+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} +
\begin{bmatrix}
0 \\ k_{p2}R(x_1)^T \\ 0 \\ -k_{i2}
\end{bmatrix} d
\end{bmatrix} d \label{orde_dua_ss}
\end{align}
\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
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}
Implementasi berhasil. Penelitian mengalami kekurangan apabila vref diberikan
pada robot yang berpotensi menghasilkan lipatan pada graph.

View File

@ -1,5 +1,7 @@
clear -all
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
conRobot = [1 2 1;
3 2 1;
@ -14,22 +16,25 @@ corRobot = [1.5; 1.7;0;
2; 2.5;0;
2.5; 2.8;0;
]; % xy xy xy
robStateLen = length(corRobot)/length(dRobot)
robStateLen = size(omni.origin.A,1);
B = [
1 0; 0 1;
0 0; 0 0;
0 0; 0 0;
];
kp = 80;
ki = 1;
kp = 150;
ki = 3;
% fvref = fncSpeedRef('ysin',50,2,robStateLen);
% fvref = fncSpeedRef('xsin',50,2,robStateLen);
% fvref = fncSpeedRef('cw',-300,1,robStateLen);
% fvref = fncSpeedRef('s',50,50,robStateLen);
fvref = fncSpeedRef('s',0,0,robStateLen);
h = .1;
h = .01;
tspan = 1:h:10;
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
[R,K,d] = rigidityMatrixFnc(conRobot,robStateLen);
@ -37,16 +42,34 @@ _zero = zeros(size(R(corRobot,K),1),1);
sInit = [corRobot; _zero;];
sAnsInit =[_zero; _zero;];
s2ndInit = [corRobot; %x1
zeros(length(corRobot),1); %x2
zeros(length(corRobot),1); %xi1
_zero]; %xi2
zeros(length(corRobot),1); %x2
zeros(length(corRobot),1); %xi1
_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
printf("Mulai memecakan masalah \n\n");
startExe = tic;
dydt = @(t, y) sys.ss(y,fvref(t));
[t,y] = ode45(dydt, tspan, s2ndInit);
% continue
% 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);
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)
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])
% save DataOutMotion.data y
% 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));
endif
elseif (param == 's')
strSfx = strcat(sprintf("%i",r));
strSfy = strcat(sprintf("%i",v));
elseif (param(1) == 's')
strSinOcos = strcat(sprintf("%s", param(3:end)));
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
printf("Karepmu opo ? \n\n bukak fungsi speedRef sek diwoco komen e \n\n");
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 = [kron(obj.Kb,eye(robStateLen)); zeros(obj.m,robStateLen)];
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;
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);

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

View File

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

26
SOURCE/sgn.m Normal file
View File

@ -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