4/bab4.tex
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@ -24,7 +24,6 @@ teria yang diinginkan.
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\caption{State-feedback Sistem}
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\label{fig:state-feedback}
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\end{figure}
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\todo{ Ganti notasi K untuk friction ke $k$}
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Pada persamaan~\eqref{eq:ss1} diketahui bahwa state memiliki dimensi $6 \times 1$. Dimensi
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tersebut tidak menunjukan sistem memiliki orde 6. Apabila diperhatikan orde
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dari sistem adalah orde 2. Dengan membaginya kedalam 3 persamaan state-space
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@ -35,17 +34,17 @@ akan lebih mudah dalam analisis parameter kendalinya. Berikut adalah persamaan
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\begin{bmatrix}0 & A_{14} \\ 0 & A_{44} \end{bmatrix}
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\begin{bmatrix}{x}_p \\ \dot{x}_r\end{bmatrix} +
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\begin{bmatrix}0 & 0& 0 \\ B_{11} & B_{12} & B_{13} \end{bmatrix}
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\begin{bmatrix}u_1 \\ u_2 \\ u_3 \end{bmatrix} + K_{44}sgn(\dot{x}_r) \label{eq:ssx} \\
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\begin{bmatrix}u_1 \\ u_2 \\ u_3 \end{bmatrix} + k_{44}sgn(\dot{x}_r) \label{eq:ssx} \\
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\begin{bmatrix}\dot{y}_p \\ \ddot{y}_r \end{bmatrix} & =
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\begin{bmatrix}0 & A_{25} \\ 0 & A_{55} \end{bmatrix}
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\begin{bmatrix}{y}_p \\ \dot{y}_r\end{bmatrix} +
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\begin{bmatrix}0 & 0& 0 \\ B_{21} & B_{22} & B_{23} \end{bmatrix}
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\begin{bmatrix}u_1 \\ u_2 \\ u_3 \end{bmatrix} + K_{55}sgn(\dot{y}_r)\label{eq:ssy} \\
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\begin{bmatrix}u_1 \\ u_2 \\ u_3 \end{bmatrix} + k_{55}sgn(\dot{y}_r)\label{eq:ssy} \\
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\begin{bmatrix}\dot{\theta}_p \\ \ddot{\theta}_r\end{bmatrix} & =
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\begin{bmatrix}0 & A_{34} \\ 0 & A_{66} \end{bmatrix}
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\begin{bmatrix}{\theta}_p \\ \dot{\theta}_r\end{bmatrix} +
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\begin{bmatrix}0 & 0& 0 \\ B_{31} & B_{32} & B_{33} \end{bmatrix}
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\begin{bmatrix}u_1 \\ u_2 \\ u_3 \end{bmatrix} + K_{66}sgn(\dot{\theta}_r) \label{eq:ssthe}
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\begin{bmatrix}u_1 \\ u_2 \\ u_3 \end{bmatrix} + k_{66}sgn(\dot{\theta}_r) \label{eq:ssthe}
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\end{align}
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State feedback membutuhkan kembalian nilai state dari sistem dan mengka-
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maka \textit{observer} tidak dibutuhkan dalam desain kendali robot.
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\subsubsection{Desain Kendali}
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Kriteria didefinisi menggunakan analisis sistem orde dua pada domain waktu.
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Berikut adalah transfer fungsi tertutup dari sistem orde dua (\kutip{Richard2010}).
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\begin{align}
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Y(s) = \frac{\omega_n^2}{s^2+2\zeta\omega_n s+\omega_n^2} R(s)
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\label{eq:Gref}
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\end{align}
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Dengan input $R(s) = 1/s$ sebagai unit step, maka didapat persamaan keluaran sistem dalam domain waktu.
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\begin{align}
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y(t) = 1 - \frac{1}{\beta}e^{-\zeta\omega_n t}sin(\omega_n\beta t + \theta)
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\end{align}
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dimana $\beta = \sqrt{1-\zeta^2}$, $\theta = \cos^{-1}\zeta$, dan $0<\zeta<1$.
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Dari persamaan domain waktu tersebut didapat 4 kriteria dalam sistem,
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yaitu \textit{satling time} ($T_s$), Prosentase \textit{overshoot} ($P.O$),
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\textit{peek time} ($T_p$), dan \textit{Transient Time} ($T_{r1}$).
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Dari keempat kriteria tersebut, merupakan fungsi dari $\zeta$ dan $\omega_n$.
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Berikut adalah rumus dari keempat kriteria tersebut.
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\begin{itemize}
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\item $T_s$ adalah rumus pendekatan untuk mengetahui waktu respon sistem
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mulai dari kondisi inisial sampai sistem mencapai 2\% dari set poin yang terakhir.
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\begin{align}
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T_s = \frac{4}{\zeta \omega_n}
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\end{align}
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\item $P.O$ adalah prosentase \textit{overshoot} dari sistem.
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Arti dari \textit{overshoot} pada sistem adalah respon sistem yang melebihi dari nilai set poin.
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\begin{align}
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P.O. = 100e^{-\zeta \pi/\sqrt{1-\zeta^2}}
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\end{align}
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\item $T_p$ adalah waktu dimana respon sistem mengalami \textit{overshoot} dimulai dari kondisi inisial.
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\begin{align}
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T_p = \frac{\pi}{\omega_n \sqrt{1-\zeta^2}}
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\end{align}
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\item $T_{r1}$ adalah pendekatan nilai waktu respon sistem dimulai dari respon 10\% menuju ke 90\% set poin.
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Akurasi dari rumus ini adalah $0.3 \leq \zeta \leq 0.8$.
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\begin{align}
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T_{r1} = \frac{2.16\zeta + 0.6}{\omega_n}
|
||||
\end{align}
|
||||
\end{itemize}
|
||||
Apabila menggunakan $\zeta = 0.9$ dan $\omega_n = 9.1$, akan diperoleh kriteria $T_s= 0.48$, $T_p=14.75$, $P.O.=0.15$, dan $T_{r1}=0.27$. Grafik step response dapat diperhatiakn pada gamabar~\ref{fig:stepResGref}.
|
||||
\begin{figure}
|
||||
\begin{center}
|
||||
\begin{subfigure}[t]{.4\textwidth}
|
||||
\begin{tikzpicture}
|
||||
%%https://www.latex-tutorial.com/tutorials/pgfplots/
|
||||
\begin{axis}[
|
||||
width=\linewidth, % Scale the plot to \linewidth
|
||||
grid=major, % Display a grid
|
||||
grid style={dashed,gray!30}, % Set the style
|
||||
xlabel=$s$, % Set the labels
|
||||
ylabel=Response,
|
||||
no marks
|
||||
]
|
||||
\addplot
|
||||
table[x=column 2,y=column 1,col sep=comma] {BAB4/Gref.csv};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\caption{}
|
||||
\label{fig:stepResGref}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.4\textwidth}
|
||||
\begin{tikzpicture}
|
||||
\begin{axis}[
|
||||
width=\linewidth, % Scale the plot to \linewidth
|
||||
grid=major, % Display a grid
|
||||
grid style={dashed,gray!30}, % Set the style
|
||||
xlabel=Re, % Set the labels
|
||||
ylabel=Im,
|
||||
legend pos=south east,
|
||||
only marks
|
||||
]
|
||||
\addplot
|
||||
table[x=real,y=imag,col sep=comma] {BAB4/poleGref.csv};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\caption{}
|
||||
\label{fig:poleSystem}
|
||||
\end{subfigure}
|
||||
\caption{(a) Step Respon dari persamaan~\eqref{eq:Gref} dengan parameter $\zeta = 0.9$ dan $\omega_n = 9.1$ \\
|
||||
(b) Pole sistem adalah -8.19+3.96j dan -8.19+3.96j }
|
||||
\end{center}
|
||||
\end{figure}
|
||||
|
||||
|
||||
Untuk mendesain parameter K pada \textit{state feedback},
|
||||
diasumsikan bahwa \textit{state} pada sistem dapat diperoleh dari sensor, $x(t)$ untuk semua $t$.
|
||||
Persamaan rumus masukan ke sistem menjadi
|
||||
\begin{align}
|
||||
u(t) = -K_s x(t)
|
||||
\end{align}
|
||||
sehingga persamaan \textit{state space} menjadi berikut.
|
||||
\begin{align}
|
||||
\dot{x}(t) = (A-BK_s)x(t)
|
||||
\end{align}
|
||||
Dapat diperhatikan bahwa $(A-BK_s)$ merupakan matriks karakteristik dari sistem.
|
||||
Sehingga dengan mengatur besaran $K_s$ dapat menjadikan sistem sesuai dengan kriterianya.
|
||||
\begin{align}
|
||||
\det[\lambda I-(A-BK_s)]=0
|
||||
\label{eq:eigen}
|
||||
\end{align}
|
||||
Perhatikan persamaan~\eqref{eq:ssx}, matriks pada persamaan tersebut akan diterapkan pada
|
||||
persamaan~\eqref{eq:eigen}.
|
||||
Berdasarkan \kutip{Richard2010}, bahwa kendali optimal berdasarkan indeks kinerja sistem. Indeks tersebut adalah hasil dari meminimalisasi pada integral kuadrat error atau \textit{integration square error} (ISE).
|
||||
Kendali optimal dilakukan oleh komputer untuk mengkalkulasi minimal indeks tersebut.
|
||||
Apabila sebuah sistem \textit{state space}
|
||||
\begin{align*}
|
||||
0 & =\det \Big[
|
||||
\begin{bmatrix}\lambda & 0\\ 0 & \lambda \end{bmatrix} -
|
||||
\Big(
|
||||
\begin{bmatrix}0 & A_{14} \\ 0 & A_{44} \end{bmatrix} -
|
||||
\begin{bmatrix}0 & 0& 0 \\ B_{11} & B_{12} & B_{13} \end{bmatrix}
|
||||
\begin{bmatrix}k_{11} & k_{12} \\ k_{21} & k_{22} \\ k_{31} & k_{32} \end{bmatrix}
|
||||
\Big)
|
||||
\Big] \\
|
||||
0 & = \det \Big[
|
||||
\begin{bmatrix}\lambda & 0\\ 0 & \lambda \end{bmatrix} -
|
||||
\Big(
|
||||
\begin{bmatrix}0 & A_{14} \\ -B_{11}k_{11}-B_{12}k_{21}-B_{13}k_{31} &
|
||||
A_{44}- B_{11}k_{12}-B_{12}k_{22}-B_{13}k_{32}\end{bmatrix}
|
||||
\Big)
|
||||
\Big] \\
|
||||
0 & = \det \Big[
|
||||
\begin{bmatrix}\lambda & 0\\ 0 & \lambda \end{bmatrix} -
|
||||
\begin{bmatrix}0 & A_{14} \\ Z_{21}& Z_{22}\end{bmatrix}
|
||||
\Big]
|
||||
= \det \Big[ \begin{bmatrix}\lambda & -A_{14}\\ -Z_{21} & \lambda-Z_{22} \end{bmatrix}\Big]
|
||||
\dot{x} & = Ax + Bu \\
|
||||
u & = -K_sx
|
||||
\end{align*}
|
||||
Hasil dari diterminan sebagai berikut.
|
||||
maka indeks kinerja
|
||||
\begin{align}
|
||||
0 & = \lambda^2 -Z_{22} \lambda + Z_{21}A_{14}
|
||||
J & = \int_0^{\infty} (x^T Q x + u^TRu ) dt
|
||||
\end{align}
|
||||
Dimana
|
||||
\begin{align*}
|
||||
Z_{21} &= B_{11}k_{11} +B_{12}k_{21} +B_{13}k_{31} \\
|
||||
Z_{22} &= A_{44}- B_{11}k_{12}-B_{12}k_{22}-B_{13}k_{32}
|
||||
dimana $Q$ adalah matriks diagonal $n \times n$, $R$ adalah matriks diagonal $m \times m$ dan keduanya adalah matriks pembobot terhadap state sistem dan input.
|
||||
Ketika indeks terminimalisasi, maka
|
||||
\begin{align}
|
||||
K_s = R^{-1}B^TP
|
||||
\end{align}
|
||||
dengan matriks P $n \times n$ ditentukan dari solusi persamaan \textit{Riccati}.
|
||||
\begin{align}
|
||||
A^TP+PA-PBR^{-1}B^TP+Q=0
|
||||
\end{align}
|
||||
% here is it KST from octave
|
||||
% 0.00000 -21.08185 3.33333 0.00000 -3.74993 0.99738
|
||||
% 18.25742 10.54093 3.33333 3.25168 1.87496 0.99738
|
||||
% -18.25742 10.54093 3.33333 -3.25168 1.87496 0.99738
|
||||
Kalkulasi konstanta $K_s$ akan dikalkulasi menggunakan persamaan-\eqref{eq:ssx}~\eqref{eq:ssthe}.
|
||||
Sehingga konstanta $K_s$ akan terbagi dalam sub matriks $K_{sx}, K_{sy},$ dan $K_{s\theta}$.
|
||||
Berikut adalah hasil kalkulasi.
|
||||
\begin{align*}
|
||||
K_{s}^{x} & = \begin{bmatrix}
|
||||
0.00000 & 0.00000 \\
|
||||
18.25742 & 3.25168 \\
|
||||
-18.25742 & -3.25168 \\
|
||||
\end{bmatrix} = \begin{bmatrix} K_{s}^{x1} & K_{s}^{x2} \end{bmatrix} \\
|
||||
K_{s}^{y} & = \begin{bmatrix}
|
||||
-21.08185 & -3.74993 \\
|
||||
10.54093 & 1.87496 \\
|
||||
10.54093 & 1.87496 \\
|
||||
\end{bmatrix} = \begin{bmatrix} K_{s}^{y1} & K_{s}^{y2} \end{bmatrix} \\
|
||||
K_{s}^{\theta} & = \begin{bmatrix}
|
||||
3.33333 & 0.99738 \\
|
||||
3.33333 & 0.99738 \\
|
||||
3.33333 & 0.99738 \\
|
||||
\end{bmatrix} = \begin{bmatrix} K_{s}^{\theta 1} & K_{s}^{\theta 2} \end{bmatrix}
|
||||
\end{align*}
|
||||
Dengan asumsi persamaan orde dua mengunakan parameter $\zeta~=~0.9$ dan $\omega_n~=~9.1$
|
||||
(hasil analisa pada gambar~\ref{fig:stepResGref}) sebagai berikut.
|
||||
Apabila diintegrasi terhadap persamaan~\eqref{eq:ss1} terhadap diagram~\ref{fig:state-feedback}
|
||||
\begin{align}
|
||||
\triangle \lambda &= \lambda^2+2\zeta\omega_n \lambda +\omega_n^2 \\
|
||||
&= \lambda^2+16.38 \lambda + 82.81
|
||||
\end{align}
|
||||
Sehingga akan diperoleh besaran $Z_{21}$ dan $Z_{22}$
|
||||
|
||||
|
||||
% Untuk mendapatkan konstanta $K_s$, digunakan aplikasi Matlab/Octave dengan fungsi yang bernama
|
||||
% $place()$.
|
||||
% Fungsi tersebut akan mengatur nilai $K_s$ dengan kriteria pole(perhatikan pada gambar \ref{fig:poleSystem}) yang diinginkan.
|
||||
% Berikut adalah hasil kalkulasi dari fungsi $place()$ menggunakan matriks pada persamaan~\eqref{eq:ssx},\eqref{eq:ssy}, dan \eqref{eq:ssthe}.
|
||||
\begin{align}
|
||||
K_s^{x} & =
|
||||
\begin{bmatrix}
|
||||
-0.00000 & -0.00000 \\
|
||||
71.71556 & 8.38602 \\
|
||||
-71.71556 & -8.38602
|
||||
\end{bmatrix};
|
||||
K_s^{y}=
|
||||
\begin{bmatrix}
|
||||
-82.81000 & -9.67000 & \\
|
||||
41.40500 & 4.83500 & \\
|
||||
41.40500 & 4.83500 &
|
||||
\end{bmatrix}; \nonumber \\
|
||||
K_s^{\theta} & =
|
||||
\begin{bmatrix}
|
||||
6.90083 & 1.02817 \\
|
||||
6.90083 & 1.02817 \\
|
||||
6.90083 & 1.02817
|
||||
K_s = \begin{bmatrix}
|
||||
K_{s}^{x1} & K_{s}^{y1} & K_{s}^{\theta 1} &
|
||||
K_{s}^{x2} & K_{s}^{y2} & K_{s}^{\theta 2}
|
||||
\end{bmatrix}
|
||||
\end{align}
|
||||
|
||||
|
||||
Setelah mendapatkan konstanta $K_s$, sistem sudah dalam keadaan stabil.
|
||||
Akan tetapi sistem tidak mencapai set poin yang diinginkan.
|
||||
Maka permasalahan tersebut dapat diselesaikan dengan \textit{input refrence}.
|
||||
|
|
@ -262,24 +148,58 @@ Sehingga dapat diperoleh persamaan $N$.
|
|||
\end{align}
|
||||
Berikut adalah hasil kalkulasi dari rumus $N$ menggunakan matriks pada persamaan~\eqref{eq:ssx},\eqref{eq:ssy}, dan \eqref{eq:ssthe}.
|
||||
|
||||
% 0.00000 -21.08185 3.33333 0.00000 0.00000 0.00000
|
||||
% 18.25742 10.54093 3.33333 0.00000 0.00000 0.00000
|
||||
% -18.25742 10.54093 3.33333 0.00000 0.00000 0.00000
|
||||
\begin{align*}
|
||||
N^x & = \begin{bmatrix}
|
||||
0.00000 & 0.00000 \\
|
||||
18.25742 & 0.00000 \\
|
||||
-18.25742 & 0.00000
|
||||
\end{bmatrix} = \begin{bmatrix}N^{x1} & N^{x2}\end{bmatrix}\\
|
||||
N^y & = \begin{bmatrix}
|
||||
-21.08185& 0.00000 \\
|
||||
10.54093 & 0.00000 \\
|
||||
10.54093 & 0.00000
|
||||
\end{bmatrix} = \begin{bmatrix}N^{y1} & N^{y2}\end{bmatrix}\\
|
||||
N^\theta & = \begin{bmatrix}
|
||||
3.33333 & 0.00000 \\
|
||||
3.33333 & 0.00000 \\
|
||||
3.33333 & 0.00000
|
||||
\end{bmatrix} = \begin{bmatrix}N^{\theta 1} & N^{\theta 2}\end{bmatrix}\\
|
||||
\end{align*}
|
||||
Apabila diintegrasi terhadap persamaan~\eqref{eq:ss1} terhadap diagram~\ref{fig:state-feedback}
|
||||
\begin{align}
|
||||
N^x & = \begin{bmatrix}
|
||||
-0.00000 & -0.00000 \\
|
||||
71.71556 & -0.00000 \\
|
||||
-71.71556 & -0.00000
|
||||
\end{bmatrix};
|
||||
N^y = \begin{bmatrix}
|
||||
-82.81000 & -0.00000 \\
|
||||
41.40500 & -0.00000 \\
|
||||
41.40500 & -0.00000
|
||||
\end{bmatrix} \nonumber \\
|
||||
N^\theta & = \begin{bmatrix}
|
||||
6.90083 & -0.00000 \\
|
||||
6.90083 & -0.00000 \\
|
||||
6.90083 & -0.00000
|
||||
\end{bmatrix}
|
||||
N = \begin{bmatrix}
|
||||
N^{x1} & N^{y1} & N^{\theta 1} &
|
||||
N^{x2} & N^{y2} & N^{\theta 2}
|
||||
\end{bmatrix}
|
||||
\end{align}
|
||||
|
||||
\begin{figure}
|
||||
\begin{center}
|
||||
\begin{subfigure}[t]{.3\linewidth}
|
||||
\dataGraph{t}{x}{t}{x}{BAB4/data_response.csv}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.3\linewidth}
|
||||
\dataGraph{t}{y}{t}{y}{BAB4/data_response.csv}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.3\linewidth}
|
||||
\dataGraph{t}{theta}{t}{$\theta$}{BAB4/data_response.csv}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.3\linewidth}
|
||||
\dataGraph{t}{dx}{t}{$\dot{x}$}{BAB4/data_response.csv}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.3\linewidth}
|
||||
\dataGraph{t}{dy}{t}{$\dot{y}$}{BAB4/data_response.csv}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.3\linewidth}
|
||||
\dataGraph{t}{dtheta}{t}{$\dot{\theta}$}{BAB4/data_response.csv}
|
||||
\end{subfigure}
|
||||
\captionsetup{singlelinecheck=off}
|
||||
\caption[.]{\centering Grafik state terhadap t dengan state refrensi $ r = \begin{bmatrix}6 & -3 & -90 &0 &0 &0\end{bmatrix} $ }
|
||||
\end{center}
|
||||
\end{figure}
|
||||
|
||||
\subsection{Kendali Formasi Multi Robot}
|
||||
Pada sub bab~\ref{subbab:KendaliFormasi} dijabarkan bagaimana kendali formasi menggunakan
|
||||
|
|
@ -387,86 +307,6 @@ Sedangkan komunikasi dengan PC akan mempresentasikan aktuator dan sensor untuk s
|
|||
kendali. PC akan merekam setiap keluaran dari model dan masukan dari setiap prangkat kendali
|
||||
sebagai tampilan pergerakan robotnya.
|
||||
|
||||
\subsection{Kestabilan Model}
|
||||
\todo{
|
||||
Untuk proposal, kestabilan model tidak perlu dimasukkan
|
||||
masukkan kestabilan ini pada laporan thesis saja.
|
||||
}
|
||||
Pada persamaan~\eqref{eq:disstab} apabila model dikalkulasi akan bergantung dengan besarnya \textit{step size}, $h$.
|
||||
Oleh karena itu, setelah persamaan~\eqref{eq:ss1}-\eqref{eq:ss2} dilakukan parameterisasi harus dilakukan penentuan \textit{step size} agar model tersebut stabil dalam mensimulasikan modelnya.
|
||||
Penentuan \textit{step size} harus berdasarkan kriteria kestabilan pada gamabar~\ref{fig:explicit_euler}.
|
||||
|
||||
Apabila didefinisi ulang \textit{state} pada persamaan~\eqref{eq:ss1}-\eqref{eq:ss2} dengan
|
||||
$x(t) = \begin{bmatrix}\dot{x}_r & \dot{y}_r & \dot{\theta}_r \end{bmatrix}^T$,
|
||||
maka akan lebih mudah untuk menghitung kestabilan dari matriks $A \in \mathbb{R}^{3 \times 3}$.
|
||||
Dengan menggunakan parameter dari penelitian oleh \kutip{CORREIA20127}, maka akan diperoleh matriks $A, B, K,$ dan $C$.
|
||||
\begin{align*}
|
||||
A & = \begin{bmatrix}
|
||||
-6.69666 & 0.00000 & 0.00000 \\
|
||||
0.00000 & -6.71000 & 0.00000 \\
|
||||
0.00000 & 0.00000 & -4.04200 \\
|
||||
\end{bmatrix} ; \quad
|
||||
B = \begin{bmatrix}
|
||||
0.00000 & 0.57735 & -0.57735 \\
|
||||
-0.66667 & 0.33333 & 0.33333 \\
|
||||
4.00000 & 4.00000 & 4.00000 \\
|
||||
\end{bmatrix} ; \\
|
||||
K & = \begin{bmatrix}
|
||||
-1.46667 & 0.00000 & 0.00000 \\
|
||||
0.00000 & -1.00000 & 0.00000 \\
|
||||
0.00000 & 0.00000 & -0.06600 \\
|
||||
\end{bmatrix}; \quad
|
||||
C = \begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
0 & 1 & 0 \\
|
||||
0 & 0 & 1
|
||||
\end{bmatrix}.
|
||||
\end{align*}
|
||||
|
||||
Dengan menggunakan pendekatan pada persamaan~\eqref{eq:desdotode1} untuk persamaan~\eqref{eq:ss1} maka diperoleh bentuk diskretnya
|
||||
\begin{align}
|
||||
x[k+1] & = (I + Ah)x[k] + Bhu[k] + Khsgn(x[k]) \\
|
||||
\end{align}
|
||||
Pengali $sgn(.)$ bersifat penambah dari sistem, maka dalam penentuan kestabilan ini akan dianggap penambah dari matriks sistem.
|
||||
\begin{align}
|
||||
x[k+1] & = (I + (A+K)h)x[k] + Bhu[k] \\
|
||||
\end{align}
|
||||
Kriteria kestabilan akan bergantung dari hasil penentuan $h$ pada $I+(A+K)h~=~\Lambda$.
|
||||
Untuk semua nilai $\lambda$ pada matriks $\Lambda$ harus memenuhi kriteris $\lambda \leq 1$.
|
||||
Dimungkinkan akan mengalami kebingungan ketika menentukan besar $h$,
|
||||
akan tetapi nantinya persamaan ini akan diterapkan dan diselesaikan oleh komputer.
|
||||
Alangkah baiknya apabila diidentifikasi terlebih dahulu konsumsi waktu yang dibutuhkan untuk menyelesaikan
|
||||
satu iterasi dari persamaan tersebut.
|
||||
Setelah dilakukan identifikasi, waktu yang dibutuhkan untuk satu kali iterasi berkisar $0.001$ ms (Pembulatan).
|
||||
Sehingga penentuan \textit{step size} sebesar $0.1$ ms sangat dimungkinkan, dengan pertimbangan
|
||||
sisa dari waktu yang digunakan kalkulasi dapat digunakan untuk waktu \textit{idle} dan menjalankan program yang lain. Berikut adalah matriks $\Lambda$ setelah dikalkulasi menggunakan $h=0.1$
|
||||
\begin{align*}
|
||||
\Lambda = \begin{bmatrix}
|
||||
0.18367 & 0.00000 & 0.00000 \\
|
||||
0.00000 & 0.22900 & 0.00000 \\
|
||||
0.00000 & 0.00000 & 0.58920 \\
|
||||
\end{bmatrix}.
|
||||
\end{align*}
|
||||
Terbukti bahwa semua nilai item didalam matriks kurang dari sama dengan satu.
|
||||
Sehingga menggunakan algoritma \textit{Expilicit Euler} sudah cukup untuk menjalankan model robot \textit{omni 3-wheel} sebagai model \textit{holonomic} yang akan digunakan untuk percobaan kendali multi robot.
|
||||
Hasil plot dari simulasi model dapat dilihat pada gambar~\ref{fig:sim_model}.
|
||||
\begin{figure}
|
||||
\centering
|
||||
\begin{subfigure}[t]{.6\textwidth}
|
||||
\includegraphics[scale=.4]{BAB3/img/speedRobot_-6_3_3.png}
|
||||
\caption{}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.6\textwidth}
|
||||
\includegraphics[scale=.4]{BAB3/img/speedRobot_0_6_-6.png}
|
||||
\caption{}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.6\textwidth}
|
||||
\includegraphics[scale=.4]{BAB3/img/speedRobot_6_6_6.png}
|
||||
\caption{}
|
||||
\end{subfigure}
|
||||
\caption{(a)$w_1=-6; w_2=3; w_3=3$. (b) $w_1=0; w_2=6; w_3=-6$ (c) $w_1=6; w_2=6; w_3=6$}
|
||||
\label{fig:sim_model}
|
||||
\end{figure}
|
||||
\todo{
|
||||
Tambahkan subsection mengenai
|
||||
\begin{itemize}
|
||||
|
|
|
|||
|
|
@ -0,0 +1,202 @@
|
|||
t,x,y,theta,dx,dy,dtheta,u1,u2,u3
|
||||
0,0,0,0,0,0,0,-6,-6,-6
|
||||
0.1,0,0,0,0,0,-7.200000000000001,-6,-6,-6
|
||||
0.2,0,0,-0.7200000000000002,0,0,-11.48316156502838,-6,-6,-6
|
||||
0.3,0,0,-1.868316156502838,0,0,-14.03507015648193,-6,-6,-6
|
||||
0.4,0,0,-3.271823172151031,0,0,-15.55549784996569,-6,-6,-6
|
||||
0.5,0,0,-4.827372957147601,0,0,-16.46136900023117,-6,-6,-6
|
||||
0.6,0,0,-6.473509857170717,0,0,-17.00108722846407,-6,-6,-6
|
||||
0.7,0,0,-8.173618580017125,0,0,-17.32265146616112,-6,-6,-6
|
||||
0.7999999999999999,0,0,-9.905883726633236,0,0,-17.51423950887784,-6,-6,-6
|
||||
0.8999999999999999,0,0,-11.65730767752102,0,0,-17.62838770637301,-6,-6,-6
|
||||
0.9999999999999999,0,0,-13.42014644815832,0,0,-17.69639722725246,-6,-6,-6
|
||||
1.1,0,0,-15.18978617088357,0,0,-17.73691731457533,-6,-6,-6
|
||||
1.2,0,0,-16.9634779023411,0,0,-17.76105919140995,-6,-6,-6
|
||||
1.3,0,0,-18.7395838214821,0,0,-17.77544292687561,-6,-6,-6
|
||||
1.4,0,0,-20.51712811416966,0,0,-17.78401275959258,-6,-6,-6
|
||||
1.5,0,0,-22.29552939012892,0,0,-17.78911866778813,-6,-6,-6
|
||||
1.6,0,0,-24.07444125690773,0,0,-17.79216076900088,-6,-6,-6
|
||||
1.7,0,0,-25.85365733380782,0,0,-17.79397325356469,-6,-6,-6
|
||||
1.8,0,0,-27.63305465916429,0,0,-17.79505313226177,-6,-6,-6
|
||||
1.900000000000001,0,0,-29.41255997239047,0,0,-17.79569652422423,-6,-6,-6
|
||||
2,0,0,-31.19212962481289,0,0,-17.7960798572953,-6,-6,-6
|
||||
2.100000000000001,0,0,-32.97173761054242,0,0,-17.79630824722238,-6,-6,-6
|
||||
2.200000000000001,0,0,-34.75136843526466,0,0,-17.79644432199057,-6,-6,-6
|
||||
2.300000000000001,0,0,-36.53101286746372,0,0,-17.79652539536704,-6,-6,-6
|
||||
2.400000000000001,0,0,-38.31066540700042,0,0,-17.79657369890236,-6,-6,-6
|
||||
2.500000000000001,0,0,-40.09032277689066,0,0,-17.7966024781592,-6,-6,-6
|
||||
2.600000000000001,0,0,-41.86998302470658,0,0,-17.79661962484669,-6,-6,-6
|
||||
2.700000000000001,0,0,-43.64964498719124,0,0,-17.79662984084682,-6,-6,-6
|
||||
2.800000000000001,0,0,-45.42930797127593,0,0,-17.79663592754192,-6,-6,-6
|
||||
2.900000000000001,0,0,-47.20897156403012,0,0,-17.79663955399618,-6,-6,-6
|
||||
3.000000000000001,0,0,-48.98863551942974,0,0,-17.79664171463842,-6,-6,-6
|
||||
3.100000000000001,0,0,-50.76829969089358,0,0,-17.79664300194953,-6,-6,-6
|
||||
3.200000000000002,0,0,-52.54796399108853,0,0,-17.79664376892978,-6,-6,-6
|
||||
3.300000000000002,0,0,-54.3276283679815,0,0,-17.79664422589677,-6,-6,-6
|
||||
3.400000000000002,0,0,-56.10729279057118,0,0,-17.7966444981578,-6,-6,-6
|
||||
3.500000000000002,0,0,-57.88695724038696,0,0,-17.79664466037099,-6,-6,-6
|
||||
3.600000000000002,0,0,-59.66662170642406,0,0,-17.79664475701764,-6,-5.439518511540825,-6
|
||||
3.700000000000002,0,0,-61.44628618212582,0.03235941382377067,0.01868271628197249,-17.57245221921606,-6,0.1288396765704363,-6
|
||||
3.800000000000002,0.003235941382377067,0.001868271628197249,-63.20353140404743,0.2178714617982618,0.1104412763107329,-15.21153498121775,-6,2.777551370504568,-6
|
||||
3.900000000000002,0.02502308756220325,0.01291239925927054,-64.7246849021692,0.4320757831354202,0.2289202655998398,-12.74541530006381,-6,3.955547003829054,-6
|
||||
4.000000000000002,0.06823066587574528,0.03580442581925451,-65.99922643217559,0.570846297818427,0.3071664171087584,-10.80490240465426,-4.073762954202039,4.640483844719824,-6
|
||||
4.100000000000001,0.125315295657588,0.06652106753013035,-67.07971667264101,0.6562317217217651,0.2273248542783189,-8.604274845094073,-2.318825785567043,4.553311799447982,-6
|
||||
4.200000000000001,0.1909384678297645,0.08925355295796224,-67.94014415715041,0.6794045239704957,0.08115540509776736,-6.626034417423328,-1.492672241842257,4.209327809288538,-6
|
||||
4.300000000000001,0.258878920226814,0.09736909346773898,-68.60274759889275,0.6671993564433742,-0.03347743255648465,-5.254530519190626,-0.9106779314377604,3.978753141179709,-6
|
||||
4.4,0.3255988558711514,0.09402135021209052,-69.12820065081181,0.6498553436785263,0.0823228793627177,-4.296820341588298,0.2492977753005903,3.431493189920275,-6
|
||||
4.5,0.3905843902390041,0.1022536381483623,-69.55788268497064,0.6125299638276007,-0.1751524882221678,-3.481130107408541,0.07605685200238099,3.381096727007133,-6
|
||||
4.6,0.4518373866217642,0.08473838932614551,-69.9059956957115,0.5972904920185457,-0.04999246464506385,-3.084596643066232,0.9410261872838817,3.027167843893864,-6
|
||||
4.699999999999999,0.5115664358236187,0.07973914286163912,-70.21445536001812,0.5718222873827973,-0.07827702333504719,-2.643925737951274,1.318250597174625,2.713895885305419,-6
|
||||
4.799999999999999,0.5687486645618984,0.0719114405281344,-70.47884793381324,0.545322516262899,-0.1231733460031737,-2.355792936376408,1.578801102814623,2.516685664895618,-6
|
||||
4.899999999999999,0.6232809161881884,0.05959410592781703,-70.71442722745088,0.5251828115520312,-0.1618879601487998,-2.158787236476023,1.762726829425958,2.377754751061246,-6
|
||||
4.999999999999998,0.6757991973433914,0.04340530991293706,-70.93030595109849,0.5105088084163244,-0.1915178277966191,-2.023413272542434,1.894903769626779,2.277397935804004,-6
|
||||
5.099999999999998,0.7268500781850239,0.02425352713327515,-71.13264727835274,0.4998673873007586,-0.213423088175544,-1.930029385427802,1.990337554253045,2.204224070297528,-6
|
||||
5.199999999999998,0.7768368169150998,0.002911218315720745,-71.32565021689551,0.4921274722423473,-0.2294313079345741,-1.865487277538594,2.059342696238247,2.150715611769641,-6
|
||||
5.299999999999997,0.8260495641393345,-0.02003191247773667,-71.51219894464937,0.4864814052039073,-0.2410819761179505,-1.82083440224608,2.109263119299129,2.111556699575772,-6
|
||||
5.399999999999997,0.8746977046597252,-0.04414011008953171,-71.69428238487397,0.4823554781638162,-0.2495483754482159,-1.78992560509402,2.145386318898659,2.082897312364594,-6
|
||||
5.499999999999996,0.9229332524761068,-0.06909494763435331,-71.87327494538337,0.4793378949447339,-0.2556973501087135,-1.768524612076989,2.171530908472647,2.061926067770173,-6
|
||||
5.599999999999996,0.9708670419705802,-0.09466468264522467,-72.05012740659107,0.4771303101569855,-0.2601623791243841,-1.753704557793788,2.190457021414403,2.04658458068576,-6
|
||||
5.699999999999996,1.018580072986279,-0.1206809205576631,-72.22549786237045,0.475515329345884,-0.263404499053706,-1.743440915887557,2.204160299166176,2.035364716417121,-6
|
||||
5.799999999999995,1.066131605920867,-0.1470213704630337,-72.3998419539592,0.4743340676006392,-0.2657587050107316,-1.736332470415614,2.214083913723726,2.027161479428372,-6
|
||||
5.899999999999995,1.113565012680931,-0.1735972409641068,-72.57347520100076,0.4734702429344836,-0.2674682551602582,-1.731409106030782,2.221271711031079,2.02116543750617,-6
|
||||
5.999999999999995,1.160912036974379,-0.2003440664801326,-72.74661611160384,0.4728387108983692,-0.2687097523300102,-1.727999062306072,2.22647885765295,2.016783851780787,-6
|
||||
6.099999999999994,1.208195908064216,-0.2272150417131337,-72.91941601783445,0.4723771236171816,-0.2696114013142595,-1.72563713315507,2.230251790656069,2.013582812228577,-6
|
||||
6.199999999999994,1.255433620425934,-0.2541761818445596,-73.09197973114996,0.4720398336800257,-0.2702662743420041,-1.724001137873139,2.232985994068059,2.011244784805399,-6
|
||||
6.299999999999994,1.302637603793937,-0.2812028092787601,-73.26437984493728,0.4717934293723789,-0.2707419422802816,-1.722867941133031,2.234967758904077,2.009537474234889,-6
|
||||
6.399999999999993,1.349816946731175,-0.3082770035067882,-73.43666663905059,0.4716134621050727,-0.2710874652123823,-1.722083000562754,2.236404373113487,2.008290994908322,-6
|
||||
6.499999999999993,1.396978292941682,-0.3353857500280265,-73.60887493910685,0.4714820473351016,-0.2713384659737307,-1.721539278847227,2.23744595203658,2.007381139853123,-6
|
||||
6.599999999999993,1.444126497675192,-0.3625195966253995,-73.78102886699158,0.4713861061023753,-0.2715208124118585,-1.721162639783773,2.238201227753137,2.006717123773029,-6
|
||||
6.699999999999992,1.49126510828543,-0.3896716778665854,-73.95314513096996,0.4713160764941486,-0.2716532900398357,-1.720901734293313,2.238748971703075,2.006232607212951,-6
|
||||
6.799999999999992,1.538396715934844,-0.4168370068705689,-74.12523530439928,0.4712649697782223,-0.2717495420427655,-1.720720995789442,2.239146260110545,2.005879125923514,-6
|
||||
6.899999999999991,1.585523212912667,-0.4440119610748455,-74.29730740397822,0.471227679256119,-0.2718194775900782,-1.720595788902336,2.239434456164389,2.005621282594547,-6
|
||||
6.999999999999991,1.632645980838278,-0.4711939088338533,-74.46936698286845,0.4712004743486026,-0.2718702942583685,-1.720509049521832,2.239643540591317,2.005433229410585,-6
|
||||
7.099999999999991,1.679766028273139,-0.4983809382596902,-74.64141788782064,0.4711806303953259,-0.2719072203619063,-1.720448957682887,2.239795247247827,2.005296095693126,-6
|
||||
7.19999999999999,1.726884091312671,-0.5255716602958808,-74.81346278358893,0.4711661578500355,-0.2719340539643635,-1.720407325776562,2.239905333919125,2.005196107247031,-6
|
||||
7.29999999999999,1.774000707097675,-0.5527650656923171,-74.98550351616659,0.4711556042450379,-0.2719535542889162,-1.720378482187642,2.239985227141403,2.005123211790448,-6
|
||||
7.39999999999999,1.821116267522179,-0.5799604211212087,-75.15754136438535,0.471147909412549,-0.2719677259661298,-1.720358498064816,2.240043213822645,2.005070074542772,-6
|
||||
7.499999999999989,1.868231058463433,-0.6071571937178217,-75.32957721419183,0.4711422996696709,-0.2719780254734058,-1.720344651746667,2.2400853046816,2.00503134446879,-6
|
||||
7.599999999999989,1.915345288430401,-0.6343549962651623,-75.50161167936649,0.4711382105007107,-0.2719855110747605,-1.720335057793314,2.240115859993494,2.005003118371093,-6
|
||||
7.699999999999989,1.962459109480472,-0.6615535473726384,-75.67364518514582,0.4711352300759056,-0.2719909517310343,-1.720328410028142,2.240138043147823,2.004982549567899,-6
|
||||
7.799999999999988,2.009572632488062,-0.6887526425457418,-75.84567802614863,0.4711330580007593,-0.2719949062126478,-1.720323803547754,2.240154149450376,2.004967562207014,-6
|
||||
7.899999999999988,2.056685938288138,-0.7159521331670066,-76.01771040650341,0.4711314751954649,-0.2719977805707309,-1.72032061142907,2.240165844518827,2.00495664274041,-6
|
||||
7.999999999999988,2.103799085807684,-0.7431519112240796,-76.18974246764631,0.4711303219058443,-0.2719998698890317,-1.720318399323325,2.240174337154571,2.004948687746264,-6
|
||||
8.099999999999987,2.150912117998269,-0.7703518982129828,-76.36177430757864,0.4711294816536206,-0.2720013886176974,-1.720316866293603,2.240180504717387,2.004942892893638,-6
|
||||
8.199999999999987,2.198025066163631,-0.7975520370747525,-76.53380599420801,0.4711288695240259,-0.2720024926125872,-1.720315803830085,2.240184984063262,2.004938671937339,-6
|
||||
8.299999999999986,2.245137953116033,-0.8247522863360113,-76.70583757459102,0.4711284236199692,-0.2720032951489075,-1.72031506745826,2.240188237513394,2.004935597631857,-6
|
||||
8.399999999999986,2.29225079547803,-0.851952615850902,-76.87786908133684,0.4711280988277246,-0.2720038785571726,-1.720314557069906,2.240190600716431,2.004933358640415,-6
|
||||
8.499999999999986,2.339363605360803,-0.8791530037066192,-77.04990053704383,0.4711278622696708,-0.2720043026786203,-1.720314203295776,2.240192317374976,2.00493172811062,-6
|
||||
8.599999999999985,2.38647639158777,-0.9063534339744812,-77.2219319573734,0.4711276899878931,-0.2720046110096265,-1.720313958065572,2.240193564447338,2.004930540764349,-6
|
||||
8.699999999999985,2.433589160586559,-0.9335538950754438,-77.39396335317996,0.471127564525948,-0.2720048351670057,-1.720313788066927,2.240194470436762,2.004929676195331,-6
|
||||
8.799999999999985,2.480701917039154,-0.9607543785921444,-77.56599473198665,0.4711274731657245,-0.2720049981331268,-1.720313670213535,2.240195128665988,2.004929046693348,-6
|
||||
8.899999999999984,2.527814664355726,-0.987954878405457,-77.738026099008,0.4711274066420502,-0.2720051166143875,-1.720313588505561,2.240195606913659,2.004928588371286,-6
|
||||
8.999999999999984,2.574927405019931,-1.015155390066896,-77.91005745785856,0.4711273582058024,-0.2720052027553453,-1.720313531853689,2.24019595440916,2.004928254697745,-6
|
||||
9.099999999999984,2.622040140840511,-1.04235591034243,-78.08208881104393,0.4711273229410269,-0.2720052653845698,-1.720313492571708,2.240196206911207,2.004928011784187,-6
|
||||
9.199999999999983,2.669152873134614,-1.069556436880887,-78.2541201603011,0.4711272972672624,-0.2720053109201958,-1.720313465332098,2.240196390395766,2.004927834952127,-6
|
||||
9.299999999999983,2.71626560286134,-1.096756967972907,-78.42615150683432,0.4711272785769491,-0.2720053440281391,-1.720313446441734,2.240196523733204,2.004927706230603,-6
|
||||
9.399999999999983,2.763378330719035,-1.123957502375721,-78.59818285147848,0.4711272649711682,-0.2720053681005444,-1.720313433340485,2.24019662063273,2.004927612534232,-6
|
||||
9.499999999999982,2.810491057216152,-1.151158039185775,-78.77021419481254,0.4711272550671578,-0.2720053856035552,-1.720313424253496,2.240196691054564,2.004927544335402,-6
|
||||
9.599999999999982,2.857603782722868,-1.178358577746131,-78.94224553723789,0.4711272478580681,-0.2720053983301355,-1.720313417950265,2.240196742235554,2.004927494697341,-6
|
||||
9.699999999999982,2.904716507508675,-1.205559117579144,-79.11427687903291,0.4711272426108082,-0.2720054075838531,-1.720313413577626,2.240196779433973,2.004927458569938,-6
|
||||
9.799999999999981,2.951829231769755,-1.23275965833753,-79.28630822039068,0.4711272387916449,-0.2720054143124707,-1.720313410544001,2.240196806470777,2.004927432276759,-6
|
||||
9.899999999999981,2.99894195564892,-1.259960199768777,-79.45833956144509,0.4711272360120091,-0.2720054192050814,-1.720313408439117,2.240196826122371,2.004927413141417,-6
|
||||
9.99999999999998,3.046054679250121,-1.287160741689285,-79.630370902289,0.4711272339890222,-0.2720054227627031,-1.720313406978525,2.240196840406526,2.004927399215745,-6
|
||||
10.09999999999998,3.093167402649023,-1.314361283965555,-79.80240224298686,0.4711272325167625,-0.2720054253496279,-1.720313405964911,2.240196850789516,2.004927389081757,-6
|
||||
10.19999999999998,3.140280125900699,-1.341561826500518,-79.97443358358335,0.4711272314453394,-0.2720054272307261,-1.720313405261399,2.240196858337015,2.004927381707148,-6
|
||||
10.29999999999998,3.187392849045233,-1.36876236922359,-80.14646492410949,0.471127230665639,-0.2720054285985949,-1.72031340477309,2.24019686382357,2.004927376340987,-6
|
||||
10.39999999999998,3.234505572111797,-1.39596291208345,-80.3184962645868,0.4711272300982623,-0.2720054295932667,-1.720313404433998,2.240196867811875,2.004927372435986,-6
|
||||
10.49999999999998,3.281618295121623,-1.423163455042777,-80.49052760503019,0.4711272296853832,-0.2720054303165678,-1.720313404198645,2.240196870711202,2.004927369594526,-6
|
||||
10.59999999999998,3.328731018090161,-1.450363998074433,-80.66255894545006,0.4711272293849436,-0.2720054308425379,-1.720313404035276,2.240196872819126,2.004927367527159,-6
|
||||
10.69999999999998,3.375843741028655,-1.477564541158687,-80.83459028585358,0.4711272291663389,-0.2720054312250227,-1.720313403921716,2.240196874351369,2.00492736602277,-6
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||||
10.79999999999998,3.422956463945289,-1.504765084281189,-81.00662162624575,0.4711272290072703,-0.2720054315031561,-1.720313403842917,2.240196875465472,2.004927364928278,-6
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||||
10.89999999999998,3.470069186846017,-1.531965627431505,-81.17865296663004,0.4711272288915341,-0.2720054317054188,-1.720313403788123,2.240196876275434,2.004927364131902,-6
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||||
10.99999999999998,3.51718190973517,-1.559166170602047,-81.35068430700885,0.4711272288073237,-0.2720054318525066,-1.720313403750043,2.240196876864189,2.004927363552412,-6
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||||
11.09999999999998,3.564294632615902,-1.586366713787298,-81.52271564738385,0.4711272287460494,-0.2720054319594652,-1.720313403723649,2.240196877292391,2.004927363130889,-6
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||||
11.19999999999998,3.611407355490507,-1.613567256983244,-81.69474698775622,0.4711272287014717,-0.2720054320372522,-1.720313403705252,2.240196877603609,2.004927362824191,-6
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||||
11.29999999999998,3.658520078360654,-1.640767800186969,-81.86677832812674,0.471127228669039,-0.2720054320938152,-1.720313403692483,2.240196877829959,2.00492736260108,-6
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||||
11.39999999999998,3.705632801227558,-1.667968343396351,-82.03880966849599,0.4711272286454441,-0.2720054321349517,-1.720313403683579,2.240196877994464,2.004927362438707,-6
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||||
11.49999999999998,3.752745524092103,-1.695168886609846,-82.21084100886435,0.4711272286282753,-0.2720054321648649,-1.720313403677422,2.240196878114176,2.004927362320672,-6
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||||
11.59999999999997,3.79985824695493,-1.722369429826333,-82.38287234923209,0.471127228615789,-0.2720054321866217,-1.720313403673083,2.240196878201147,2.004927362234724,-6
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||||
11.69999999999997,3.846970969816509,-1.749569973044995,-82.5549036895994,0.4711272286067023,-0.2720054322024427,-1.720313403670088,2.240196878264385,2.004927362172197,-6
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||||
11.79999999999997,3.894083692677179,-1.776770516265239,-82.72693502996641,0.4711272286000906,-0.2720054322139479,-1.720313403668019,2.240196878310371,2.004927362126722,-6
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||||
11.89999999999997,3.941196415537188,-1.803971059486634,-82.89896637033321,0.471127228595281,-0.2720054322223147,-1.720313403666582,2.240196878343795,2.004927362093639,-6
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||||
11.99999999999997,3.988309138396716,-1.831171602708866,-83.07099771069987,0.4711272285917822,-0.2720054322283983,-1.72031340366559,2.240196878368181,2.004927362069651,-6
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||||
12.09999999999997,4.035421861255895,-1.858372145931706,-83.24302905106643,0.4711272285892415,-0.2720054322328253,-1.720313403664839,2.240196878385802,2.004927362052058,-6
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||||
12.19999999999997,4.082534584114819,-1.885572689154988,-83.41506039143292,0.4711272285873864,-0.2720054322360429,-1.720313403664381,2.240196878398706,2.00492736203941,-6
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||||
12.29999999999997,4.129647306973557,-1.912773232378592,-83.58709173179936,0.4711272285860435,-0.2720054322383834,-1.720313403664005,2.240196878408028,2.004927362030088,-6
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||||
12.39999999999997,4.176760029832161,-1.93997377560243,-83.75912307216576,0.4711272285850616,-0.2720054322400856,-1.720313403663781,2.240196878414878,2.004927362023381,-6
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||||
12.49999999999997,4.223872752690667,-1.967174318826439,-83.93115441253214,0.47112722858435,-0.2720054322413258,-1.720313403663591,2.240196878419766,2.004927362018435,-6
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||||
12.59999999999997,4.270985475549102,-1.994374862050572,-84.1031857528985,0.4711272285838294,-0.2720054322422246,-1.720313403663501,2.240196878423347,2.004927362014911,-6
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||||
12.69999999999997,4.318098198407485,-2.021575405274794,-84.27521709326484,0.471127228583454,-0.2720054322428765,-1.720313403663424,2.240196878425962,2.004927362012239,-6
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||||
12.79999999999997,4.36521092126583,-2.048775948499082,-84.44724843363119,0.4711272285831758,-0.2720054322433544,-1.720313403663401,2.240196878427895,2.004927362010363,-6
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||||
12.89999999999997,4.412323644124148,-2.075976491723417,-84.61927977399753,0.4711272285829755,-0.272005432243703,-1.720313403663365,2.240196878429344,2.004927362009084,-6
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||||
12.99999999999997,4.459436366982445,-2.103177034947787,-84.79131111436386,0.4711272285828355,-0.2720054322439569,-1.720313403663275,2.240196878430169,2.004927362007948,-6
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||||
13.09999999999997,4.506549089840729,-2.130377578172183,-84.9633424547302,0.4711272285827237,-0.2720054322441333,-1.720313403663346,2.24019687843105,2.004927362007379,-6
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||||
13.19999999999997,4.553661812699001,-2.157578121396596,-85.13537379509653,0.4711272285826539,-0.272005432244269,-1.720313403663264,2.240196878431476,2.004927362006754,-6
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||||
13.29999999999997,4.600774535557266,-2.184778664621023,-85.30740513546286,0.4711272285825947,-0.2720054322443629,-1.720313403663294,2.240196878431959,2.004927362006441,-6
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||||
13.39999999999997,4.647887258415526,-2.211979207845459,-85.47943647582919,0.4711272285825572,-0.2720054322444364,-1.720313403663244,2.240196878432187,2.004927362006072,-6
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||||
13.49999999999997,4.694999981273781,-2.239179751069903,-85.65146781619552,0.4711272285825234,-0.2720054322444881,-1.720313403663271,2.240196878432442,2.004927362005958,-6
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||||
13.59999999999997,4.742112704132034,-2.266380294294352,-85.82349915656185,0.4711272285825057,-0.272005432244526,-1.720313403663231,2.240196878432556,2.004927362005759,-6
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||||
13.69999999999997,4.789225426990285,-2.293580837518804,-85.99553049692817,0.4711272285824883,-0.2720054322445526,-1.72031340366324,2.240196878432641,2.004927362005617,-6
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||||
13.79999999999997,4.836338149848534,-2.32078138074326,-86.1675618372945,0.4711272285824745,-0.2720054322445719,-1.720313403663269,2.240196878432812,2.004927362005645,-6
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||||
13.89999999999997,4.883450872706781,-2.347981923967717,-86.33959317766083,0.4711272285824715,-0.2720054322445886,-1.720313403663207,2.240196878432783,2.004927362005503,-6
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||||
13.99999999999997,4.930563595565029,-2.375182467192176,-86.51162451802715,0.4711272285824624,-0.2720054322445969,-1.720313403663237,2.240196878432869,2.004927362005475,-6
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||||
14.09999999999997,4.977676318423275,-2.402383010416635,-86.68365585839346,0.4711272285824576,-0.2720054322446063,-1.720313403663233,2.24019687843284,2.004927362005418,-6
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||||
14.19999999999997,5.024789041281521,-2.429583553641096,-86.85568719875978,0.4711272285824528,-0.2720054322446094,-1.720313403663265,2.240196878432869,2.00492736200539,-6
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||||
14.29999999999997,5.071901764139766,-2.456784096865557,-87.02771853912611,0.4711272285824495,-0.2720054322446133,-1.720313403663283,2.240196878432926,2.004927362005446,-6
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||||
14.39999999999996,5.119014486998011,-2.483984640090019,-87.19974987949244,0.4711272285824517,-0.2720054322446164,-1.720313403663249,2.240196878432897,2.004927362005361,-6
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||||
14.49999999999996,5.166127209856256,-2.51118518331448,-87.37178121985878,0.4711272285824476,-0.2720054322446184,-1.720313403663274,2.240196878432982,2.004927362005446,-6
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||||
14.59999999999996,5.213239932714501,-2.538385726538942,-87.54381256022511,0.471127228582451,-0.2720054322446218,-1.720313403663221,2.240196878432926,2.004927362005361,-6
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||||
14.69999999999996,5.260352655572746,-2.565586269763404,-87.71584390059142,0.4711272285824474,-0.272005432244622,-1.720313403663246,2.240196878432926,2.00492736200539,-6
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||||
14.79999999999996,5.307465378430991,-2.592786812987867,-87.88787524095775,0.4711272285824477,-0.2720054322446211,-1.720313403663249,2.240196878432982,2.004927362005446,-6
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||||
14.89999999999996,5.354578101289236,-2.619987356212329,-88.05990658132409,0.4711272285824512,-0.2720054322446228,-1.720313403663206,2.240196878432926,2.004927362005333,-6
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||||
14.99999999999996,5.401690824147481,-2.647187899436791,-88.2319379216904,0.4711272285824457,-0.2720054322446234,-1.720313403663249,2.240196878432982,2.004927362005418,-6
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||||
15.09999999999996,5.448803547005726,-2.674388442661253,-88.40396926205673,0.4711272285824488,-0.2720054322446245,-1.720313403663217,2.240196878432926,2.004927362005304,-6
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||||
15.19999999999996,5.495916269863971,-2.701588985885716,-88.57600060242305,0.4711272285824433,-0.2720054322446248,-1.720313403663266,2.240196878432982,2.00492736200539,-6
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||||
15.29999999999996,5.543028992722215,-2.728789529110178,-88.74803194278938,0.4711272285824464,-0.2720054322446259,-1.720313403663239,2.240196878432926,2.004927362005333,-6
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||||
15.39999999999996,5.59014171558046,-2.755990072334641,-88.9200632831557,0.4711272285824442,-0.2720054322446244,-1.720313403663268,2.240196878432954,2.004927362005361,-6
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||||
15.49999999999996,5.637254438438704,-2.783190615559103,-89.09209462352203,0.471127228582445,-0.2720054322446248,-1.720313403663263,2.240196878432982,2.00492736200539,-6
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||||
15.59999999999996,5.684367161296949,-2.810391158783565,-89.26412596388836,0.4711272285824469,-0.2720054322446259,-1.720313403663237,2.240196878432954,2.004927362005361,-6
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||||
15.69999999999996,5.731479884155194,-2.837591702008028,-89.43615730425468,0.4711272285824459,-0.2720054322446254,-1.720313403663244,2.240196878432954,2.004927362005333,-4.736135544421643
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||||
15.79999999999996,5.778592607013438,-2.86479224523249,-89.60818864462101,0.3981579802177075,-0.2298766170586809,-1.214767621431917,1.893955848266813,1.65898871525863,-3.836305370186949
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||||
15.89999999999996,5.818408405035209,-2.887779906938358,-89.7296654067642,0.3021292823254496,-0.1744704353396091,-0.830503135561766,1.638767511172148,1.404400887913283,-3.261534076599673
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||||
15.99999999999996,5.848621333267753,-2.905226950472319,-89.81271572032037,0.2225246964937034,-0.1285564434673798,-0.5755602196957549,1.465685164890544,1.232019571040439,-2.84839174525996
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||||
16.09999999999996,5.870873802917123,-2.918082594819057,-89.87027174228994,0.1624233958772837,-0.09388653327358509,-0.3965937077329987,1.33802986961183,1.105038302078071,-2.553687519343384
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||||
16.19999999999996,5.887116142504852,-2.927471248146416,-89.90993111306324,0.1182238877356172,-0.06837900200939401,-0.2739383563343258,1.245615009618604,1.013220947016322,-2.339863373340506
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||||
16.29999999999996,5.898938531278413,-2.934309148347355,-89.93732494869667,0.08597708057558767,-0.04975913128514597,-0.189023498930849,1.177903005544096,0.9460174688224186,-2.185086533312756
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||||
16.39999999999996,5.907536239335972,-2.93928506147587,-89.95622729858975,0.06250883394683596,-0.03619994140525762,-0.1304866653285993,1.128471903159522,0.8970087774933404,-2.072773543483493
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||||
16.49999999999996,5.913787122730655,-2.942905055616396,-89.96927596512261,0.04544256970422139,-0.02633341291363989,-0.09006112869827251,1.09233043341078,0.8612123990723148,-1.991307827148376
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||||
16.59999999999997,5.918331379701077,-2.94553839690776,-89.97828207799243,0.03303487736940883,-0.01915557888511432,-0.06216443792068518,1.065927861235394,0.8350882539296833,-1.932190738543341
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||||
16.69999999999997,5.921634867438017,-2.947453954796271,-89.9844985217845,0.02401479358145081,-0.01393413262893982,-0.04290743497682567,1.046639332602183,0.8160221528815725,-1.88929128733281
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||||
16.79999999999997,5.924036346796163,-2.948847368059165,-89.98878926528218,0.017457573141376,-0.01013592800476378,-0.02961617982539144,1.032552641635476,0.8021117158106961,-1.858155998146742
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||||
16.89999999999997,5.9257821041103,-2.949860960859641,-89.99175088326471,0.0126907860624581,-0.007373042839128111,-0.0204419826577186,1.022266748353019,0.7919645399671822,-1.835557216074449
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||||
16.99999999999997,5.927051182716546,-2.950598265143554,-89.99379508153049,0.009225566908744348,-0.005363272858919702,-0.01410970881254045,1.014757812395146,0.7845641473385569,-1.819152944040127
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||||
17.09999999999997,5.92797373940742,-2.951134592429446,-89.99520605241175,0.006706525304492866,-0.003901332763293464,-0.009738961300038682,1.009277150145465,0.7791679936194953,-1.80724430036787
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||||
17.19999999999997,5.92864439193787,-2.951524725705775,-89.99617994854175,0.004875308038754134,-0.002837893460456029,-0.006722137900636764,1.005277639991277,0.7752339925988281,-1.798598580783846
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||||
17.29999999999998,5.929131922741745,-2.951808515051821,-89.99685216233182,0.003544104764155842,-0.002064330248840535,-0.004639830499853513,1.002359502094379,0.7723664412598907,-1.792321305410439
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||||
17.39999999999998,5.92948633321816,-2.952014948076704,-89.9973161453818,0.002576386650445323,-0.001501627677700831,-0.003202556842817728,1.000230707771948,0.7702765774004661,-1.787763338310924
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17.49999999999998,5.929743971883205,-2.952165110844474,-89.99763640106609,0.00187290405026902,-0.001092308598444322,-0.002210505318478817,0.9986779820703475,0.7687537209189372,-1.784453554663855
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17.59999999999998,5.929931262288232,-2.952274341704319,-89.99785745159794,0.001361507435242326,-0.0007945631874581444,-0.001525760219064456,0.9975456010263599,0.7676441944169596,-1.782049993849228
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17.69999999999998,5.930067413031756,-2.952353798023065,-89.99801002761984,0.0009897477106860508,-0.0005779782926904342,-0.00105312763252865,0.9967198847877228,0.7668359223513619,-1.780304427398335
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17.79999999999998,5.930166387802824,-2.952411595852333,-89.99811534038309,0.0007194970114987043,-0.0004204308884295516,-0.0007269017760736466,0.9961178622458817,0.7662471846529968,-1.779036652410923
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||||
17.89999999999998,5.930238337503974,-2.952453638941176,-89.9981880305607,0.0005230382894066687,-0.0003058283229279424,-0.0005017304410056076,0.9956789865784685,0.7658184056179209,-1.778115839711973
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17.99999999999999,5.930290641332915,-2.952484221773469,-89.9982382036048,0.0003802226386099006,-0.0002224645374035578,-0.0003463101120430492,0.995359082327866,0.7655061606066056,-1.777446999130632
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18.09999999999999,5.930328663596776,-2.95250646822721,-89.998272834616,0.0002764028137896557,-0.0001618243527244101,-0.0002390341184950002,0.9951259239410319,0.7652788025078223,-1.776961157143944
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18.19999999999999,5.930356303878155,-2.952522650662482,-89.99829673802785,0.0002009310012461019,-0.000117713687944096,-0.0001649888577929604,0.9949560067975085,0.7651132709380875,-1.776608227974123
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18.29999999999999,5.930376396978279,-2.952534422031276,-89.99831323691363,0.0001460667737396282,-8.56268670134247e-05,-0.0001138804927464905,0.9948321896106336,0.7649927648170944,-1.776351839105814
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18.39999999999999,5.930391003655654,-2.952542984717978,-89.9983246249629,0.0001061832283577591,-6.228638726744895e-05,-7.860389356632944e-05,0.9947419734058371,0.7649050450442019,-1.776165575099412
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18.49999999999999,5.93040162197849,-2.952549213356704,-89.99833248535226,7.718988854488185e-05,-4.53081395385968e-05,-5.425487662189758e-05,0.9946762454331406,0.7648411969218785,-1.776030250737278
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||||
18.59999999999999,5.930409340967344,-2.952553744170658,-89.99833791083992,5.611318270479226e-05,-3.295788371159014e-05,-3.744842018819222e-05,0.9946283625780268,0.7647947279564562,-1.775931931282685
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||||
18.7,5.930414952285615,-2.952557039959029,-89.99834165568194,4.079147324623222e-05,-2.397410509033526e-05,-2.584807616877894e-05,0.9945934826254756,0.7647609102613444,-1.775860495048562
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18.8,5.930419031432939,-2.952559437369538,-89.99834424048956,2.965335790003354e-05,-1.743915719888689e-05,-1.784115409657165e-05,0.9945680764309657,0.7647363013201414,-1.775808589655185
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||||
18.9,5.93042199676873,-2.952561181285258,-89.99834602460497,2.155650592894354e-05,-1.268552893535224e-05,-1.231452511992349e-05,0.9945495721189275,0.7647183947896963,-1.775770874096679
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||||
19,5.930424152419323,-2.952562449838152,-89.99834725605749,1.567050009168569e-05,-9.227661776620155e-06,-8.499871965474137e-06,0.9945360956067191,0.7647053660870711,-1.775743468326652
|
||||
19.1,5.930425719469332,-2.952563372604329,-89.99834810604469,1.139166866406804e-05,-6.71235250142288e-06,-5.866878709602681e-06,0.994526281408497,0.7646958870640219,-1.775723553513501
|
||||
19.2,5.930426858636198,-2.952564043839579,-89.99834869273256,8.281172541396709e-06,-4.882675287115612e-06,-4.049504003247016e-06,0.9945191346951674,0.7646889910184314,-1.77570908171225
|
||||
19.3,5.930427686753452,-2.952564532107108,-89.99834909768296,6.019997649431286e-06,-3.551738076784661e-06,-2.795094825945588e-06,0.9945139307406237,0.7646839743877081,-1.775698564988659
|
||||
19.40000000000001,5.930428288753217,-2.952564887280916,-89.99834937719244,4.376236761499674e-06,-2.58359252056084e-06,-1.929262235677957e-06,0.9945101416280977,0.7646803251606684,-1.775690922245246
|
||||
19.50000000000001,5.930428726376893,-2.952565145640168,-89.99834957011866,3.181304934624096e-06,-1.87934756766539e-06,-1.331637451544056e-06,0.9945073828319835,0.7646776707532865,-1.775685367955646
|
||||
19.60000000000001,5.930429044507386,-2.952565333574924,-89.99834970328241,2.312649347024909e-06,-1.367068241456271e-06,-9.191380334677354e-07,0.9945053742897016,0.7646757400597153,-1.775681331337523
|
||||
19.70000000000001,5.930429275772321,-2.952565470281749,-89.99834979519622,1.681180235274526e-06,-9.94427853714952e-07,-6.344178826158883e-07,0.9945039120360377,0.7646743358262711,-1.775678397634351
|
||||
19.80000000000001,5.930429443890344,-2.952565569724534,-89.99834985863801,1.222133822642579e-06,-7.233631293124265e-07,-4.378951294304809e-07,0.9945028475355855,0.764673314542506,-1.775676265455502
|
||||
19.90000000000001,5.930429566103727,-2.952565642060847,-89.99834990242752,8.884300757294739e-07,-5.261862038308251e-07,-3.022489774443318e-07,0.994502072625437,0.7646725718044252,-1.775674715784191
|
||||
20.00000000000001,5.930429654946734,-2.952565694679468,-89.99834993265242,6.458441658696579e-07,-3.827564730302102e-07,-2.086217381538219e-07,0.994501508546108,0.7646720316622577,-1.775673589459473
|
||||
|
|
|
@ -343,7 +343,7 @@
|
|||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node at (30.809367\du,11.042461\du){K};
|
||||
\node at (30.809367\du,11.042461\du){$k$};
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
|
|
|
|||
|
|
@ -1,3 +0,0 @@
|
|||
real,imag
|
||||
-8.190000000000001,3.966598038622012
|
||||
-8.190000000000001,-3.966598038622012
|
||||
|
Binary file not shown.
Binary file not shown.
36
uithesis.sty
36
uithesis.sty
|
|
@ -176,6 +176,10 @@
|
|||
round-mode = places,
|
||||
round-precision = 2,
|
||||
}
|
||||
%
|
||||
% Digunakan untuk penulisan formula pada caption gambar
|
||||
%
|
||||
\usepackage{caption}
|
||||
|
||||
%-----------------------------------------------------------------------------%
|
||||
% Konfigurasi
|
||||
|
|
@ -235,6 +239,36 @@
|
|||
% Perintah Baru
|
||||
%-----------------------------------------------------------------------------%
|
||||
|
||||
%
|
||||
% Untuk mengimport data *.csv menjadi grafik
|
||||
% nb: Pada line pertama di file *.csv harus diberi nama colomnya
|
||||
% contoh pada file *.csv :
|
||||
% 1>colom_x,colom_y,colom_z
|
||||
% 2>0.0334,0.4455,0.11223
|
||||
% 3>...,...,...
|
||||
% Parameter : 1 -> no marks / only marks
|
||||
% 2 -> nama colom untuk menjadi sumbu X
|
||||
% 3 -> nama colom untuk menjadi sumbu Y
|
||||
% 4 -> label untuk sumbu x
|
||||
% 5 -> label untuk sumbu y
|
||||
% 6 -> path dari file *.csv
|
||||
\newcommand{\dataGraph}[6][no marks]{
|
||||
\begin{tikzpicture}
|
||||
%%https://www.latex-tutorial.com/tutorials/pgfplots/
|
||||
\begin{axis}[
|
||||
width=\linewidth, % Scale the plot to \linewidth
|
||||
grid=major, % Display a grid
|
||||
grid style={dashed,gray!30}, % Set the style
|
||||
xlabel=#4, % Set the labels
|
||||
ylabel=#5,
|
||||
#1
|
||||
]
|
||||
\addplot
|
||||
table[x=#2,y=#3,col sep=comma]{#6};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
}
|
||||
|
||||
%
|
||||
% Mengganti .et.al pada sitasi dengan dkk
|
||||
\DefineBibliographyStrings{english}{andothers={\addcomma~dkk}}
|
||||
|
|
@ -350,7 +384,7 @@
|
|||
\newcommand{\equ}{Persamaan}
|
||||
%
|
||||
%
|
||||
%%% Coloring the comment as blue in algorthm
|
||||
%%% Merubah comment menjadi biru pada perintah algorthm
|
||||
\newcommand\mycommfont[1]{\footnotesize\ttfamily\textcolor{blue}{#1}}
|
||||
\SetCommentSty{mycommfont}
|
||||
\SetKwInput{KwInput}{Masukan} % Set the Input
|
||||
|
|
|
|||
Loading…
Reference in New Issue