4.8
0
False
C:\users\wouter\My Documents\studie\ma\mahd\implementation\SCARA\04_path_planning\path_planning.emx
2020-7-21 13:21:44
True
parameters
real A = 0.05 {m};
real B = 0.05 {m};
variables
real J0_1_BF1[2];
real J1_2_BF1[2];
real J1_2_BF2[2];
real EE1_BF2[2];
initialequations
J0_1_BF1 = [A/2;0];
J1_2_BF1 = [-A/2;0];
J1_2_BF2 = [B/2;0];
EE1_BF2 = [-B/2;0];
';
type Mainmodel
end;
implementation bg
submodels
C1 640 264
description '4.01False
Bond Graph\3D\C-3.emx
2007-9-25 12:12:8
';
type 'C-3'
ports
power in p [3,1];
signal out state [3,1];
restrictions
causality preferred out p;
end;
icon bg bottom
figures
text 'C' 640 264 color 0 18 bold;
end;
implementation eq
parameters
real c[3,3] = [0.1, 0.0, 0.0; 0.0, 0.1, 0.0; 0.0, 0.0, 0.1] {mN/m};
equations
state = int(p.f);
p.e = inverse(c) *state;
implementation_end;
C2 304 272
description '4.01False
Bond Graph\3D\C-3.emx
2007-9-25 12:12:8
';
type 'C-3'
ports
power in p [3,1];
signal out state [3,1];
restrictions
causality preferred out p;
end;
icon bg bottom
figures
text 'C' 304 272 color 0 18 bold;
end;
implementation eq
parameters
real c[3,3] = [0.1, 0.0, 0.0; 0.0, 0.1, 0.0; 0.0, 0.0, 0.1] {mN/m};
equations
state = int(p.f);
p.e = inverse(c) *state;
implementation_end;
C3 304 224
description '4.01False
Bond Graph\2D\C-2.emx
2007-9-25 12:7:27
';
type 'C-2'
ports
power in p [2,1];
signal out state [2,1];
restrictions
causality preferred out p;
end;
icon bg bottom
figures
text 'C' 304 224 color 0 18 bold;
end;
implementation eq
parameters
real c[2,2] = [0.1, 0.0; 0.0, 0.1] {mN.m/rad};
equations
state = int(p.f);
p.e = inverse(c) *state;
implementation_end;
C4 640 216
description '4.01False
Bond Graph\2D\C-2.emx
2007-9-25 12:7:27
';
type 'C-2'
ports
power in p [2,1];
signal out state [2,1];
restrictions
causality preferred out p;
end;
icon bg bottom
figures
text 'C' 640 216 color 0 18 bold;
end;
implementation eq
parameters
real c[2,2] = [0.1, 0.0; 0.0, 0.1] {mN.m/rad};
equations
state = int(p.f);
p.e = inverse(c) *state;
implementation_end;
COM 376 208
description '4.81Bond Graph\MR\center_of_mass_v2.emx2020-7-21 12:24:38parameters
real I [3,1] = [1.6399999999999998e-6; 4.7e-8; 1.61e-6] {N.m.s};
real m = 0.00455 {kg};';
type Submodel
ports
signal in Hin [4,4];
signal out Hout [4,4];
power out p [6,1];
end;
icon bg bottom
figures
rectangle 344 192 408 224 color 0 fill 139;
text 'COM' 376 208 color 0 'Clear Sans' 16;
terminals
Hin 392 192 fixed;
p 360 192 fixed;
end;
implementation bg
submodels
AdHi0 544 400
description '4.01False2007-9-25 12:3:3True';
type MTF
ports
power in p1 [6,1];
power out p2 [6,1];
signal in H [4,4];
restrictions
causality constraint not_equal p1 p2;
end;
icon bg left
figures
text 'MTF' 544 400 color 0 18 bold;
end;
implementation eq
variables
real onlyRotH[4,4];
code
//Only rotations with respect to the inertial system matter!
onlyRotH = H;
onlyRotH[1,4] = 0;
onlyRotH[2,4] = 0;
onlyRotH[3,4] = 0;
p2.e = transpose(Adjoint(onlyRotH)) * p1.e;
p1.f = Adjoint(onlyRotH) * p2.f;
implementation_end;
EJS 616 336
description '4.01False2007-10-31 11:43:6True';
type MGY
ports
power in p1 [6,1];
end;
icon bg top
figures
text 'MGY' 616 336 color 0 18 bold;
end;
implementation eq
//EJS / Gyroscopic effects
parameters
real global I[3];
real global m;
variables
real II[6,6]; //Inertial tensor
real Q[6,6];
real QI[6,6];
real Ia[6];
initialequations
Ia[1:3] = I;
Ia[4:6] = m;
II = diag(Ia);
equations
Q = transpose(adjoint(p1.f));
QI = Q*II;
p1.e = QI*p1.f;implementation_end;
Gravity 624 400
description '4.01False2007-9-25 12:3:26True';
type Se
ports
power out p [6,1];
restrictions
causality fixed out p;
end;
icon bg bottom
figures
text 'Se' 624 400 color 0 18 bold;
end;
implementation eq
parameters
real global m;
variables
real effort[6];
equations
effort = [0;0;0;0;0;-g_n*m];
p.e = effort;
implementation_end;
InertialTensor 544 272
description '4.01False
Bond Graph\3D\I-3.emx
2007-9-25 12:12:14
';
type 'I-3'
ports
power in p [6,1];
signal out state [6,1];
restrictions
causality preferred in p;
end;
icon bg bottom
figures
text 'I' 544 272 color 0 18 bold;
end;
implementation eq
parameters
real global I[3];
real global m;
variables
real II[6,6]; //Inertial tensor
real Ia[6];
initialequations
Ia[1:3] = I;
Ia[4:6] = m;
II = diag(Ia);
equations
state = int(p.e); //state = generalized momentum
p.f = inverse(II)*state;
implementation_end;
plug Hin 433.4 496;
plug Hout 691.2 496;
plug p 439.4 336;
Splitter1 544 496
description '4.0
Signal\Block Diagram\Splitter.emx
2008-01-17 11:28:29
1
False
';
knot Splitter
ports
signal knot duplicatable out output [4,4];
signal knot in input [4,4];
end;
icon bg ellipse
figures
ellipse 540.8 492.8 547.2 499.2 color -1 fill 0;
ellipse 539.7 491.7 548.3 500.3 color -1;
terminals
input 544 496 fixed;
end;
implementation eq
equations
collect (output) = input;
implementation_end;
Ta0j 544 336
description '
4.0
1
False
Bond Graph\OneJunction.emx
2007-9-27 9:51:18
True
';
knot OneJunction
ports
power knot duplicatable none p [6,1];
signal knot out flow [6,1];
restrictions
causality constraint one_out p;
end;
icon bg bottom
figures
text '1' 544 336 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
ZeroJunction1 504 336
description '
4.2
1
False
Bond Graph\ZeroJunction.emx
2011-11-29 16:45:16
';
knot ZeroJunction
ports
power knot duplicatable none p [6,1];
signal knot out effort [6,1];
restrictions
causality constraint one_in p;
end;
icon bg
figures
text '0' 504 336 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.f)) = 0;
equal (collect (p.e));
effort = first (p.e);
implementation_end;
end;
connections
AdHi0\p2 => Ta0j\p;
Gravity\p => AdHi0\p1;
Hin -> Splitter1\input;
Splitter1\output -> AdHi0\H;
Splitter1\output -> Hout;
Ta0j\p => EJS\p1;
Ta0j\p => InertialTensor\p;
ZeroJunction1\p => p;
ZeroJunction1\p => Ta0j\p;
end;
implementation_end;
COM1 720 200
description '4.81Bond Graph\MR\center_of_mass_v2.emx2020-7-21 12:24:38parameters
real I [3,1] = [7.583333333333335e-7; 3.645833333333334e-8; 7.364583333333335e-7] {N.m.s};
real m = 0.0035 {kg};';
type Submodel
ports
signal in Hin [4,4];
signal out Hout [4,4];
power out p [6,1];
end;
icon bg bottom
figures
rectangle 688 184 752 216 color 0 fill 139;
text 'COM' 720 200 color 0 'Clear Sans' 16;
terminals
Hin 736 184 fixed;
p 704 184 fixed;
end;
implementation bg
submodels
AdHi0 544 400
description '4.01False2007-9-25 12:3:3True';
type MTF
ports
power in p1 [6,1];
power out p2 [6,1];
signal in H [4,4];
restrictions
causality constraint not_equal p1 p2;
end;
icon bg left
figures
text 'MTF' 544 400 color 0 18 bold;
end;
implementation eq
variables
real onlyRotH[4,4];
code
//Only rotations with respect to the inertial system matter!
onlyRotH = H;
onlyRotH[1,4] = 0;
onlyRotH[2,4] = 0;
onlyRotH[3,4] = 0;
p2.e = transpose(Adjoint(onlyRotH)) * p1.e;
p1.f = Adjoint(onlyRotH) * p2.f;
implementation_end;
EJS 616 336
description '4.01False2007-10-31 11:43:6True';
type MGY
ports
power in p1 [6,1];
end;
icon bg top
figures
text 'MGY' 616 336 color 0 18 bold;
end;
implementation eq
//EJS / Gyroscopic effects
parameters
real global I[3];
real global m;
variables
real II[6,6]; //Inertial tensor
real Q[6,6];
real QI[6,6];
real Ia[6];
initialequations
Ia[1:3] = I;
Ia[4:6] = m;
II = diag(Ia);
equations
Q = transpose(adjoint(p1.f));
QI = Q*II;
p1.e = QI*p1.f;implementation_end;
Gravity 624 400
description '4.01False2007-9-25 12:3:26True';
type Se
ports
power out p [6,1];
restrictions
causality fixed out p;
end;
icon bg bottom
figures
text 'Se' 624 400 color 0 18 bold;
end;
implementation eq
parameters
real global m;
variables
real effort[6];
equations
effort = [0;0;0;0;0;-g_n*m];
p.e = effort;
implementation_end;
InertialTensor 544 272
description '4.01False
Bond Graph\3D\I-3.emx
2007-9-25 12:12:14
';
type 'I-3'
ports
power in p [6,1];
signal out state [6,1];
restrictions
causality preferred in p;
end;
icon bg bottom
figures
text 'I' 544 272 color 0 18 bold;
end;
implementation eq
parameters
real global I[3];
real global m;
variables
real II[6,6]; //Inertial tensor
real Ia[6];
initialequations
Ia[1:3] = I;
Ia[4:6] = m;
II = diag(Ia);
equations
state = int(p.e); //state = generalized momentum
p.f = inverse(II)*state;
implementation_end;
plug Hin 433.4 496;
plug Hout 691.2 496;
plug p 439.4 336;
Splitter1 544 496
description '4.0
Signal\Block Diagram\Splitter.emx
2008-01-17 11:28:29
1
False
';
knot Splitter
ports
signal knot duplicatable out output [4,4];
signal knot in input [4,4];
end;
icon bg ellipse
figures
ellipse 540.8 492.8 547.2 499.2 color -1 fill 0;
ellipse 539.7 491.7 548.3 500.3 color -1;
terminals
input 544 496 fixed;
end;
implementation eq
equations
collect (output) = input;
implementation_end;
Ta0j 544 336
description '
4.0
1
False
Bond Graph\OneJunction.emx
2007-9-27 9:51:18
True
';
knot OneJunction
ports
power knot duplicatable none p [6,1];
signal knot out flow [6,1];
restrictions
causality constraint one_out p;
end;
icon bg bottom
figures
text '1' 544 336 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
ZeroJunction1 504 336
description '
4.2
1
False
Bond Graph\ZeroJunction.emx
2011-11-29 16:45:16
';
knot ZeroJunction
ports
power knot duplicatable none p [6,1];
signal knot out effort [6,1];
restrictions
causality constraint one_in p;
end;
icon bg
figures
text '0' 504 336 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.f)) = 0;
equal (collect (p.e));
effort = first (p.e);
implementation_end;
end;
connections
AdHi0\p2 => Ta0j\p;
Gravity\p => AdHi0\p1;
Hin -> Splitter1\input;
Splitter1\output -> AdHi0\H;
Splitter1\output -> Hout;
Ta0j\p => EJS\p1;
Ta0j\p => InertialTensor\p;
ZeroJunction1\p => p;
ZeroJunction1\p => Ta0j\p;
end;
implementation_end;
COM2 904 184
description '4.81Bond Graph\MR\center_of_mass_v2.emx2020-7-21 12:24:38parameters
real I [3,1] = [0.018;0.159;0.159] {mN.m.s};
real m = 0.015 {kg};';
type Submodel
ports
signal in Hin [4,4];
signal out Hout [4,4];
power out p [6,1];
end;
icon bg bottom
figures
rectangle 872 168 936 200 color 0 fill 139;
text 'COM' 904 184 color 0 'Clear Sans' 16;
terminals
Hin 920 168 fixed;
p 888 168 fixed;
end;
implementation bg
submodels
AdHi0 544 400
description '4.01False2007-9-25 12:3:3True';
type MTF
ports
power in p1 [6,1];
power out p2 [6,1];
signal in H [4,4];
restrictions
causality constraint not_equal p1 p2;
end;
icon bg left
figures
text 'MTF' 544 400 color 0 18 bold;
end;
implementation eq
variables
real onlyRotH[4,4];
code
//Only rotations with respect to the inertial system matter!
onlyRotH = H;
onlyRotH[1,4] = 0;
onlyRotH[2,4] = 0;
onlyRotH[3,4] = 0;
p2.e = transpose(Adjoint(onlyRotH)) * p1.e;
p1.f = Adjoint(onlyRotH) * p2.f;
implementation_end;
EJS 616 336
description '4.01False2007-10-31 11:43:6True';
type MGY
ports
power in p1 [6,1];
end;
icon bg top
figures
text 'MGY' 616 336 color 0 18 bold;
end;
implementation eq
//EJS / Gyroscopic effects
parameters
real global I[3];
real global m;
variables
real II[6,6]; //Inertial tensor
real Q[6,6];
real QI[6,6];
real Ia[6];
initialequations
Ia[1:3] = I;
Ia[4:6] = m;
II = diag(Ia);
equations
Q = transpose(adjoint(p1.f));
QI = Q*II;
p1.e = QI*p1.f;implementation_end;
Gravity 624 400
description '4.01False2007-9-25 12:3:26True';
type Se
ports
power out p [6,1];
restrictions
causality fixed out p;
end;
icon bg bottom
figures
text 'Se' 624 400 color 0 18 bold;
end;
implementation eq
parameters
real global m;
variables
real effort[6];
equations
effort = [0;0;0;0;0;-g_n*m];
p.e = effort;
implementation_end;
InertialTensor 544 272
description '4.01False
Bond Graph\3D\I-3.emx
2007-9-25 12:12:14
';
type 'I-3'
ports
power in p [6,1];
signal out state [6,1];
restrictions
causality preferred in p;
end;
icon bg bottom
figures
text 'I' 544 272 color 0 18 bold;
end;
implementation eq
parameters
real global I[3];
real global m;
variables
real II[6,6]; //Inertial tensor
real Ia[6];
initialequations
Ia[1:3] = I;
Ia[4:6] = m;
II = diag(Ia);
equations
state = int(p.e); //state = generalized momentum
p.f = inverse(II)*state;
implementation_end;
plug Hin 433.4 496;
plug Hout 691.2 496;
plug p 424 336;
Splitter1 544 496
description '4.0
Signal\Block Diagram\Splitter.emx
2008-01-17 11:28:29
1
False
';
knot Splitter
ports
signal knot duplicatable out output [4,4];
signal knot in input [4,4];
end;
icon bg ellipse
figures
ellipse 540.8 492.8 547.2 499.2 color -1 fill 0;
ellipse 539.7 491.7 548.3 500.3 color -1;
terminals
input 544 496 fixed;
end;
implementation eq
equations
collect (output) = input;
implementation_end;
Ta0j 544 336
description '
4.0
1
False
Bond Graph\OneJunction.emx
2007-9-27 9:51:18
True
';
knot OneJunction
ports
power knot duplicatable none p [6,1];
signal knot out flow [6,1];
restrictions
causality constraint one_out p;
end;
icon bg bottom
figures
text '1' 544 336 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
ZeroJunction1 480 336
description '
4.2
1
False
Bond Graph\ZeroJunction.emx
2011-11-29 16:45:16
';
knot ZeroJunction
ports
power knot duplicatable none p [6,1];
signal knot out effort [6,1];
restrictions
causality constraint one_in p;
end;
icon bg
figures
text '0' 480 336 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.f)) = 0;
equal (collect (p.e));
effort = first (p.e);
implementation_end;
end;
connections
AdHi0\p2 => Ta0j\p;
Gravity\p => AdHi0\p1;
Hin -> Splitter1\input;
Splitter1\output -> AdHi0\H;
Splitter1\output -> Hout;
Ta0j\p => EJS\p1;
Ta0j\p => InertialTensor\p;
ZeroJunction1\p => p;
ZeroJunction1\p => Ta0j\p;
end;
implementation_end;
Integrate 184 288
description '
4.3
1
False
Signal\Block Diagram\Integrate.emx
2013-3-8 14:47:42
';
type Integrate
ports
signal in input;
signal out output;
end;
icon bg bottom
figures
rectangle 168 272 200 304 color 0 fill 15132390;
text '∫' 184 288.3 color 16711680 'Lucida Sans' 21 italic;
end;
implementation eq
parameters
real initial = 0; // initial value
equations
output = int (input, initial);
implementation_end;
Integrate1 520 360
description '
4.3
1
False
Signal\Block Diagram\Integrate.emx
2013-3-8 14:47:42
';
type Integrate
ports
signal in input;
signal out output;
end;
icon bg bottom
figures
rectangle 504 344 536 376 color 0 fill 15132390;
text '∫' 520 360.3 color 16711680 'Lucida Sans' 21 italic;
end;
implementation eq
parameters
real initial = 0; // initial value
equations
output = int (input, initial);
implementation_end;
inverse_kinematics1 272 552
description '
4.8
SCARA\inverse_kinematics_v1.emx
1
False
2020-7-10 12:26:18
False
';
type 'Submodel-Equation'
ports
signal in input [2,1] {m} ;
signal out angle1 {rad} ;
signal out angle2 {rad} ;
signal out a {rad} ;
signal out b {rad} ;
signal out c {rad} ;
signal out phi {rad} ;
signal out abs_angle2;
end;
implementation eq
parameters
real A_length = 0.065 {m}; // length of first arm
real B_length = 0.05 {m}; // length of second arm
real to_rad = 1 {rad};
variables
real x {m}, y {m};
real C_length {m}; // length to x and y.
equations
x = input[1];
y = input[2];
phi = atan2(y, x);
C_length = sqrt(x^2 + y^2);
a = arccos ((B_length^2 + C_length^2 - A_length^2) / (2 * B_length * C_length));
b = arccos ((A_length^2 + C_length^2 - B_length^2) / (2 * A_length * C_length));
c = arccos ((A_length^2 + B_length^2 - C_length^2) / (2 * A_length * B_length));
angle1 = b + phi;
abs_angle2 = angle1 - pi * to_rad + c;
angle2 = c - pi * to_rad;
implementation_end;
Joint 192 120
description '
4.8
1
Bond Graph\MR\joint-v3.emx
2020-7-21 12:08:53
';
type 'Submodel-v3'
ports
power in Pin [6,1];
power in Pdiff [6,1];
signal in Hin [4,4];
signal out Hout [4,4];
signal out Hdiff [4,4];
power out Pout [6,1];
end;
icon bg bottom
figures
rectangle 168 88 216 152 color 0 fill 14745599;
text 'Joint' 192 120 color 0 'Clear Sans' 16;
terminals
Pin 216 104 fixed;
Hin 168 136 fixed;
Hout 216 136 fixed;
Pout 168 104 fixed;
end;
implementation bg
submodels
AdHji 424 424
description '
4.0
1
False
Bond Graph\MTF.emx
2007-9-25 12:3:3
True
';
type MTF
ports
power out p1 [6,1];
power in p2 [6,1];
signal in H [4,4];
restrictions
causality constraint not_equal p1 p2;
end;
icon bg bottom
figures
text 'MTF' 424 424 color 0 18 bold;
end;
implementation eq
equations
p2.e = transpose(Adjoint(H)) * p1.e;
p1.f = Adjoint(H) * p2.f;implementation_end;
FlowSensor2 184 311.9
description '
4.2
1
False
Bond Graph\FlowSensor.emx
2011-11-29 15:50:53
';
knot FlowSensor
ports
power knot in p1 [6,1];
power knot out p2 [6,1];
signal knot out flow [6,1];
restrictions
causality constraint not_equal p1 p2;
end;
icon bg ellipse
figures
ellipse 177.1 304.8 190.9 319.1 color 0 fill 16777215;
text 'f' 184 311.2 color 0;
end;
implementation eq
equations
p2.f = p1.f;
p1.e = p2.e;
flow = p1.f;
implementation_end;
Hmatrix 256 312
description '4.0Template\Submodel-Equation.emx1False2007-11-1 22:32:1False';
type 'Submodel-Equation'
ports
signal in flow [6,1];
signal out H [4,4];
end;
icon bg
figures
rectangle 224 296 288 328 color 0 fill 15132390;
text 'name' 256 312 color 0 'Clear Sans' 16;
end;
implementation eq
parameters
real init[4] = [1;0;0;0];
variables
real q[4]; //quaternions
real W[3,4]; //Quaternion Rates Matrix
real R[3,3]; //Rotation Matrix
real p[3]; //Position Vector
real dq[4];
real Wb[3,4];
equations
dq = transpose(Wb) * flow[1:3] ./ 2;
q = int(dq,init);
p = int(flow[4:6]);
W = [-q[2], q[1], -q[4], q[3];
-q[3], q[4], q[1], -q[2];
-q[4], -q[3], q[2], q[1]];
Wb = [ -q[2], q[1], q[4], -q[3];
-q[3], -q[4], q[1], q[2];
-q[4], q[3], -q[2], q[1]];
R = [q[1]^2+q[2]^2-q[3]^2-q[4]^2, 2*(q[2]*q[3]+q[1]*q[4]), 2*(q[2]*q[4]-q[1]*q[3]);
2*(q[2]*q[3]-q[1]*q[4]), q[1]^2-q[2]^2+q[3]^2-q[4]^2, 2*(q[3]*q[4]+q[1]*q[2]);
2*(q[2]*q[4]+q[1]*q[3]), 2*(q[3]*q[4]-q[1]*q[2]), q[1]^2-q[2]^2-q[3]^2+q[4]^2];
H = homogeneous(R,p);
implementation_end;
MatrixMul 320 576
description '
4.0
1
False
Signal\Block Diagram\Gain.emx
2007-9-26 12:15:12
True
';
type Gain
ports
signal in input1 [4,4];
signal out output [4,4];
signal in input2 [4,4];
end;
icon bg bottom
figures
rectangle 304.1 560 335.9 592 color 0 fill 15132390;
text 'X' 320 576 color 16711680 16 bold;
end;
implementation eq
equations
output = input2*input1; implementation_end;
plug Pin 492.1 424;
plug Pdiff 184 225;
plug Hin 130.8 576;
plug Hout 478.4 576;
plug Hdiff 320 222;
plug Pout 134.7 424;
Splitter2 320 312
description '4.0
Signal\Block Diagram\Splitter.emx
2008-01-17 11:28:29
1
False
';
knot Splitter
ports
signal knot duplicatable out output [4,4];
signal knot in input [4,4];
end;
icon bg ellipse
figures
ellipse 316.8 308.8 323.2 315.2 color -1 fill 0;
ellipse 315.7 307.7 324.3 316.3 color -1;
terminals
input 320 312 fixed;
end;
implementation eq
equations
collect (output) = input;
implementation_end;
Wbai 184 424
description '
4.0
1
False
Bond Graph\ZeroJunction.emx
2007-9-27 9:51:43
True
';
knot ZeroJunction
ports
power knot duplicatable none p [6,1];
signal knot out effort [6,1];
restrictions
causality constraint one_in p;
end;
icon bg bottom
figures
text '0' 184 424 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.f)) = 0;
equal (collect (p.e));
effort = first (p.e);
implementation_end;
end;
connections
FlowSensor2\flow -> Hmatrix\flow;
FlowSensor2\p2 => Wbai\p;
Hin -> MatrixMul\input2;
Hmatrix\H -> Splitter2\input;
MatrixMul\output -> Hout;
Pdiff => FlowSensor2\p1;
Pin => AdHji\p2;
Splitter2\output -> AdHji\H 424 312;
Splitter2\output -> Hdiff;
Splitter2\output -> MatrixMul\input1;
Wbai\p <= AdHji\p1;
Wbai\p => Pout;
end;
implementation_end;
Joint1 536 120
description '
4.8
1
Bond Graph\MR\joint-v3.emx
2020-7-21 12:08:53
';
type 'Submodel-v3'
ports
power in Pin [6,1];
power in Pdiff [6,1];
signal in Hin [4,4];
signal out Hout [4,4];
signal out Hdiff [4,4];
power out Pout [6,1];
end;
icon bg bottom
figures
rectangle 512 88 560 152 color 0 fill 14745599;
text 'Joint' 536 120 color 0 'Clear Sans' 16;
terminals
Pin 560 104 fixed;
Hin 512 136 fixed;
Hout 560 136 fixed;
Pout 512 104 fixed;
end;
implementation bg
submodels
AdHji 424 424
description '
4.0
1
False
Bond Graph\MTF.emx
2007-9-25 12:3:3
True
';
type MTF
ports
power out p1 [6,1];
power in p2 [6,1];
signal in H [4,4];
restrictions
causality constraint not_equal p1 p2;
end;
icon bg bottom
figures
text 'MTF' 424 424 color 0 18 bold;
end;
implementation eq
equations
p2.e = transpose(Adjoint(H)) * p1.e;
p1.f = Adjoint(H) * p2.f;implementation_end;
FlowSensor2 184 311.9
description '
4.2
1
False
Bond Graph\FlowSensor.emx
2011-11-29 15:50:53
';
knot FlowSensor
ports
power knot in p1 [6,1];
power knot out p2 [6,1];
signal knot out flow [6,1];
restrictions
causality constraint not_equal p1 p2;
end;
icon bg ellipse
figures
ellipse 177.1 304.8 190.9 319.1 color 0 fill 16777215;
text 'f' 184 311.2 color 0;
end;
implementation eq
equations
p2.f = p1.f;
p1.e = p2.e;
flow = p1.f;
implementation_end;
Hmatrix 256 312
description '4.0Template\Submodel-Equation.emx1False2007-11-1 22:32:1False';
type 'Submodel-Equation'
ports
signal in flow [6,1];
signal out H [4,4];
end;
icon bg
figures
rectangle 224 296 288 328 color 0 fill 15132390;
text 'name' 256 312 color 0 'Clear Sans' 16;
end;
implementation eq
parameters
real init[4] = [1;0;0;0];
variables
real q[4]; //quaternions
real W[3,4]; //Quaternion Rates Matrix
real R[3,3]; //Rotation Matrix
real p[3]; //Position Vector
real dq[4];
real Wb[3,4];
equations
dq = transpose(Wb) * flow[1:3] ./ 2;
q = int(dq,init);
p = int(flow[4:6]);
W = [-q[2], q[1], -q[4], q[3];
-q[3], q[4], q[1], -q[2];
-q[4], -q[3], q[2], q[1]];
Wb = [ -q[2], q[1], q[4], -q[3];
-q[3], -q[4], q[1], q[2];
-q[4], q[3], -q[2], q[1]];
R = [q[1]^2+q[2]^2-q[3]^2-q[4]^2, 2*(q[2]*q[3]+q[1]*q[4]), 2*(q[2]*q[4]-q[1]*q[3]);
2*(q[2]*q[3]-q[1]*q[4]), q[1]^2-q[2]^2+q[3]^2-q[4]^2, 2*(q[3]*q[4]+q[1]*q[2]);
2*(q[2]*q[4]+q[1]*q[3]), 2*(q[3]*q[4]-q[1]*q[2]), q[1]^2-q[2]^2-q[3]^2+q[4]^2];
H = homogeneous(R,p);
implementation_end;
MatrixMul 320 576
description '
4.0
1
False
Signal\Block Diagram\Gain.emx
2007-9-26 12:15:12
True
';
type Gain
ports
signal in input1 [4,4];
signal out output [4,4];
signal in input2 [4,4];
end;
icon bg bottom
figures
rectangle 304.1 560 335.9 592 color 0 fill 15132390;
text 'X' 320 576 color 16711680 16 bold;
end;
implementation eq
equations
output = input2*input1; implementation_end;
plug Pin 492.1 424;
plug Pdiff 184 225;
plug Hin 130.8 576;
plug Hout 478.4 576;
plug Hdiff 320 222;
plug Pout 134.7 424;
Splitter2 320 312
description '4.0
Signal\Block Diagram\Splitter.emx
2008-01-17 11:28:29
1
False
';
knot Splitter
ports
signal knot duplicatable out output [4,4];
signal knot in input [4,4];
end;
icon bg ellipse
figures
ellipse 316.8 308.8 323.2 315.2 color -1 fill 0;
ellipse 315.7 307.7 324.3 316.3 color -1;
terminals
input 320 312 fixed;
end;
implementation eq
equations
collect (output) = input;
implementation_end;
Wbai 184 424
description '
4.0
1
False
Bond Graph\ZeroJunction.emx
2007-9-27 9:51:43
True
';
knot ZeroJunction
ports
power knot duplicatable none p [6,1];
signal knot out effort [6,1];
restrictions
causality constraint one_in p;
end;
icon bg bottom
figures
text '0' 184 424 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.f)) = 0;
equal (collect (p.e));
effort = first (p.e);
implementation_end;
end;
connections
FlowSensor2\flow -> Hmatrix\flow;
FlowSensor2\p2 => Wbai\p;
Hin -> MatrixMul\input2;
Hmatrix\H -> Splitter2\input;
MatrixMul\output -> Hout;
Pdiff => FlowSensor2\p1;
Pin => AdHji\p2;
Splitter2\output -> AdHji\H 424 312;
Splitter2\output -> Hdiff;
Splitter2\output -> MatrixMul\input1;
Wbai\p <= AdHji\p1;
Wbai\p => Pout;
end;
implementation_end;
Link 288 120
description '
4.8
Bond Graph\MR\link-v3.emx
1
False
2020-7-21 11:14:41
False
';
type 'Submodel-Equation'
ports
signal in Hin [4,4];
signal out Hout [4,4];
power in Pin [6,1];
power out Pout [6,1];
restrictions
causality constraint not_equal Pin Pout;
end;
icon bg bottom
figures
rectangle 256 96 320 144 color 0 fill 8454041;
text 'Link' 288 120 color 0 'Clear Sans' 16;
terminals
Hin 256 136 fixed;
Hout 320 136 fixed;
Pin 320 104 fixed;
Pout 256 104 fixed;
end;
implementation eq
parameters
real offset[6]= [0;0;0;0;0.0325;0]; //coordinates of joint_1
variables
real Hab[4,4];
real AdHab[6,6];
real R[3,3];
real omega[3];
initialequations
omega = offset[1:3];
R = dll('EulerAngles.dll','RotationMatrixFromEulXYZs',omega);
Hab = homogeneous(R,offset[4:6]);
AdHab = Adjoint(Hab);
equations
Hout = Hin * Hab;
Pout.e = transpose(AdHab) * Pin.e;
Pin.f = AdHab * Pout.f;
implementation_end;
Link1 456 120
description '
4.8
Bond Graph\MR\link-v3.emx
1
False
2020-7-21 11:14:41
False
';
type 'Submodel-Equation'
ports
signal in Hin [4,4];
signal out Hout [4,4];
power in Pin [6,1];
power out Pout [6,1];
restrictions
causality constraint not_equal Pin Pout;
end;
icon bg bottom
figures
rectangle 424 96 488 144 color 0 fill 8454041;
text 'Link' 456 120 color 0 'Clear Sans' 16;
terminals
Hin 424 136 fixed;
Hout 488 136 fixed;
Pin 488 104 fixed;
Pout 424 104 fixed;
end;
implementation eq
parameters
real offset[6]= [0;0;0;0;0.0325;0]; //coordinates of joint_1
variables
real Hab[4,4];
real AdHab[6,6];
real R[3,3];
real omega[3];
initialequations
omega = offset[1:3];
R = dll('EulerAngles.dll','RotationMatrixFromEulXYZr',omega);
Hab = homogeneous(R,offset[4:6]);
AdHab = Adjoint(Hab);
equations
Hout = Hin * Hab;
Pout.e = transpose(AdHab) * Pin.e;
Pin.f = AdHab * Pout.f;
implementation_end;
Link2 624 120
description '
4.8
Bond Graph\MR\link-v3.emx
1
False
2020-7-19 15:22:34
False
';
type 'Submodel-Equation'
ports
signal in Hin [4,4];
signal out Hout [4,4];
power in Pin [6,1];
power out Pout [6,1];
restrictions
causality constraint not_equal Pin Pout;
end;
icon bg bottom
figures
rectangle 592 96 656 144 color 0 fill 8454041;
text 'Link' 624 120 color 0 'Clear Sans' 16;
terminals
Hin 592 136 fixed;
Hout 656 136 fixed;
Pin 656 104 fixed;
Pout 592 104 fixed;
end;
implementation eq
parameters
real offset[3]= [0;0.025;0]; //coordinates of joint_1
variables
real Hab[4,4];
real AdHab[6,6];
equations
Hab = homogeneous(eye(3),offset);
AdHab = Adjoint(eye(3),offset);
Hout = Hin * Hab;
Pout.e = transpose(AdHab) * Pin.e;
Pin.f = AdHab * Pout.f;
implementation_end;
Link3 800 120
description '
4.8
Bond Graph\MR\link-v3.emx
1
False
2020-7-19 15:22:34
False
';
type 'Submodel-Equation'
ports
signal in Hin [4,4];
signal out Hout [4,4];
power in Pin [6,1];
power out Pout [6,1];
restrictions
causality constraint not_equal Pin Pout;
end;
icon bg bottom
figures
rectangle 768 96 832 144 color 0 fill 8454041;
text 'Link' 800 120 color 0 'Clear Sans' 16;
terminals
Hin 768 136 fixed;
Hout 832 136 fixed;
Pin 832 104 fixed;
Pout 768 104 fixed;
end;
implementation eq
parameters
real offset[3]= [0;0.025;0]; //coordinates of joint_1
variables
real Hab[4,4];
real AdHab[6,6];
equations
Hab = homogeneous(eye(3),offset);
AdHab = Adjoint(eye(3),offset);
Hout = Hin * Hab;
Pout.e = transpose(AdHab) * Pin.e;
Pin.f = AdHab * Pout.f;
implementation_end;
motor_joint1 112 384
description '
4.8
1
';
type Submodel
ports
signal in input;
power out p2;
end;
implementation bg
submodels
Gain1 552 88
description '4.01False
Signal\Block Diagram\Gain.emx
2007-9-26 12:15:12
';
type Gain
ports
signal in input;
signal out output;
end;
icon bg bottom
figures
rectangle 536.1 72 567.9 104 color 0 fill 15132390;
text 'K' 552 88 color 16711680 16 bold;
end;
implementation eq
parameters
real K = 12.0; // gain
equations
output = K * input;
implementation_end;
GY 624 208
description '
4.2
1
False
Bond Graph\GY.emx
2011-11-29 15:53:45
';
type GY
ports
power in p1;
power out p2;
restrictions
causality constraint equal p1 p2;
end;
icon bg bottom
figures
text 'GY' 624 208 color 0 18 bold;
end;
implementation eq
parameters
real r = 0.127;
equations
p1.e = r * p2.f;
p2.e = r * p1.f;
implementation_end;
MSe 624 88
description '
4.2
1
False
Bond Graph\MSe.emx
2011-11-29 16:12:33
';
type MSe
ports
power out p;
signal in effort;
restrictions
causality fixed out p;
end;
icon bg bottom
figures
text 'MSe' 624 88 color 0 18 bold;
end;
implementation eq
variables
real flow;
equations
p.e = effort;
flow = p.f;
implementation_end;
plug input 424 88;
plug p2 624 296;
OneJunction2 624 136
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [1];
signal knot out flow [1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 624 136 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
R 680 136
description '
4.2
1
False
Bond Graph\R.emx
2011-11-29 16:35:37
';
type R
ports
power in p;
end;
icon bg bottom
figures
text 'R' 680 136 color 0 18 bold;
end;
implementation eq
parameters
real r = 2;
equations
p.e = r * p.f;
implementation_end;
SignalLimiter2 488 88
description '4.01False
Signal\Block Diagram Non-Linear\SignalLimiter-Limit.emx
2007-9-26 12:47:40
';
type 'SignalLimiter-Limit'
ports
signal in input;
signal out output;
end;
icon bg bottom
figures
group
rectangle 472 72 504 104 color 0 fill 15132390;
line 487.9 76.5 487.9 101 color 0 fill 15132390;
line 475 88.2 500.7 88.2 color 0 fill 15132390;
spline 481.9 95.1 493.9 81.4 color 16711680 fill 15132390 width 2;
spline 493.3 82.2 501.9 81.8 color 16711680 fill 15132390 width 2;
spline 475 95.6 481.9 95.1 color 16711680 fill 15132390 width 2;
end;
end;
implementation eq
parameters
real maximum = 1;
real minimum = -1;
equations
output = limit (input, minimum, maximum);
implementation_end;
end;
connections
Gain1\output -> MSe\effort;
GY\p2 => p2;
input -> SignalLimiter2\input;
MSe\p => OneJunction2\p;
OneJunction2\p => GY\p1;
R\p <= OneJunction2\p;
SignalLimiter2\output -> Gain1\input;
end;
implementation_end;
motor_joint2 680 432
description '
4.8
1
';
type Submodel
ports
signal in input;
power out p2;
end;
implementation bg
submodels
Gain1 552 88
description '4.01False
Signal\Block Diagram\Gain.emx
2007-9-26 12:15:12
';
type Gain
ports
signal in input;
signal out output;
end;
icon bg bottom
figures
rectangle 536.1 72 567.9 104 color 0 fill 15132390;
text 'K' 552 88 color 16711680 16 bold;
end;
implementation eq
parameters
real K = 12.0; // gain
equations
output = K * input;
implementation_end;
GY 624 200
description '
4.2
1
False
Bond Graph\GY.emx
2011-11-29 15:53:45
';
type GY
ports
power in p1;
power out p2;
restrictions
causality constraint equal p1 p2;
end;
icon bg bottom
figures
text 'GY' 624 200 color 0 18 bold;
end;
implementation eq
parameters
real r = 0.127;
equations
p1.e = r * p2.f;
p2.e = r * p1.f;
implementation_end;
MSe 624 88
description '
4.2
1
False
Bond Graph\MSe.emx
2011-11-29 16:12:33
';
type MSe
ports
power out p;
signal in effort;
restrictions
causality fixed out p;
end;
icon bg bottom
figures
text 'MSe' 624 88 color 0 18 bold;
end;
implementation eq
variables
real flow;
equations
p.e = effort;
flow = p.f;
implementation_end;
plug input 424 88;
plug p2 624 256;
OneJunction2 624 136
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [1];
signal knot out flow [1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 624 136 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
R 664 136
description '
4.2
1
False
Bond Graph\R.emx
2011-11-29 16:35:37
';
type R
ports
power in p;
end;
icon bg bottom
figures
text 'R' 664 136 color 0 18 bold;
end;
implementation eq
parameters
real r = 2;
equations
p.e = r * p.f;
implementation_end;
SignalLimiter2 488 88
description '4.01False
Signal\Block Diagram Non-Linear\SignalLimiter-Limit.emx
2007-9-26 12:47:40
';
type 'SignalLimiter-Limit'
ports
signal in input;
signal out output;
end;
icon bg bottom
figures
group
rectangle 472 72 504 104 color 0 fill 15132390;
line 487.9 76.5 487.9 101 color 0 fill 15132390;
line 475 88.2 500.7 88.2 color 0 fill 15132390;
spline 481.9 95.1 493.9 81.4 color 16711680 fill 15132390 width 2;
spline 493.3 82.2 501.9 81.8 color 16711680 fill 15132390 width 2;
spline 475 95.6 481.9 95.1 color 16711680 fill 15132390 width 2;
end;
end;
implementation eq
parameters
real maximum = 1;
real minimum = -1;
equations
output = limit (input, minimum, maximum);
implementation_end;
end;
connections
Gain1\output -> MSe\effort;
GY\p2 => p2;
input -> SignalLimiter2\input;
MSe\p => OneJunction2\p;
OneJunction2\p => GY\p1;
R\p <= OneJunction2\p;
SignalLimiter2\output -> Gain1\input;
end;
implementation_end;
Negate1 272 448
description '4.01False
Signal\Block Diagram\Negate.emx
2007-9-26 12:14:11
';
type Negate
ports
signal in input;
signal out output;
end;
icon bg bottom
figures
rectangle 256 432 288 464 color 0 fill 15132390;
text '-1' 272 448 color 16711680 16 bold;
end;
implementation eq
equations
output = - input;
implementation_end;
Negate2 520 552
description '4.01False
Signal\Block Diagram\Negate.emx
2007-9-26 12:14:11
';
type Negate
ports
signal in input;
signal out output;
end;
icon bg bottom
figures
rectangle 504 536 536 568 color 0 fill 15132390;
text '-1' 520 552 color 16711680 16 bold;
end;
implementation eq
equations
output = - input;
implementation_end;
new_joint1 376 280
description '4.0
Template\Submodel-Equation.emx
1
False
2007-11-1 22:32:1
False
';
type 'Submodel-Equation'
ports
signal in input [4,4];
end;
implementation eq
variables
real position[3];
real rotation[3];
real R[3,3];
equations
position = input[1:3,4];
rotation = dll('EulerAngles.dll','EulXYZsFromHMatrix',input);
//[input[3,2];input[1,3];input[2,1]];
R = input[1:3,1:3];implementation_end;
new_joint2 720 256
description '4.0
Template\Submodel-Equation.emx
1
False
2007-11-1 22:32:1
False
';
type 'Submodel-Equation'
ports
signal in input [4,4];
end;
implementation eq
variables
real position[3];
real rotation[3];
real R[3,3];
equations
// start typing here
position = input[1:3,4];
rotation = [input[3,2];input[1,3];input[2,1]];
R = input[1:3,1:3];implementation_end;
new_joint3 1016 184
description '4.0
Template\Submodel-Equation.emx
1
False
2007-11-1 22:32:1
False
';
type 'Submodel-Equation'
ports
signal in input [4,4];
end;
implementation eq
variables
real position[3];
real rotation[3];
real R[3,3];
equations
position = input[1:3,4];
rotation = [input[3,2];input[1,3];input[2,1]];
R = input[1:3,1:3];implementation_end;
OneJunction1 360 104
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [6,1];
signal knot out flow [6,1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 360 104 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
OneJunction12 888 104
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [6,1];
signal knot out flow [6,1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 888 104 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
OneJunction17 520 288
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [1];
signal knot out flow [1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 520 288 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
OneJunction2 120 104
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [6,1];
signal knot out flow [6,1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 120 104 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
OneJunction3 704 104
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [6,1];
signal knot out flow [6,1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 704 104 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
OneJunction4 593 232
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [2,1];
signal knot out flow [2,1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 593 232 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
OneJunction5 257 240
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [2,1];
signal knot out flow [2,1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 257 240 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
OneJunction6 257 256
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [3,1];
signal knot out flow [3,1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 257 256 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
OneJunction7 593 248
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [3,1];
signal knot out flow [3,1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 593 248 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
PID1 584 432
description '
4.0
1
False
Signal\Control\PID Control\Continuous\PD.emx
2008-1-17 10:49:7
';
type PD
ports
signal in error;
signal out output;
end;
icon bg bottom
figures
rectangle 568 416 600 448 color 0 fill 15132390;
text 'PD' 584.5 432.1 color 16711680 18 bold;
end;
implementation eq
parameters
real kp = 2 {}; // Proportional gain
real tauD = 0.6 {s}; // Derivative time constant: tauD > 0
real beta = 0.2{}; // Tameness constant: 0 < beta << 1
variables
real state, rate;
equations
rate = (kp * error - output) / (beta * tauD);
state = int (rate);
output = state + kp * error / beta;
implementation_end;
PID2 200 384
description '
4.0
1
False
Signal\Control\PID Control\Continuous\PD.emx
2008-1-17 10:49:7
';
type PD
ports
signal in error;
signal out output;
end;
icon bg bottom
figures
rectangle 184 368 216 400 color 0 fill 15132390;
text 'PD' 200.5 384.1 color 16711680 18 bold;
end;
implementation eq
parameters
real kp = 2 {}; // Proportional gain
real tauD = 0.6 {s}; // Derivative time constant: tauD > 0
real beta = 0.2{}; // Tameness constant: 0 < beta << 1
variables
real state, rate;
equations
rate = (kp * error - output) / (beta * tauD);
state = int (rate);
output = state + kp * error / beta;
implementation_end;
PlusMinus4 272 384
description '4.01False
Signal\Block Diagram\PlusMinus.emx
2007-9-27 10:15:13
';
knot PlusMinus
ports
signal knot duplicatable in plus [1];
signal knot duplicatable in minus [1];
signal knot out output [1];
end;
icon bg ellipse
figures
ellipse 264 376 280 392 color 0 fill 16777215;
end;
implementation eq
equations
output = sum (collect (plus)) - sum (collect (minus));
implementation_end;
PlusMinus5 520 432
description '4.01False
Signal\Block Diagram\PlusMinus.emx
2007-9-27 10:15:13
';
knot PlusMinus
ports
signal knot duplicatable in plus [1];
signal knot duplicatable in minus [1];
signal knot out output [1];
end;
icon bg ellipse
figures
ellipse 512 424 528 440 color 0 fill 16777215;
end;
implementation eq
equations
output = sum (collect (plus)) - sum (collect (minus));
implementation_end;
PowerMux 192 214
specifications active 'rot_x'
specification 'rot_x'
description '
4.8
Bond Graph\MR\PowerMux-Rotation.emx
2020-7-20 14:35:23
1
False
True
';
type 'PowerMux-Rotation'
ports
power in input;
power out output [6,1];
power in input_rot2 [2,1];
power in input_pos3 [3,1];
restrictions
causality constraint not_equal input output;
causality constraint not_equal input_rot2 output;
causality constraint not_equal input_pos3 output;
end;
icon bg bottom
figures
line 168 216 216 216 color 0 width 2;
rectangle 168 208 216 220 color -1;
text '1' 186 211 color 8421504 8;
terminals
input 176 216 fixed;
output 192 216 fixed;
input_rot2 208 216 fixed;
input_pos3 192 216 fixed;
end;
implementation eq
equations
output.e[1] = input.e;
output.e[2:3] = input_rot2.e;
output.e[4:6] = input_pos3.e;
output.f[1] = input.f;
output.f[2:3] = input_rot2.f;
output.f[4:6] = input_pos3.f;implementation_end;
specification_end;
specification 'rot_y'
description '
4.1
Bond Graph\PowerMux.emx
2011-3-4 15:12:50
1
False
True
';
type PowerMux
ports
power in input;
power out output [6,1];
power in input_rot2 [2,1];
power in input_pos3 [3,1];
restrictions
causality constraint not_equal input output;
end;
icon bg bottom
figures
line 808 216 808 264 color 0 width 2;
rectangle 804 216 816 264 color -1;
text '1' 813 234 color 8421504 8;
terminals
input 808 224 fixed;
output 808 240 fixed;
input_rot2 808 256 fixed;
input_pos3 808 240 fixed;
end;
implementation eq
equations
output.e[1] = input_rot2.e[1];
output.e[2] = input.e;
output.e[3] = input_rot2.e[2];
output.e[4:6] = input_pos3.e;
output.f[1] = input_rot2.f[1];
output.f[2] = input.f;
output.f[3] = input_rot2.f[2];
output.f[4:6] = input_pos3.f;implementation_end;
specification_end;
specification 'rot_z'
description '
4.1
Bond Graph\PowerMux.emx
2011-3-4 15:12:50
1
False
True
';
type PowerMux
ports
power in input;
power out output [6,1];
power in input_rot2 [2,1];
power in input_pos3 [3,1];
restrictions
causality constraint not_equal input output;
end;
icon bg bottom
figures
line 808 216 808 264 color 0 width 2;
rectangle 804 216 816 264 color -1;
text '1' 813 234 color 8421504 8;
terminals
input 808 224 fixed;
output 808 240 fixed;
input_rot2 808 256 fixed;
input_pos3 808 240 fixed;
end;
implementation eq
equations
output.e[3] = input.e;
output.e[1:2] = input_rot2.e;
output.e[4:6] = input_pos3.e;
output.f[3] = input.f;
output.f[1:2] = input_rot2.f;
output.f[4:6] = input_pos3.f;implementation_end;
specification_end;
end;
PowerMux1 536 206
specifications active 'rot_x'
specification 'rot_x'
description '
4.8
Bond Graph\MR\PowerMux-Rotation.emx
2020-7-20 14:35:23
1
False
True
';
type 'PowerMux-Rotation'
ports
power in input;
power out output [6,1];
power in input_rot2 [2,1];
power in input_pos3 [3,1];
restrictions
causality constraint not_equal input output;
causality constraint not_equal input_rot2 output;
causality constraint not_equal input_pos3 output;
end;
icon bg bottom
figures
line 512 208 560 208 color 0 width 2;
rectangle 512 200 560 212 color -1;
text '1' 530 203 color 8421504 8;
terminals
input 520 208 fixed;
output 536 208 fixed;
input_rot2 552 208 fixed;
input_pos3 536 208 fixed;
end;
implementation eq
equations
output.e[1] = input.e;
output.e[2:3] = input_rot2.e;
output.e[4:6] = input_pos3.e;
output.f[1] = input.f;
output.f[2:3] = input_rot2.f;
output.f[4:6] = input_pos3.f;implementation_end;
specification_end;
specification 'rot_y'
description '
4.1
Bond Graph\PowerMux.emx
2011-3-4 15:12:50
1
False
True
';
type PowerMux
ports
power in input;
power out output [6,1];
power in input_rot2 [2,1];
power in input_pos3 [3,1];
restrictions
causality constraint not_equal input output;
end;
icon bg bottom
figures
line 808 216 808 264 color 0 width 2;
rectangle 804 216 816 264 color -1;
text '1' 813 234 color 8421504 8;
terminals
input 808 224 fixed;
output 808 240 fixed;
input_rot2 808 256 fixed;
input_pos3 808 240 fixed;
end;
implementation eq
equations
output.e[1] = input_rot2.e[1];
output.e[2] = input.e;
output.e[3] = input_rot2.e[2];
output.e[4:6] = input_pos3.e;
output.f[1] = input_rot2.f[1];
output.f[2] = input.f;
output.f[3] = input_rot2.f[2];
output.f[4:6] = input_pos3.f;implementation_end;
specification_end;
specification 'rot_z'
description '
4.1
Bond Graph\PowerMux.emx
2011-3-4 15:12:50
1
False
True
';
type PowerMux
ports
power in input;
power out output [6,1];
power in input_rot2 [2,1];
power in input_pos3 [3,1];
restrictions
causality constraint not_equal input output;
end;
icon bg bottom
figures
line 808 216 808 264 color 0 width 2;
rectangle 804 216 816 264 color -1;
text '1' 813 234 color 8421504 8;
terminals
input 808 224 fixed;
output 808 240 fixed;
input_rot2 808 256 fixed;
input_pos3 808 240 fixed;
end;
implementation eq
equations
output.e[3] = input.e;
output.e[1:2] = input_rot2.e;
output.e[4:6] = input_pos3.e;
output.f[3] = input.f;
output.f[1:2] = input_rot2.f;
output.f[4:6] = input_pos3.f;implementation_end;
specification_end;
end;
R1 472 288
description '
4.2
1
False
Bond Graph\R.emx
2011-11-29 16:35:37
';
type R
ports
power in p;
end;
icon bg bottom
figures
text 'R' 472 288 color 0 18 bold;
end;
implementation eq
parameters
real r = 0.0001;
equations
p.e = r * p.f;
implementation_end;
R2 257 184
description '4.01False
Bond Graph\2D\R-2.emx
2007-9-25 12:6:54
';
type 'R-2'
ports
power in p [2,1];
end;
icon bg bottom
figures
text 'R' 257 184 color 0 18 bold;
end;
implementation eq
parameters
real r[2,2] = [1.0, 0.0; 0.0, 1.0] {kN.m.s/rad};
equations
p.e = r * p.f;
implementation_end;
R3 257 312
description '4.01False
Bond Graph\3D\R-3.emx
2007-9-25 12:11:54
';
type 'R-3'
ports
power in p [3,1];
end;
icon bg bottom
figures
text 'R' 257 312 color 0 18 bold;
end;
implementation eq
parameters
real r[3,3] = [1.0, 0.0, 0.0; 0.0, 1.0, 0.0; 0.0, 0.0, 1.0] {kN.s/m};
equations
p.e = r * p.f;
implementation_end;
R4 593 176
description '4.01False
Bond Graph\2D\R-2.emx
2007-9-25 12:6:54
';
type 'R-2'
ports
power in p [2,1];
end;
icon bg bottom
figures
text 'R' 593 176 color 0 18 bold;
end;
implementation eq
parameters
real r[2,2] = [1.0, 0.0; 0.0, 1.0] {kN.m.s/rad};
equations
p.e = r * p.f;
implementation_end;
R5 593 304
description '4.01False
Bond Graph\3D\R-3.emx
2007-9-25 12:11:54
';
type 'R-3'
ports
power in p [3,1];
end;
icon bg bottom
figures
text 'R' 593 304 color 0 18 bold;
end;
implementation eq
parameters
real r[3,3] = [1.0, 0.0, 0.0; 0.0, 1.0, 0.0; 0.0, 0.0, 1.0] {kN.s/m};
equations
p.e = r * p.f;
implementation_end;
R7 56 288
description '
4.2
1
False
Bond Graph\R.emx
2011-11-29 16:35:37
';
type R
ports
power in p;
end;
icon bg bottom
figures
text 'R' 56 288 color 0 18 bold;
end;
implementation eq
parameters
real r = 0.0001;
equations
p.e = r * p.f;
implementation_end;
rectanglepath 104 552
description '
4.8
setpoint\rectanglepath.emx
1
False
2020-7-10 12:30:38
False
';
type 'Submodel-Equation'
ports
signal out output [2,1];
end;
implementation eq
/*
This will generate coordinates for the box that has to be drawn
*/
parameters
real w = 0.07{m} ;
real h = 0.05 {m};
real t = 0.5 {s};
real origin[2] = [0.01,0.03]{m};
variables
real v {m/s};
real t_w {s};
real t_h {s};
real period {s};
initialequations
v = (2*w + 2*h)/t;
t_w = w / v;
t_h = h / v;
equations
period = floor(time / t) * t;
output[1] = v*(ramp(period+t_h) - ramp(period + t_w+t_h) - ramp(period + t_w + t_h + t_h)) + origin[1];
output[2] = v*(ramp(period) - ramp(period + t_h) - ramp(period + t_h + t_w) + ramp(period + 2 * t_h + t_w))+ origin[2];
implementation_end;
rectanglepath1 272 656
description '
4.8
setpoint\rectanglepath.emx
1
False
2020-7-10 12:30:38
False
';
type 'Submodel-Equation'
ports
signal out output [2,1];
end;
icon bg
figures
rectangle 216 640 328 672 color 0 fill 15132390;
text 'name' 272 656 color 0 'Clear Sans' 16;
end;
implementation eq
/*
This will generate coordinates for the box that has to be drawn
*/
parameters
real w = 0.07{m} ;
real h = 0.05 {m};
real t = 0.5 {s};
real origin[2] = [0.01,0.03]{m};
variables
real v {m/s};
real t_w {s};
real t_h {s};
real period {s};
boolean y;
initialequations
v = (2*w + 2*h)/t;
t_w = w / v;
t_h = h / v;
code
y = frequencyevent (t,0);
period = time - floor(time / t) * t;
if period < t_w or time < 2 then
output = origin;
else
if period < t_w + t_h then
output = origin + [w;0];
else
if period < 2 * t_w + t_h then
output = origin + [w;h];
else
output = origin + [0;h];
end;
end;
end;
//output[1] = v*(ramp(period+t_h) - ramp(period + t_w+t_h) - ramp(period + t_w + t_h + t_h)) + origin[1];
//output[2] = v*(ramp(period) - ramp(period + t_h) - ramp(period + t_h + t_w) + ramp(period + 2 * t_h + t_w))+ origin[2];
implementation_end;
Sf2 64 104
description '4.01False
Bond Graph\2D\Sf-2.emx
2007-9-25 12:7:5
';
type 'Sf-2'
ports
power out p [6,1];
restrictions
causality fixed in p;
end;
icon bg bottom
figures
text 'Sf' 64 104 color 0 18 bold;
end;
implementation eq
parameters
real flow[6,1] = 0;
variables
real effort [6];
equations
p.f = flow;
effort = p.e;
implementation_end;
Splitter1 392 136
description '4.0
Signal\Block Diagram\Splitter.emx
2008-01-17 11:28:29
1
False
';
knot Splitter
ports
signal knot duplicatable out output [4,4];
signal knot in input [4,4];
end;
icon bg ellipse
figures
ellipse 388.8 132.8 395.2 139.2 color -1 fill 0;
ellipse 387.7 131.7 396.3 140.3 color -1;
terminals
input 392 136 fixed;
end;
implementation eq
equations
collect (output) = input;
implementation_end;
Splitter2 736 136
description '4.0
Signal\Block Diagram\Splitter.emx
2008-01-17 11:28:29
1
False
';
knot Splitter
ports
signal knot duplicatable out output [4,4];
signal knot in input [4,4];
end;
icon bg ellipse
figures
ellipse 732.8 132.8 739.2 139.2 color -1 fill 0;
ellipse 731.7 131.7 740.3 140.3 color -1;
terminals
input 736 136 fixed;
end;
implementation eq
equations
collect (output) = input;
implementation_end;
Zero 112 136
description '4.01False
Signal\Sources\Zero.emx
2007-9-27 15:54:36
';
type Zero
ports
signal out output [4,4];
end;
icon bg bottom
figures
rectangle 96.1 120 127.9 152 color 0 fill 15132390;
text '0' 112 136 color 16711680 18 bold;
end;
implementation eq
equations
output = eye(4);implementation_end;
ZeroJunction1 112 328
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [1];
signal knot out flow [1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 112 328 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
ZeroJunction2 656 368
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [1];
signal knot out flow [1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 656 368 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
ZeroJunction7 112 288
description '
4.2
1
False
Bond Graph\OneJunction.emx
2011-11-29 16:17:51
';
knot OneJunction
ports
power knot duplicatable none p [1];
signal knot out flow [1];
restrictions
causality constraint one_out p;
end;
icon bg
figures
text '1' 112 288 color 0 18 bold;
end;
implementation eq
equations
sum (direct (p.e)) = 0;
equal (collect (p.f));
flow = first (p.f);
implementation_end;
end;
connections
C1\p <= OneJunction7\p;
C2\p <= OneJunction6\p;
COM\Hout -> new_joint1\input;
COM1\Hout -> new_joint2\input;
COM2\Hin <- Link3\Hout 920 136;
COM2\Hout -> new_joint3\input;
COM2\p => OneJunction12\p;
Integrate\input <- ZeroJunction7\flow;
Integrate\output -> PlusMinus4\minus;
Integrate1\output -> PlusMinus5\minus;
inverse_kinematics1\angle1 -> Negate1\input;
inverse_kinematics1\angle2 -> Negate2\input;
Joint\Hout -> Link\Hin;
Joint\Pdiff <= PowerMux\output;
Joint\Pin <= Link\Pout;
Joint\Pout => OneJunction2\p;
Link\Pin <= OneJunction1\p;
Link1\Hout -> Joint1\Hin;
Link1\Pin <= Joint1\Pout;
Link1\Pout => OneJunction1\p;
Link2\Hin <- Joint1\Hout;
Link2\Hout -> Splitter2\input;
Link2\Pin <= OneJunction3\p;
Link2\Pout => Joint1\Pin;
Link3\Pin <= OneJunction12\p;
Link3\Pout => OneJunction3\p;
motor_joint1\p2 => ZeroJunction1\p;
motor_joint2\p2 => ZeroJunction2\p;
Negate1\output -> PlusMinus4\plus;
Negate2\output -> PlusMinus5\plus;
OneJunction1\p <= COM\p;
OneJunction17\flow -> Integrate1\input;
OneJunction3\p <= COM1\p;
OneJunction4\p => C4\p;
OneJunction4\p => R4\p;
OneJunction5\p => C3\p;
OneJunction5\p => R2\p;
OneJunction6\p => R3\p;
OneJunction7\p => R5\p;
PID1\error <- PlusMinus5\output;
PID1\output -> motor_joint2\input;
PID2\output -> motor_joint1\input;
PlusMinus4\output -> PID2\error;
PowerMux\input_pos3 <= OneJunction6\p;
PowerMux\input_rot2 <= OneJunction5\p;
PowerMux1\input <= OneJunction17\p;
PowerMux1\input_pos3 <= OneJunction7\p;
PowerMux1\input_rot2 <= OneJunction4\p;
PowerMux1\output => Joint1\Pdiff;
R1\p <= OneJunction17\p;
R7\p <= ZeroJunction7\p;
rectanglepath1\output -> inverse_kinematics1\input;
Sf2\p => OneJunction2\p;
Splitter1\input <- Link\Hout;
Splitter1\output -> COM\Hin;
Splitter1\output -> Link1\Hin;
Splitter2\output -> COM1\Hin;
Splitter2\output -> Link3\Hin;
Zero\output -> Joint\Hin;
ZeroJunction1\p => ZeroJunction7\p;
ZeroJunction2\p => OneJunction17\p;
ZeroJunction7\p => PowerMux\input;
end;
implementation_end;
]]>
Experiment 1
4.8
C1\state_initial
3
1
0 0 0
C2\state_initial
3
1
0 0 0
C3\state_initial
2
1
0 0
C4\state_initial
2
1
0 0
COM1\InertialTensor\state_initial
6
1
0 0 0 0 0 0
COM\InertialTensor\state_initial
6
1
0 0 0 0 0 0
Joint1\Hmatrix\p_initial
3
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Joint\Hmatrix\p_initial
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PID1\state_initial
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PID2\state_initial
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COM2\InertialTensor\p.e_initial
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time
new_joint1\position[1]
new_joint1\position[2]
new_joint1\position[3]
new_joint1\R[1,3]
new_joint1\R[2,3]
new_joint1\R[3,3]
new_joint1\R[1,2]
new_joint1\R[2,2]
new_joint1\R[3,2]
new_joint2\R[1,3]
new_joint2\R[2,3]
new_joint2\R[3,3]
new_joint2\R[1,2]
new_joint2\R[2,2]
new_joint2\R[3,2]
new_joint2\position[1]
new_joint2\position[2]
new_joint2\position[3]
new_joint3\position[3]
new_joint3\position[2]
rectanglepath1\output[2]
rectanglepath1\output[1]
Integrate1\output
motor_joint2\SignalLimiter2\output
Submodel3\dimension[1]
Submodel3\dimension[2]
Submodel3\dimension[3]
Submodel4\dimension[1]
Submodel4\dimension[2]
Submodel4\dimension[3]
Step\output
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motor_joint2\p2.e
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Center
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Submodel3\dimension[1]
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Block
new_joint1\position[1]
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new_joint1\R[1,3]
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new_joint1\R[2,3]
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new_joint1\R[1,2]
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new_joint1\R[2,2]
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new_joint1\R[3,2]
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Matrix
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Center
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Submodel4\dimension[1]
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Block
new_joint2\position[1]
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new_joint2\position[3]
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new_joint2\R[1,3]
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new_joint2\R[2,3]
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new_joint2\R[3,3]
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new_joint2\R[1,2]
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new_joint2\R[2,2]
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new_joint2\R[3,2]
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Matrix
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GraphPlot
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model(2)
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new_joint3\position[2]
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new_joint3\position[3]
6076255
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6076255
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1
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rectanglepath1\output[1]
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rectanglepath1\output[2]
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motor_joint1\p2.e
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time
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motor_joint2\p2.e
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Step\output
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time
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Integrate1\output
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time
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motor_joint2\SignalLimiter2\output
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Window 1
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Base
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Base
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Base
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MultipleRun
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BroydonFletcherGoldfarbShanno
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