prepare for second order system

SOURCE/DataErrorEdge.data

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+ 19.533341512108194 16.560233973308566 19.905248843657077 17.998628159863269 21.190809758297341 19.156654642404991 21.278735297806563 17.428634986590893 20.906257494424732 15.989862949951366 19.185607093706015 14.865985287880795 -8.4667764542102244 8.6527535385895131 -8.6243148938813352 0.1239858623999419 0.083995612000674347 -8.6372549908895859 0.0902086583473201 -8.494647805010894 8.6376441855951676 0.069315401527552209
+ 19.530432487303663 16.55743337989659 19.903306302393219 18.004880351466042 21.190435848265061 19.156032418791668 21.281563055150698 17.431225622320447 20.907992777646406 15.98363255642133 19.186269529240878 14.866795671103818 -8.7066069160595561 8.8905470463881784 -8.8626140096877322 0.12287372718740405 0.083216989534306895 -8.8752070446104945 0.089376033146873715 -8.733932124945559 8.8754845984758539 0.068689134800338975
+ 19.534434066092555 16.561082422388989 19.905802422090083 17.996661515035761 21.190898132465218 19.157247290125465 21.277741575675904 17.427902170090416 20.905792752395527 15.991835725532342 19.18533105128061 14.865270876826902 -8.9462183467532927 9.1285714058831644 -9.1008116622012611 0.12168533817143985 0.082378122352154678 -9.1130494139189704 0.088489579544776528 -8.9730073978281144 9.113733373518965 0.067996917774731352
+ 19.534724154133745 16.56128031484544 19.905987835688396 17.996139743120651 21.19091452699962 19.157494813771397 21.277483980680778 17.427738657658399 20.905612750499593 15.992398734604581 19.185276751997947 14.864947735999543 -9.1859278815789267 9.3664820146360945 -9.3390677383001055 0.12055534432894008 0.081584865431017894 -9.3509593037783425 0.087646392730475878 -9.2121793516739245 9.3517751816662553 0.067354028114848821
+ 19.53455528100038 16.561119485460313 19.905833641544959 17.996405366474541 21.190788708650093 19.157342787602925 21.277616095330256 17.427880283125031 20.905766047974879 15.992105129603086 19.185440225499409 14.865146947734031 -9.4256431810058956 9.6043755702955735 -9.5773317554254724 0.11944003213548021 0.080805120407522052 -9.5888869120694569 0.086815204385511741 -9.4513682122134064 9.5897857083993436 0.066717763337873937
+
+

SOURCE/RP_2015_Rozenheck.tex

@@ -92,6 +92,7 @@ dan menyingkat perhitungannya dan menghasilkan persamaan
 
 \section{Kendali}
 
+\subsection{Orde Satu}
 Error jarak dinotasikan dengan $\delta \in \mathbb{R}^m$ dimana
 \begin{equation}
   \delta_k = || e_k ||^2 - d_k^2,  k \in \{1, \dots, m\}
@@ -149,14 +150,71 @@ lalu kombinasi persamaan tersebut diperoleh state- space close loop
   \begin{bmatrix} B \\ 0 \end{bmatrix}.v_{ref}
 \end{equation}
 
+\subsection{Orde Dua}
+
+Definisi persamaan orde dua
+\begin{align}
+  \begin{cases}
+    \dot{x}_1 = x_2\\
+    \dot{x}_2 = u
+  \end{cases}
+\end{align}
+Dengan fungsi potensial
+\begin{equation}
+  \Phi(e) =
+  \frac{1}{2}\sum_{i\in V} || x_{2i} ||^2 + \frac{1}{2} \sum_{k=1}^{m} \delta_k^2
+\end{equation}
+Maka persamaan state space nya
+\begin{align}
+  \begin{cases}
+    \dot{x}_1 &= \triangledown_{x_2} \Phi = x_{2}\\
+    \dot{x}_2 &= c(-\triangledown_{x_2}\phi -\triangledown_{x_1}\phi)\\
+    &= c(-x_2(t) - R(x_1)^T(R(x_1)x_1(t) - d ))
+  \end{cases}
+\end{align}
+Dengan menerapkan kendali PI
+\begin{align}
+    \dot{x}_2 =& C(-x_2(t) - R(x_1)^T(R(x_1)x_1(t) - d )) \\
+    =& -K_{p1}x_2(t) -R(x_1)^T K_{p2}(R(x_1)x_1(t) - d )) \\
+    & -K_{i1} \int_0^\tau x_2(\tau) d\tau
+    -R(x_1)^T K_{i2} \int_0^{\tau} (R(x_1)x_1(\tau) - d )) d\tau \\
+\end{align}
+Menghasilkan state baru dan Ditulis ulang
+\begin{align}
+    \dot{x}_1 =& x_{2}(t)\\
+    \dot{x}_2 =& -k_{p1}x_2(t) -R(x_1)^T k_{p2}(R(x_1)x_1(t) - d )) - \xi_1 - R(x_1) \xi_2 \\
+  \dot{\xi}_1 =& k_{i1} x_2(t)\\
+  \dot{\xi}_2 =& k_{i2} (R(x_1)x_1(t) - d)
+\end{align}
+Dalam bentuk matrix
+\begin{align}
+  \begin{bmatrix}
+    \dot{x}_1 \\ \dot{x}_2 \\ \dot{\xi}_1 \\ \dot{\xi}_2
+  \end{bmatrix} =
+  \begin{bmatrix}
+    0 & 1 & 0 & 0\\
+    -k_{p2}R(x_1)^T R(x_1) & -k_{p1} & -1 & -R(x_1) \\
+    0 & k_{i1} & 0 & 0 \\
+    k_{i2}R(x_1) & 0 & 0 & 0 \\
+  \end{bmatrix}
+  \begin{bmatrix}
+    x_1 \\ x_2 \\ \xi_1 \\ \xi_2
+  \end{bmatrix} +
+  \begin{bmatrix}
+    0 \\  k_{p2}R(x_1)^T \\ 0 \\ -k_{i2}
+  \end{bmatrix} d
+\end{align}
+
 \subsection{Implementasi}
 
 Pada seksi implementasi ini akan dibahas mengenai code yang digunakan
 untuk menyimulasi persamaan yang diciptakan oleh peneliti.
 \begin{figure}
   \centering
-  \includegraphics[scale=.5]{./IMG/SIM_FIG1.png}
+  \includegraphics[scale=.3]{./IMG/SIM_FIG1.png}
-  \includegraphics[scale=.5]{./IMG/SIM_FIG2.png}
+  \includegraphics[scale=.3]{./IMG/SIM_FIG2.png}
+  \includegraphics[scale=.3]{./IMG/circle_form.png}
+  \includegraphics[scale=.3]{./IMG/sin_form.png}
   \caption{Hasil Membuat Ulang Simulasi}
   \label{sim_fig1}
 \end{figure}

SOURCE/SM_2015_Rozenheck.m

@@ -1,21 +1,32 @@
 clear -all
-close all
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% config nang kene
 conRobot = [1 2 1;
-            1 4 1;
+            %% 2 1 -1;
             1 5 1;
+            %% 5 1 -1;
             1 6 1;
+            %% 6 1 -1;
             2 3 1;
+            %% 3 2 -1;
             2 4 1;
+            %% 4 2 -1;
             3 4 1;
+            %% 4 3 -1;
             4 5 1;
+            %% 5 4 -1;
             5 6 1;
+            %% 6 5 -1;
+            1 4 1;
+            %% 4 1 -1;
             5 2 1;
+            %% 2 5 -1
             %% 6 3 1;
             %% 6 4 1;
             %% 6 2 1;
             %% 3 1 1;
             %% 3 5 1;
            ];
+length_d = 3;
 dRobot = [ 1;
            1;
            1;
@@ -24,25 +35,21 @@ dRobot = [ 1;
            1;
            1;
            1;
-           1;
+           1.41;
-           1;
+           1.41;
-           %% 1;
-           %% 2;
-           %% 2;
-           %% 2;
-           %% 2;
            %% 2;
+           %% 3.014;
+           %% 3.014;
+           %% 3.014;
+           %% 3.014;
 ];
-corRobot = [2; 2.5;
+corRobot = [1.5; 1.7;
-            2.7; 2.6;
+            2; 2.5;
-            3; 2.3;
+            2.5; 2.8;
-            2.5; 1.5;
+            2.5; 2;
-            1.8; 1.5;
+            2.2; 1;
-            1.5; 2;
+            1.5; 0.2;
-           ]; % xy xy xy
+           ]*10; % xy xy xy
-%% figure(1)
-[R,K,d] = rigidityMatrixFnc(conRobot);
-vref = [-5; 5];
 B = [
      1 0; 0 1;
      0 0; 0 0;
@@ -51,30 +58,46 @@ B = [
      0 0; 0 0;
      0 0; 0 0;
     ];
-kp = 10;
+kp = 30;
 ki = 3;
+%% fvref = fncSpeedRef('ysin',100,2);
+%% fvref = fncSpeedRef('xsin',50,2);
+%% fvref = fncSpeedRef('cw',-100,1);
+fvref = fncSpeedRef('s',0,0);
+fvrefans = fncSpeedRef('s',0,0);
+tspan = 1:0.1:5;
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% config nang nduwur
+
+[R,K,d] = rigidityMatrixFnc(conRobot);
 _zero = zeros(size(R(corRobot,K),1),1);
 sInit = [corRobot; _zero;];
 sAnsInit =[_zero; _zero;];
-%% tspan = linspace(1,0.1,30);
+
-tspan = 1:0.01:10;
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% start solving
-dydt = @(t, y) systm_robot(t, y,(dRobot*6), R,K, kp, ki, B, vref);
+printf("Mulai memecakan masalah \n\n");
+startExe = tic;
+
+dydt = @(t, y) systm_robot(t, y,(dRobot*length_d), R,K, kp, ki, B, fvref(t));
 [t,y] = ode45(dydt, tspan, sInit);
 
 cntr = 1;
 bypassCntr = @(c) cntr;
 plusPlusCntr = @(c) cntr++;
 
-dyansdt = @(t, yin) systm_anlys_robot(t, yin, y(:,1:(2*numNodes(edgeL2adj(conRobot)))) ,bypassCntr, plusPlusCntr ,(dRobot*6), R, K, kp, ki, B, vref);
+dyansdt = @(t, yin) systm_anlys_robot(t, yin, y(:,1:(2*numNodes(edgeL2adj(conRobot)))) ,bypassCntr, plusPlusCntr ,(dRobot*6), R, K, kp, ki, B, fvref(t));
 [t,yans] = ode45(dyansdt, tspan, sAnsInit);
 
-ddYans = zeros(size(yans,1),1);
+endExe = toc(startExe);
-for i = 1:size(yans,1)
+printf("Membutuhkan waktu %i menit, %i detik \n untuk memecahkan masalah mu  \n\n",
-  ddYans(i) = norm(yans(i,1:(size(yans,2)/2)));
+       floor(endExe/60), rem(endExe,60))
-endfor
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End Solving
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% start plot it
+
+close all
 
 figure(1)
 
+                                % plot trayektori dari setiap robot
 str_tmp = "plot(";
 for i = 1:length(corRobot)-1
   str_tmp = strcat(str_tmp,sprintf("y'(%i,:),",i));
@@ -83,6 +106,8 @@ str_tmp = strcat(str_tmp,sprintf("y'(%i,:));",i+1));
 eval(str_tmp);
 
 hold on
+                                % membuat fungsi plot robot di waktu
+                                % tertentu
 str_tmp = "@(t) plot( [";
 for i = 1:2:length(corRobot)
   str_tmp = strcat( str_tmp, sprintf("y'(%i,t), ",i));
@@ -97,6 +122,8 @@ plot_rb = eval(str_tmp);
 xrb = 1:2:length(corRobot);
 yrb = 2:2:length(corRobot);
 
+                                % fungsi untuk plot coneksi di waktu
+                                % tertentu
 function plot_con (pltRb, yOut, conIn,xm,ym, time)
   pltRb(time);
   for i = 1:length(conIn)
@@ -106,23 +133,44 @@ function plot_con (pltRb, yOut, conIn,xm,ym, time)
 endfunction
 
 plot_con(plot_rb, y', conRobot, xrb, yrb, 1);
+plot_con(plot_rb, y', conRobot, xrb, yrb, round(length(tspan)/2));
 plot_con(plot_rb, y', conRobot, xrb, yrb, length(tspan));
 
 
 str_tmp = "legend(";
 for i = 1:numNodes(edgeL2adjL(conRobot))-1;
-  str_tmp =strcat(str_tmp,sprintf("\"Robot %i \", ",i));
+  str_tmp =strcat(str_tmp,sprintf("\"R%i \", ",i));
 endfor
-str_tmp =strcat(str_tmp,sprintf("\"Robot %i \" )",++i));
+str_tmp =strcat(str_tmp,sprintf("\"R%i \" )",++i));
 eval(str_tmp)
+title("Motion dari Robot");
 
 figure(2)
+                                % Plot analisis error secara keseluruhan 
+ddYans = zeros(size(yans,1),1);
+for i = 1:size(yans,1)
+  ddYans(i) = norm(yans(i,1:(size(yans,2)/2)));
+endfor
+
 plot([1:length(ddYans)],ddYans )
+hold on
+                                % Plot analisis error setiap robot
+str_tmp = "plot(";
+for i = 1:length(dRobot)-1
+  str_tmp = strcat(str_tmp,sprintf("[1:length(yans'(%i,:))], yans'(%i,:),",i,i));
+endfor
+str_tmp = strcat(str_tmp,sprintf("[1:length(yans'(%i,:))], yans'(%i,:));",i+1,i+1));
+eval(str_tmp);
 
-%% plot_rb(20);
+str_tmp = "legend(";
-%% plot_rb(40);
+str_tmp = strcat(str_tmp,sprintf("\"All\", "));
-%% plot_rb(60);
+for i = 1:numNodes(edgeL2adjL(conRobot))-1;
-%% plot_rb(80);
+  str_tmp =strcat(str_tmp,sprintf("\"R%i \", ",i));
-%% plot_rb(100);
+endfor
+str_tmp =strcat(str_tmp,sprintf("\"R%i \" )",++i));
+eval(str_tmp)
+title("Norm error setiap edge robot")
 
+save DataOutMotion.data y
+save DataErrorEdge.data yans
 

SOURCE/circleDataErrorEdge.data

@@ -0,0 +1,48 @@
+# Created by Octave 4.4.1, Tue Jul 23 08:17:46 2019 WIB <adnr@morilin.fedo>
+# name: yans
+# type: matrix
+# rows: 41
+# columns: 18
+ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+ -0.096911478315354516 -0.075730185298846384 -0.012818693778102748 0.02494319515544317 -0.071455460399853357 0.058061517393821691 -0.00046049687370259293 0.031894441863279527 -0.00020103212281644091 -0.023675953022652619 -0.020957934876851849 -0.0036309652191249529 0.0093563014520160383 -0.013149718234368087 0.01202648390515818 -0.0012963378978132847 0.0062554711548290943 -0.0022820491653563553
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+
+

SOURCE/fncSpeedRef.m

@@ -0,0 +1,40 @@
+function fncSr = fncSpeedRef(param,r,v)
+  sp = [1, 2]; % 1 = x; 2 = y
+  if (length(param) == 4)
+                                % 'xsin' / 'xcos'
+    strSinOcos = strcat(sprintf("%s", param(2:length(param))));
+
+    if (param(1) == 'x')
+      strSfx = strcat(sprintf("%i*%s(%i*t)",r,strSinOcos,v));
+      strSfy = strcat(sprintf("%i",r));
+                                % 'ysin' / 'ycos'
+    elseif (param(1) == 'y')
+      strSfx = strcat(sprintf("%i",r));
+      strSfy = strcat(sprintf("%i*%s(%i*t)",r,strSinOcos,v));
+    endif
+
+  elseif (param(1) == 'c')
+    if(param(2) == 'c')
+                                %'circle'
+      strSfx = strcat(sprintf("%i*cos(%i*t)",r,v));
+      strSfy = strcat(sprintf("%i*sin(%i*t)",r,v));
+
+    else
+      strSfx = strcat(sprintf("%i*sin(%i*t)",r,v));
+      strSfy = strcat(sprintf("%i*cos(%i*t)",r,v));
+    endif
+
+  elseif (param == 's')
+    strSfx = strcat(sprintf("%i",r));
+    strSfy = strcat(sprintf("%i",v));
+  else
+    printf("Karepmu opo ? \n\n bukak fungsi speedRef sek diwoco komen e \n\n");
+  endif
+
+  strAll = strcat("fncSr = @(t) [",strSfx, ";\ ", strSfy, "];");
+  %% printf(strAll)
+  eval(strAll);
+
+  %% spx = sfx(t);
+  %% spy = sfy(t);
+endfunction

SOURCE/rigidityMatrixFnc.m

@@ -6,11 +6,13 @@ function [R,K, d] = rigidityMatrixFnc (edgeL)
                                 % generasi koneksi bentuk incidence
   tmp = edgeL2adj(edgeL);
   d = ones(numEdges(tmp),1);
+  printf("Jumlah Edge : %i \n", length(d));
   gInc = adj2inc(tmp);
-  %% drawCircGraph(tmp)
+  tmp = numNodes(adj2adjL(tmp));
-  tmp = getNodes(gInc,'adjacency')
+  printf("Jumlah Robot : %i \n", tmp);
                                 % generasi vector error menggunakan matrix
                                 % koneksi
+  tmp = getNodes(gInc,'adjacency');
   K = kron(adj2inc(edgeL2adj(edgeL))',eye(2));
   edgeVector = @(x,k) k*x;
                                 % hasil turunan dari fungsi edge
@@ -20,7 +22,7 @@ function [R,K, d] = rigidityMatrixFnc (edgeL)
   endfor
   str = strcat(str,sprintf("errVec(%i:%i)' ));",i+2,i+3));
                                 % return sebagai fungsi R
-  eval(str)
+  eval(str);
   R = @(x,k) errBlockDiagonal(edgeVector(x,k))*k;
 
 endfunction

SOURCE/sinDataErrorEdge.data

@@ -0,0 +1,48 @@
+# Created by Octave 4.4.1, Tue Jul 23 08:22:36 2019 WIB <adnr@morilin.fedo>
+# name: yans
+# type: matrix
+# rows: 41
+# columns: 18
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SOURCE/sinDataOutMotion.data

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+
+

SOURCE/systm_anlys_robot.m

@@ -1,21 +1,10 @@
 function dxdt = systm_anlys_robot(t,x,xRobot, C, ppC,d,R,K,kp,ki,B,vref)
   n = length(K(1,:))/2;
   m = length(K(:,1))/2;
-  %% l = length(R(ones(n*2,1),K));
   dxdt = zeros(m*2,1);
   x1 = x(1:m);
   x2 = x(length(x1)+1:length(x));
   counter = C(0);
-  %% length(x1)
-  %% length(x2)
-  %% if (t > 5) && (t < 15)
-  %% vref = [5; 10];
-  %% else
-  %% if (t > 15) && (t > 20)
-  %% vref = [5; -10];
-  %% endif
-  %% endif
-  %% size(xRobot)
   dxdt(1:length(x1)) = -(2*kp*(R(xRobot(counter,:)',K)*R(xRobot(counter,:)',K)')*x1) -(2*(R(xRobot(counter,:)',K)*R(xRobot(counter,:)',K)')*x2) +((2*R(xRobot(counter,:)',K)*B)*vref);
   dxdt(length(x1)+1:length(x)) =(ki*x1);
   ppC();

SOURCE/systm_robot.m

@@ -12,6 +12,7 @@ function dxdt = systm_robot(t,x,d,R,K,kp,ki,B,vref)
       %% vref = [5; -10];
     %% endif
   %% endif
+  %% dxdt(1:length(x1)) = -((kp*R(x1,K)'*R(x1,K))*x1)-(R(x1,K)'*x2)+((kp*R(x1,K)')*d)+(B*vref);
   dxdt(1:length(x1)) = -((kp*R(x1,K)'*R(x1,K))*x1)-(R(x1,K)'*x2)+((kp*R(x1,K)')*d)+(B*vref);
   dxdt(length(x1)+1:length(x)) = ki*R(x1,K)*x1-(ki*d);
 endfunction