+plot distance error

+formationControl 1 dan 2 model
+formationControl 2
+param sx/sy fncSpeedRef
master
a2nr 2021-01-26 12:23:22 +07:00
parent bc1085f9eb
commit d55d7c2a5c
22 changed files with 6741 additions and 15 deletions

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@ -204,7 +204,7 @@ Dalam bentuk matrix
\end{bmatrix} + \end{bmatrix} +
\begin{bmatrix} \begin{bmatrix}
0 \\ k_{p2}R(x_1)^T \\ 0 \\ -k_{i2} 0 \\ k_{p2}R(x_1)^T \\ 0 \\ -k_{i2}
\end{bmatrix} d \end{bmatrix} d \label{orde_dua_ss}
\end{align} \end{align}
\subsection{Implementasi} \subsection{Implementasi}
@ -226,6 +226,17 @@ dengan kecepatan vector $[-5;\ 5]$. Akan tetapi ada sebuah error apabila $vref$
dengan kecepatan vector $[5;\, 5]$. Ini diakibatkan ada masalah pada rigiditas dengan kecepatan vector $[5;\, 5]$. Ini diakibatkan ada masalah pada rigiditas
graph. graph.
\subsubsection{ time varian bentuk diskrit }
Sederhana dari persamaan-()\ref{orde_dua_ss})
\begin{align}
\dot{x} &= A(x)x + B(x) d \\
\frac{x[k+1]-x[k]}{h} &= A(x[k])x[k] + B(x[k])d \\
x[k+1] &= I + hA(x[k])x[k] + hB(x[k])d\\
x]k+1] &= A_d[k] x[k] + B_d[k]d \\
A_d[k] &= I +hA(x[k]) \\
B_d[k] &= hB(x[k])
\end{align}
\section{Kesimpulan} \section{Kesimpulan}
Implementasi berhasil. Penelitian mengalami kekurangan apabila vref diberikan Implementasi berhasil. Penelitian mengalami kekurangan apabila vref diberikan
pada robot yang berpotensi menghasilkan lipatan pada graph. pada robot yang berpotensi menghasilkan lipatan pada graph.

View File

@ -1,5 +1,7 @@
clear -all clear -all
graphics_toolkit('gnuplot') graphics_toolkit('gnuplot')
omni = omni = omnidirectional(0.94, 0.96, 0.01, 2.2, 1.5,0.099,0.1,1.5,0.025,30,0.035,19,0.00011,1.69,0.0059,0.0059,0.9,9.1,6,'./');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% config nang kene %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% config nang kene
conRobot = [1 2 1; conRobot = [1 2 1;
3 2 1; 3 2 1;
@ -14,22 +16,25 @@ corRobot = [1.5; 1.7;0;
2; 2.5;0; 2; 2.5;0;
2.5; 2.8;0; 2.5; 2.8;0;
]; % xy xy xy ]; % xy xy xy
robStateLen = length(corRobot)/length(dRobot) robStateLen = size(omni.origin.A,1);
B = [ B = [
1 0; 0 1; 1 0; 0 1;
0 0; 0 0; 0 0; 0 0;
0 0; 0 0; 0 0; 0 0;
]; ];
kp = 80; kp = 150;
ki = 1; ki = 3;
% fvref = fncSpeedRef('ysin',50,2,robStateLen); % fvref = fncSpeedRef('ysin',50,2,robStateLen);
% fvref = fncSpeedRef('xsin',50,2,robStateLen); % fvref = fncSpeedRef('xsin',50,2,robStateLen);
% fvref = fncSpeedRef('cw',-300,1,robStateLen); % fvref = fncSpeedRef('cw',-300,1,robStateLen);
% fvref = fncSpeedRef('s',50,50,robStateLen); % fvref = fncSpeedRef('s',50,50,robStateLen);
fvref = fncSpeedRef('s',0,0,robStateLen); fvref = fncSpeedRef('s',0,0,robStateLen);
h = .1; h = .01;
tspan = 1:h:10; tspan = 1:h:10;
sys = formationControl2ndBuilder(conRobot,robStateLen,kp,kp,ki,ki,length_d,1); sys = formationControl2ndBuilder(conRobot,robStateLen,kp,kp,ki,ki,length_d,1);
% sys = formationControl2ndModelBuilder(conRobot,omni.origin,kp,kp,ki,ki,length_d,1);
% sys = formationControl1stModelBuilder(conRobot,omni.origin,kp,kp,ki,ki,length_d,1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% config nang nduwur %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% config nang nduwur
[R,K,d] = rigidityMatrixFnc(conRobot,robStateLen); [R,K,d] = rigidityMatrixFnc(conRobot,robStateLen);
@ -37,16 +42,34 @@ _zero = zeros(size(R(corRobot,K),1),1);
sInit = [corRobot; _zero;]; sInit = [corRobot; _zero;];
sAnsInit =[_zero; _zero;]; sAnsInit =[_zero; _zero;];
s2ndInit = [corRobot; %x1 s2ndInit = [corRobot; %x1
zeros(length(corRobot),1); %x2 zeros(length(corRobot),1); %x2
zeros(length(corRobot),1); %xi1 zeros(length(corRobot),1); %xi1
_zero]; %xi2 _zero;]; %xi2
% _zero; zeros(length(corRobot),1);]; %x2*
s1stInit = [corRobot; zeros(size(corRobot)); zeros(size(dRobot))];
% state_init = sInit;
state_init = s2ndInit;
% state_init = s1stInit;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% start solving %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% start solving
printf("Mulai memecakan masalah \n\n"); printf("Mulai memecakan masalah \n\n");
startExe = tic; startExe = tic;
dydt = @(t, y) sys.ss(y,fvref(t)); % continue
[t,y] = ode45(dydt, tspan, s2ndInit); % dydt = @(t, y) sys.ss(y,fvref(t));
% [t,y] = ode45(dydt, tspan, state_init);
% discrate taylor methode
dydt = @(t, y) sys.dss(y, h, fvref(t))
t(1,:) = tspan(1);
y(1,:) = dydt(t(1), state_init);
Dd(1,:) = [norm((K*y(1,1:9)')(1:3)) norm((K*y(1,1:9)')(4:6)) norm((K*y(1,1:9)')(7:9))]';
for i = 2:length(tspan)
t(i,:) = tspan(i);
y(i,:) = dydt(t(i),y(i-1,:)');
Dd(i,:) = [norm((K*y(i,1:9)')(1:3)) norm((K*y(i,1:9)')(4:6)) norm((K*y(i,1:9)')(7:9))]';
endfor
endExe = toc(startExe); endExe = toc(startExe);
printf("Membutuhkan waktu %i menit, %i detik \n untuk memecahkan masalah mu \n\n", printf("Membutuhkan waktu %i menit, %i detik \n untuk memecahkan masalah mu \n\n",
@ -111,6 +134,11 @@ str_tmp =strcat(str_tmp,sprintf("\"R%i \" )",++i));
eval(str_tmp) eval(str_tmp)
title("Motion dari Robot"); title("Motion dari Robot");
figure(2)
plot(t,Dd(:,1),t,Dd(:,2),t,Dd(:,3))
title("distance error")
legend()
csvwrite("DataOutMotion.csv", [t y]) csvwrite("DataOutMotion.csv", [t y])
% save DataOutMotion.data y % save DataOutMotion.data y
% save DataErrorEdge.data yans % save DataErrorEdge.data yans

View File

@ -24,9 +24,21 @@ function fncSr = fncSpeedRef(param,r,v,robStateLen)
strSfy = strcat(sprintf("%i*cos(%i*t)",r,v)); strSfy = strcat(sprintf("%i*cos(%i*t)",r,v));
endif endif
elseif (param == 's') elseif (param(1) == 's')
strSfx = strcat(sprintf("%i",r)); strSinOcos = strcat(sprintf("%s", param(3:end)));
strSfy = strcat(sprintf("%i",v)); if (length(param) > 1)
if (param(2) == 'y')
strSfx = strcat(sprintf("%i*%s(%i*t)",r,strSinOcos,v));
strSfy = strcat(sprintf("%i",0));
% 'ysin' / 'ycos'
else %if (param(2) == 'x')
strSfx = strcat(sprintf("%i",0));
strSfy = strcat(sprintf("%i*%s(%i*t)",r,strSinOcos,v));
endif
else
strSfx = strcat(sprintf("%i",r));
strSfy = strcat(sprintf("%i",v));
endif
else else
printf("Karepmu opo ? \n\n bukak fungsi speedRef sek diwoco komen e \n\n"); printf("Karepmu opo ? \n\n bukak fungsi speedRef sek diwoco komen e \n\n");
endif endif

View File

@ -0,0 +1,30 @@
function obj = formationControl1stModelBuilder(edgeL,model,kp1,kp2,ki1,ki2,dScale,nNodeVref)
addpath("./networks-toolbox");
obj = struct();
robStateLen = size(model.A,1)
[obj.R, obj.K, obj.d] = rigidityMatrixFnc(edgeL,robStateLen);
obj.m = length(obj.d);
obj.n = numNodes(edgeL);
obj.nodeStateLength = robStateLen*obj.n;
obj.stateLength = 2 * obj.nodeStateLength + obj.m;
_nst = kron(eye(obj.n), model.Nst);
_kst = kron([zeros(obj.n) eye(obj.n)], model.Kst);
%obj.A = kron([zeros(obj.n) zeros(obj.n);zeros(obj.n) eye(obj.n)],model.A) + kron([zeros(obj.n) eye(obj.n);zeros(obj.n) zeros(obj.n)],eye(obj.n));
% pilih robot mana yang ingin dijalankan dengan mengganti 0 menjadi 1
% r 1 2 3 r 1 2 3
% v v v v v v
obj.A = kron([zeros(obj.n) zeros(obj.n);zeros(obj.n) diag([1 0 0])],model.A) + kron([zeros(obj.n) diag([1 0 0]);zeros(obj.n) zeros(obj.n)],eye(obj.n));
obj.B = kron([zeros(obj.n); eye(obj.n)],model.B);
obj.Ksgn = kron([zeros(obj.n) zeros(obj.n);zeros(obj.n) eye(obj.n)],model.K);
obj.controller = @(set_point,st) arrayfun(model.limit_motor,_nst * set_point + _kst * st(1:(2 * obj.nodeStateLength)));
obj.formation_controller = @(st) -obj.R(st(1:obj.nodeStateLength),obj.K)'*kp1*(obj.R(st(1:obj.nodeStateLength),obj.K)*st(1:obj.nodeStateLength)-(obj.d*dScale)) -obj.R(st(1:obj.nodeStateLength),obj.K)'*ki1*st(obj.stateLength-obj.m+1:obj.stateLength,1);
obj.formation_control_dot = @(st) [obj.R(st(1:obj.nodeStateLength),obj.K) zeros(obj.m, obj.nodeStateLength + obj.m)];
obj.stateA = @(st) [obj.A zeros(obj.stateLength-obj.m, obj.m); obj.formation_control_dot(st)];
obj.stateB = [obj.B zeros(obj.stateLength-obj.m, obj.m); zeros(obj.m, size(model.B,2)*obj.n) eye(obj.m)];
obj.stateKsgn = @(st,h) (h*[obj.Ksgn zeros(obj.stateLength-obj.m, obj.m); zeros(obj.m,obj.stateLength)])*arrayfun(model.sgn,st);
obj.stateInput = @(st) [obj.controller(obj.formation_controller(st), st); obj.d*dScale];
obj.ss = @(st,vRef) obj.stateA(st)*st + obj.stateKsgn(st,1) + obj.stateB *obj.stateInput(st);
obj.dss = @(st,h,vRef) (eye(size(obj.stateA(st))) + (h*obj.stateA(st)))*st + obj.stateKsgn(st,h) + (h*obj.stateB)*obj.stateInput(st);
endfunction

View File

@ -24,10 +24,11 @@ function obj = formationControl2ndBuilder(edgeL,robStateLen,kp1,kp2,ki1,ki2,dSca
obj.Kb(obj.n+nNodeVref) = 1; obj.Kb(obj.n+nNodeVref) = 1;
obj.Kb = [kron(obj.Kb,eye(robStateLen)); zeros(obj.m,robStateLen)]; obj.Kb = [kron(obj.Kb,eye(robStateLen)); zeros(obj.m,robStateLen)];
obj.d = obj.d*dScale; obj.d = obj.d*dScale;
obj.ssDisc = @(st,vRef,h) (eye(obj.sizeA) + (obj.A(st)*h))*st + obj.B(st)*h*obj.d + obj.Kb*vRef; obj.dss = @(st,h,vRef) (eye(obj.sizeA) + (obj.A(st)*h))*st + (obj.B(st)*h)*obj.d + (obj.Kb*h)*vRef;
obj.ss = @(st,vRef) obj.A(st)*st + obj.B(st)*obj.d + obj.Kb*vRef; obj.ss = @(st,vRef) obj.A(st)*st + obj.B(st)*obj.d + obj.Kb*vRef;
printf("============== Formation Control ============ \n"); printf("============== Formation Control ============ \n");
printf(" state model : %i \n", obj.nodeStateLength);
printf(" Node : %i \n", obj.n); printf(" Node : %i \n", obj.n);
printf(" Edge : %i \n", obj.m); printf(" Edge : %i \n", obj.m);
printf("Dimention State : %i \n", obj.stateLength); printf("Dimention State : %i \n", obj.stateLength);

View File

@ -0,0 +1,44 @@
function obj = formationControl2ndModelBuilder(edgeL,model,kp1,kp2,ki1,ki2,dScale,nNodeVref)
addpath("./networks-toolbox");
% pkg load parallel
obj = struct();
robStateLen = size(model.syscl.A,1)
[obj.R, obj.K, obj.d] = rigidityMatrixFnc(edgeL,robStateLen);
obj.m = length(obj.d);
obj.n = numNodes(edgeL);
obj.nodeStateLength = robStateLen*obj.n;
obj.stateLength = 4 * obj.nodeStateLength + obj.m;
% build matrix sistem
obj.A1 = @(st) [zeros(obj.nodeStateLength), zeros(obj.nodeStateLength), zeros(obj.nodeStateLength),zeros(obj.nodeStateLength,obj.m), eye(obj.nodeStateLength)];
obj.A2 = @(st) [-kp2*obj.R(st(1:(obj.nodeStateLength)),obj.K)'*obj.R(st(1:(obj.nodeStateLength)),obj.K), -kp1*eye(obj.nodeStateLength), -eye(obj.nodeStateLength), -obj.R(st(1:(obj.nodeStateLength)),obj.K)',zeros(obj.nodeStateLength)];
obj.A3 = @(st) [zeros(obj.nodeStateLength), ki1*eye(obj.nodeStateLength), zeros(obj.nodeStateLength), zeros(obj.nodeStateLength,obj.m), zeros(obj.nodeStateLength)];
obj.A4 = @(st) [ki2*obj.R(st(1:(obj.nodeStateLength)),obj.K), zeros(obj.m,obj.nodeStateLength), zeros(obj.m,obj.nodeStateLength), zeros(obj.m), zeros(obj.m,obj.nodeStateLength)];
obj.MOsgn =@(st) diag([model.sgn(st(1)) model.sgn(st(2)) model.sgn(st(3))]);
obj.MOdist = @(st) [obj.MOsgn(st(31:33)) zeros(robStateLen) zeros(robStateLen); zeros(robStateLen) obj.MOsgn(st(34:36)) zeros(robStateLen); zeros(robStateLen) zeros(robStateLen) obj.MOsgn(st(37:39))];
obj.MO = @(st) [zeros(obj.nodeStateLength), kron(eye(robStateLen),model.syscl.B) , zeros(obj.nodeStateLength), zeros(obj.nodeStateLength,obj.m), kron(eye(robStateLen),model.syscl.A)+obj.MOdist(st)];
obj.A = @(st) [obj.A1(st); obj.A2(st); obj.A3(st); obj.A4(st); obj.MO(st)];
obj.sizeA = size(obj.A(ones(obj.stateLength,1)));
% build matrix input
obj.B = @(st) [zeros(obj.nodeStateLength,obj.m); kp2*obj.R(st(1:(obj.nodeStateLength)),obj.K)'; zeros(obj.nodeStateLength,obj.m); -ki2*eye(obj.m,obj.m); zeros(obj.nodeStateLength,obj.m)]
obj.sizeB = size(obj.B(ones(obj.stateLength,1)));
%build state space
obj.Kb = zeros(obj.n*3,1);
obj.Kb(obj.n+nNodeVref) = 1;
obj.Kb = [kron(obj.Kb,eye(robStateLen)); zeros(obj.m,robStateLen); zeros(obj.nodeStateLength,robStateLen)];
obj.d = obj.d*dScale;
obj.dss = @(st,h,vRef) (eye(obj.sizeA) + (obj.A(st)*h))*st + obj.B(st)*h*obj.d + obj.Kb*h*vRef;
obj.ss = @(st,vRef) obj.A(st)*st + obj.B(st)*obj.d + obj.Kb*vRef;
printf("============== Formation Control ============ \n");
printf(" state model : %i \n", obj.nodeStateLength);
printf(" Node : %i \n", obj.n);
printf(" Edge : %i \n", obj.m);
printf("Dimention State : %i \n", obj.stateLength);
printf(" Dimention A : %i x %i \n", obj.sizeA);
printf(" Dimention B : %i x %i \n", obj.sizeB);
printf("============================================= \n");
endfunction

37
SOURCE/identification.m Normal file
View File

@ -0,0 +1,37 @@
omni = omnidirectional(0.94, 0.96, 0.01, 2.2, 1.5,0.099,0.1,1.5,0.025,30,0.035,19,0.00011,1.69,0.0059,0.0059,0.9,9.1,6,'./');
A = kron(eye(3), [zeros(size(omni.origin.syscl.a)) eye(size(omni.origin.syscl.a)); zeros(size(omni.origin.syscl.a)) omni.origin.syscl.a]);
B = kron(eye(3),kron([0;1],omni.origin.syscl.b));
R = @(the) [[cos(deg2rad(the)) -sin(deg2rad(the)) 0; sin(deg2rad(the)) cos(deg2rad(the)) 0; [0 0 1];] zeros(size(omni.origin.syscl.a)); zeros(size(omni.origin.syscl.a)) zeros(size(omni.origin.syscl.a))];
C = @(the1,the2, the3) kron(diag([1 0 0]), R(the1)) + kron(diag([0 1 0]), R(the2)) + kron(diag([0 0 1]), R(the3));
fvref_cw = fncSpeedRef('cw',4,6,3);
fvref_ysin = fncSpeedRef('sysin',8,6,3);
fvref_xsin = fncSpeedRef('sxsin',8,6,3);
finput = @(t) [fvref_cw(t)+[0 0 90*sin(deg2rad(5*t))]'; fvref_xsin(t); fvref_ysin(t);]
sys = @(st, input) A*st + B* input;
dydt = @(t, y) sys(y, finput(t));
RX = @(x,y,the) x*cos(deg2rad(the))-y*sin(deg2rad(the));
RY = @(x,y,the) y*cos(deg2rad(the))+x*sin(deg2rad(the));
init = [0 0 0 0 0 0 5 7 45 0 0 0 -8 4 270 0 0 0]';
tSpan = 1:.1:50;
[t, y] = ode45(dydt,tSpan,init);
for i=1:size(t,1)
out(i,:) = C(y(i,3),y(i,9)+y(i,3),y(i,15)+y(i,3))*y(i,:)';
u(i,:) = finput(t(i))';
d1(i,1) = hypot(out(i,7)-out(i,1),out(i,8)-out(i,2));
d2(i,1) = hypot(out(i,13)-out(i,1),out(i,14)-out(i,2));
endfor
close all
figure(1)
plot(out(:,1), out(:,2), out(:,7), out(:,8), out(:,13), out(:,14));
figure(2)
plot(t(:,1), d1(:,1), t(:,1), d2(:,1));
figure(3)
plot(t(:,1), u(:,1), t(:,1), u(:,2), t(:,1), u(:,3));
% figure(4)
% plot(t(:,1), u(:,4), t(:,1), u(:,5),t(:,1), u(:,6));
% figure(5)
% plot(t(:,1), u(:,7), t(:,1), u(:,8),t(:,1), u(:,9));

180
SOURCE/omnidirectional.m Normal file
View File

@ -0,0 +1,180 @@
## Omnidirectional Modeling API of Octave by Adnr
function obj = omnidirectional(
%% viscous friction coefficient related to v
%B v (N/m/s)
cBv%0.94
%% viscous friction coefficient related to v n
%B vn (N/m/s)
, cBvn%0.96
%% viscous friction coefficient related to ω
%B ω (N/rad/s)
, cBw%0.01
%% coulomb friction coefficient related to v
%C v (N )
, cCv%2.2
%% coulomb friction coefficient related to v n
%C vn (N )
, cCvn%1.5
%% coulomb friction coefficient related to ω
%C ω (N.m)
, cCw%0.099
%% radius of the robot
%b(m)
, cb%0.1
%% mass of the robot
%M (kg)
, cM%1.5
%% inertia moment of the robot
%I n (kg.m 2 )
, cIn%0.025
%% angle
, cdlt%30
%% radius of the wheels
%r 1 , r 2 , r 3 (m)
, cri%0.035
%% reduction of the motors
%l 1 , l 2 , l 3
, cli%19
%% motors armature inductance
%L a 1...3 (H)
, cLi%0.00011
%% motors armature resistance
%R a 1...3 (Ω)
, cRai%1.69
%% motors emf constant
%K v 1...3 (V olts/rad/s)
, cKv%0.0059
%% motors torque constant
%K t 1...3 (N.m/A)
, cKt%0.0059
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Criterion of canonical second-orde system
, zeta
, omega
%% Input constrain
, InCon
, path_file
)
pkg load control
obj = struct();
%%%%%%% Origin builder
obj.origin = struct();
obj.origin.A = [-((3*(cli^2)*(cKt^2))/(2*cM*cRai*(cri^2)))-(cBv/cM),0,0;
0, -((3*(cli^2)*(cKt^2))/(2*cM*cRai*(cri^2)))-(cBvn/cM),0;
0,0,-((3*(cb^2)*(cli^2)*(cKt^2))/(2*cIn*cRai*(cri^2)))-(cBw/cIn)];
obj.origin.B = [0, (cos(cdlt*pi/180)/cM), -(cos(cdlt*pi/180)/cM);
-1/cM, sin(cdlt*pi/180)/cM, sin(cdlt*pi/180)/cM;
cb/cIn, cb/cIn, cb/cIn];
obj.origin.K = [-cCv/cM, 0,0;
0, -cCvn/cM, 0;
0,0,-cCw/cM];
obj.LENGTH_STATE = size(obj.origin.A,1);
obj.LENGTH_INTPUT = size(obj.origin.B,1);
Q = [500 0 0; 0 500 0; 0 0 5;]
R = eye(3)*0.3;
kst_ = lqr(obj.origin.A,obj.origin.B,Q,R);
nst_ = -pinv(eye(size(obj.origin.A))*inv(obj.origin.A-obj.origin.B*kst_)*obj.origin.B);
syscl = ss(obj.origin.A-obj.origin.B*kst_, obj.origin.B*nst_, eye(3),0);
% step(syscl);
obj.origin.Kst = kst_;
obj.origin.Nst = nst_;
obj.origin.syscl = syscl
%%%%%%%
A = obj.origin.A;
B = obj.origin.B;
K = obj.origin.K;
obj.LENGTH_STATE = size(A,1)+3;
obj.LENGTH_INPUT = size(B,1);
obj.A = [zeros(size(A)),eye(size(A));zeros(size(A)),A;];
obj.B = [zeros(size(B));B;];
obj.K = [zeros(size(B,2),size(B,2));K];
obj.getState = @(o) zeros(size(A,1)+3,1);
obj.getInput = @(o) zeros(size(B,2),1);
obj.InCon = ones(obj.LENGTH_INPUT)*InCon;
%%%%%%%%% Make Controller
obj.controllabilityTest = @(a,b) rank(ctrb(a,b));
obj.observabilityTest = @(a,c) rank(obsv(a,c));
s = tf('s');
obj.Gref = omega^2/(s^2+(2*zeta*omega)*s+omega^2);
p = pole(obj.Gref);
Kst = zeros(3,6);
Nst = zeros(3,6);
Q = {
[ 100 0; 0 10;], %x
[ 100 0; 0 10;], %y
[2000 0; 0 10;] %theta
};
R = eye(3)*1;
for i = [1:3]
A_ = [0 1;
0 A(i,i)];
B_ = [0 0 0;
B(i,1) B(i,2) B(i,3)];
kst_ = lqr(A_,B_,Q{i},R);
nst_ = -pinv(eye(size(A_))*inv(A_-B_*kst_)*B_);
% syscl = ss(A_-B_*kst_, B_*nst_, eye(2),0); % uncomment for debugging
% step(syscl);
j = ((i-1)*2);
Kst(:,1+j:2+j) = kst_;
Nst(:,1+j:2+j) = nst_;
endfor
obj.Kst = [Kst(:,1) Kst(:,3) Kst(:,5) Kst(:,2) Kst(:,4) Kst(:,6)];
obj.Nst = [Nst(:,1) Nst(:,3) Nst(:,5) Nst(:,2) Nst(:,4) Nst(:,6)];
obj.syscl = ss(obj.A-obj.B*obj.Kst,obj.B*obj.Nst,eye(size(obj.A)),[0]);
%%%%%%%%% Generate discrete state space function
% sgn function, in octave comparison (x compare value) return integer
% result of comparison used to address to value in matrix
obj.sgn = @(x) [0,1,-1](4-(1*(x<0))-(2*(x>0))-(3*(x==0)));
obj.origin.sgn = obj.sgn;
obj.limit_motor = @(x) [x,6,-6](4-(1*(x<-6))-(2*(x>6))-(3*(x<6 & x>-6)));
obj.origin.limit_motor = obj.limit_motor;
% Kinematic function for coordinate robot to global
obj.rotationOrtogonal = @(the) [cos(the) sin(the) 0; -sin(the) cos(the) 0; 0 0 1];
% https://en.wikibooks.org/wiki/Control_Systems/State-Space_Equations#Discretization
% x[k+1] = (1 + AT)x[k] + TBu[k] + TKsgn(x[k])
% Not using function from control package becouse the system have K term
obj.Aterm = @(o,T,st) (eye(o.LENGTH_STATE,o.LENGTH_STATE)+(o.A*T))*st;
obj.Bterm = @(o,T,st,in) (T*o.B)*in;
obj.Kterm = @(o,T,st,in) ((T*o.K)*[o.sgn(st(4));o.sgn(st(5));o.sgn(st(6))]);
% Original state space robot
obj.disDotState = @(o,T,st,in) o.Aterm(o,T,st)+o.Bterm(o,T,st,in)+o.Kterm(o,T,st,in);
obj.Uterm = @(o,st,ref) (o.Nst*ref - o.Kst*st);
obj.Cons = @(u) [u,InCon,-InCon](1+(2*(u<-InCon)+(1*(u>InCon))));
obj.UCons = @(o,u) [o.Cons(u(1)); o.Cons(u(2)); o.Cons(u(3))];
obj.UIn = @(o,st,ref) o.UCons(o,o.Uterm(o,st,ref));
% State space included controller
obj.disDotStateCl = @(o,T,st,ref) o.disDotState(o,T,st,o.UCons(o,o.Uterm(o,st,ref)));
obj.Y = @(o,st) [o.rotationOrtogonal(st(3))', zeros(size(A))]*st;
% Time eq
obj.disTime = @(T,ti) (ti + abs(T));
obj.testStabilityExplicit = @(h) abs(eye(size(A))+(h*(A+K)));
obj.testStabilityImplicit = @(h) abs(eye(size(A))-(h*(A+K)));
%%%%%%%%% PRINT the matrix to file used matrix in python app
csvwrite(strcat(path_file,'A.matrix'),obj.A);
csvwrite(strcat(path_file,'B.matrix'),obj.B);
csvwrite(strcat(path_file,'C.matrix'),[eye(size(A)), zeros(size(A))]);
csvwrite(strcat(path_file,'K.matrix'),obj.K);
csvwrite(strcat(path_file,'Kst.matrix'),obj.Kst);
csvwrite(strcat(path_file,'Nst.matrix'),obj.Nst);
[y,t] = step(obj.Gref);
csvwrite(strcat(path_file,'Gref.csv'),[y,t]);
csvwrite(strcat(path_file,'poleGref.csv'),pole(obj.Gref));
endfunction

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@ -12,8 +12,9 @@ function [R,K, d] = rigidityMatrixFnc (edgeL,stateLen)
printf("Jumlah Robot : %i \n", tmp); printf("Jumlah Robot : %i \n", tmp);
% generasi vector error menggunakan matrix % generasi vector error menggunakan matrix
% koneksi % koneksi
tmp = getNodes(gInc,'adjacency'); % tmp = getNodes(gInc,'adjacency');
K = kron(adj2inc(edgeL2adj(edgeL))',eye(stateLen)); K = kron(adj2inc(edgeL2adj(edgeL))',eye(stateLen));
tmp = 1:(size(K,1)/stateLen);
edgeVector = @(x,k) k*x; edgeVector = @(x,k) k*x;
% hasil turunan dari fungsi edge % hasil turunan dari fungsi edge
str = "errBlockDiagonal = @(errVec) (blkdiag("; str = "errBlockDiagonal = @(errVec) (blkdiag(";

26
SOURCE/sgn.m Normal file
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@ -0,0 +1,26 @@
#Friction multiplied
function xo = sgn( x=[x1; x2; x3])
xo = [0;0;0;];
if x(1) > 0 ;
xo(1) = 1;
elseif x(1) < 0;
xo(1) = -1;
else;
%% xo(1) = x(1);
endif;
if x(2) > 0 ;
xo(2) = 1;
elseif x(2) < 0;
xo(2) = -1;
else;
%% xo(2) = x(2);
endif;
if x(3) > 0 ;
xo(3) = 1;
elseif x(3) < 0;
xo(3) = -1;
else;
%% xo(3) = x(3);
endif;
endfunction