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New equation notation #11

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Jan 2, 2015
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New equation notation #11

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96eb450
Changes for the equations macro and Equation[].
tshort Jan 2, 2015
e58e8f5
Disable the test for sim_PID_Controller().
tshort Jan 2, 2015
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76 changes: 47 additions & 29 deletions README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -86,7 +86,7 @@ MExpr(*(##1243,+(##1243,1)))
In a simulation, the unknowns are to be solved based on a set of
equations. Equations are built from device models.

A device model is a function that returns a list of equations or
A device model is a function that returns a vector of equations or
other devices that also return lists of equations. The equations
each are assumed equal to zero. So,

Expand All @@ -112,11 +112,11 @@ function Vanderpol()
# The following gives the return value which is a list of equations.
# Expressions with Unknowns are kept as expressions. Expressions of
# regular variables are evaluated immediately.
{
# The -1.0 in der(x, -1.0) is the initial value for the derivative
der(x, -1.0) - ((1 - y^2) * x - y) # == 0 is assumed
der(y) - x
}
Equation[
# The -1.0 in der(x, -1.0) is the initial value for the derivative
der(x, -1.0) - ((1 - y^2) * x - y) # == 0 is assumed
der(y) - x
]
end

y = sim(Vanderpol(), 10.0) # Run the simulation to 10 seconds and return
Expand All @@ -127,8 +127,26 @@ gplot(y)

Here are the results:

![plot results](https://github.com/tshort/Sims.jl/blob/master/examples/vanderpol.png?raw=true "Van Der Pol results")
![plot results](https://github.com/tshort/Sims.jl/blob/master/examples/basics/vanderpol.png?raw=true "Van Der Pol results")

An `@equations` macro is provided to return `Equation[]` allowing for
the use of equals in equations, so the example above can be:

``` julia
function Vanderpol()
y = Unknown(1.0, "y")
x = Unknown("x")
@equations begin
der(x, -1.0) = (1 - y^2) * x - y
der(y) = x
end
end

y = sim(Vanderpol(), 10.0) # Run the simulation to 10 seconds and return
# the result as an array.
# plot the results with Gaston
gplot(y)
```

Electrical example
------------------
Expand Down Expand Up @@ -159,19 +177,19 @@ voltage.
function Resistor(n1, n2, R::Real)
i = Current() # This is simply an Unknown.
v = Voltage()
{
Branch(n1, n2, v, i)
R * i - v # == 0 is implied
}
@equations begin
Branch(n1, n2, v, i)
R * i = v
end
end

function Capacitor(n1, n2, C::Real)
i = Current()
v = Voltage()
{
Branch(n1, n2, v, i)
C * der(v) - i
}
@equations begin
Branch(n1, n2, v, i)
C * der(v) = i
end
end
```

Expand All @@ -188,13 +206,13 @@ function Circuit()
n2 = Voltage("Output voltage")
n3 = Voltage()
g = 0.0 # A ground has zero volts; it's not an unknown.
{
SineVoltage(n1, g, 10.0, 60.0)
Resistor(n1, n2, 10.0)
Resistor(n2, g, 5.0)
SeriesProbe(n2, n3, "Capacitor current")
Capacitor(n3, g, 5.0e-3)
}
Equation[
SineVoltage(n1, g, 10.0, 60.0)
Resistor(n1, n2, 10.0)
Resistor(n2, g, 5.0)
SeriesProbe(n2, n3, "Capacitor current")
Capacitor(n3, g, 5.0e-3)
]
end

ckt = Circuit()
Expand All @@ -203,7 +221,7 @@ gplot(ckt_y)
```
Here are the results:

![plot results](https://github.com/tshort/Sims.jl/blob/master/examples/circuit.png?raw=true "Circuit results")
![plot results](https://github.com/tshort/Sims.jl/blob/master/examples/basics/circuit.png?raw=true "Circuit results")

Initialization and Solving Sets of Equations
--------------------------------------------
Expand All @@ -216,10 +234,10 @@ equations:
```julia
function test()
@unknown x y
{
2*x - y - exp(-x)
-x + 2*y - exp(-y)
}
@equations begin
2*x - y = exp(-x)
-x + 2*y = exp(-y)
end
end

solution = solve(create_sim(test()))
Expand All @@ -231,7 +249,7 @@ Hybrid Modeling and Structural Variability
Sims supports basic hybrid modeling, including the ability to handle
structural model changes. Consider the following example:

[Breaking pendulum](https://github.com/tshort/Sims.jl/blob/master/examples/breaking_pendulum_in_box.jl)
[Breaking pendulum](https://github.com/tshort/Sims.jl/blob/master/examples/basics/breaking_pendulum_in_box.jl)

This model starts as a pendulum, then the wire breaks, and the ball
goes into free fall. Sims handles this much like
Expand All @@ -245,7 +263,7 @@ adjusted for the "bounce".
Here is an animation of the results. Note that the actual animation
was done in R, not Julia.

![plot results](https://github.com/tshort/Sims.jl/blob/master/examples/pendulum.gif?raw=true "Pendulum")
![plot results](https://github.com/tshort/Sims.jl/blob/master/examples/basics/pendulum.gif?raw=true "Pendulum")

To Look Deeper
--------------
Expand Down
8 changes: 4 additions & 4 deletions doc/Possible-future-developments.md
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Original file line number Diff line number Diff line change
Expand Up @@ -92,10 +92,10 @@ leading "tag".
function Resistor(n1::ElectricalNode, n2::ElectricalNode, R::Signal)
i = Current(compatible_values(n1, n2))
v = Voltage(value(n1) - value(n2))
{
Branch(n1, n2, v, i)
R .* i - v # == 0 is implied
}
Equation[
Branch(n1, n2, v, i)
R .* i - v # == 0 is implied
]
end

# help info - returns a string in Markdown format
Expand Down
66 changes: 33 additions & 33 deletions doc/README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -88,10 +88,10 @@ function Vanderpol()
# The following gives the return value which is a list of equations.
# Expressions with Unknowns are kept as expressions. Regular
# variables are evaluated immediately (like normal).
{
der(x, -1.0) - ((1 - y^2) * x - y) # == 0 is assumed
der(y) - x
}
Equation[
der(x, -1.0) - ((1 - y^2) * x - y) # == 0 is assumed
der(y) - x
]
end
```

Expand All @@ -108,10 +108,10 @@ unknowns and equations as shown below:
function Capacitor(n1, n2, C::Real)
i = Current() # Unknown #1
v = Voltage() # Unknown #2
{
Branch(n1, n2, v, i) # Equation #1 - this returns n1 - n2 - v
C * der(v) - i # Equation #2
}
Equation[
Branch(n1, n2, v, i) # Equation #1 - this returns n1 - n2 - v
C * der(v) - i # Equation #2
]
end
```

Expand All @@ -127,13 +127,13 @@ function Circuit()
n2 = ElectricalNode("Output voltage")
n3 = ElectricalNode()
g = 0.0 # a ground has zero volts; it's not an Unknown.
{
VSource(n1, g, 10.0, 60.0)
Resistor(n1, n2, 10.0)
Resistor(n2, g, 5.0)
SeriesProbe(n2, n3, "Capacitor current")
Capacitor(n3, g, 5.0e-3)
}
Equation[
VSource(n1, g, 10.0, 60.0)
Resistor(n1, n2, 10.0)
Resistor(n2, g, 5.0)
SeriesProbe(n2, n3, "Capacitor current")
Capacitor(n3, g, 5.0e-3)
]
end
```

Expand Down Expand Up @@ -212,13 +212,13 @@ function VSquare(n1, n2, V::Real, f::Real)
i = Current()
v = Voltage()
v_mag = Discrete(V)
{
Branch(n1, n2, v, i)
v - v_mag
Event(sin(2 * pi * f * MTime),
{reinit(v_mag, V)}, # positive crossing
{reinit(v_mag, -V)}) # negative crossing
}
Equation[
Branch(n1, n2, v, i)
v - v_mag
Event(sin(2 * pi * f * MTime),
Equation[reinit(v_mag, V)], # positive crossing
Equation[reinit(v_mag, -V)]) # negative crossing
]
end
```

Expand All @@ -238,12 +238,12 @@ function IdealDiode(n1, n2)
v = Voltage()
s = Unknown() # dummy variable
openswitch = Discrete(false) # on/off state of diode
{
Branch(n1, n2, v, i)
BoolEvent(openswitch, -s) # openswitch becomes true when s goes negative
v - ifelse(openswitch, s, 0.0)
i - ifelse(openswitch, 0.0, s)
}
Equation[
Branch(n1, n2, v, i)
BoolEvent(openswitch, -s) # openswitch becomes true when s goes negative
v - ifelse(openswitch, s, 0.0)
i - ifelse(openswitch, 0.0, s)
]
end
```

Expand Down Expand Up @@ -274,11 +274,11 @@ function BreakingPendulum()
y = Unknown(-cos(pi/4), "y")
vx = Unknown()
vy = Unknown()
{
StructuralEvent(MTime - 5.0, # when time hits 5 sec, switch to FreeFall
Pendulum(x,y,vx,vy),
() -> FreeFall(x,y,vx,vy))
}
Equation[
StructuralEvent(MTime - 5.0, # when time hits 5 sec, switch to FreeFall
Pendulum(x,y,vx,vy),
() -> FreeFall(x,y,vx,vy))
]
end
```

Expand Down
38 changes: 19 additions & 19 deletions examples/basics/breaking_pendulum.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -6,39 +6,39 @@ using Sims
########################################

function FreeFall(x,y,vx,vy)
{
vx - der(x)
vy - der(y)
der(vx)
der(vy) + 9.81
}
@equations begin
der(x) = vx
der(y) = vy
der(vx) = 0.0
der(vy) = -9.81
end
end

function Pendulum(x,y,vx,vy)
len = sqrt(x.value^2 + y.value^2)
phi0 = atan2(x.value, -y.value)
phi = Unknown(phi0)
phid = Unknown()
{
phid - der(phi)
vx - der(x)
vy - der(y)
x - len * sin(phi)
y + len * cos(phi)
der(phid) + 9.81 / len * sin(phi)
}
@equations begin
der(phi) = phid
der(x) = vx
der(y) = vy
x = len * sin(phi)
y = -len * cos(phi)
der(phid) = -9.81 / len * sin(phi)
end
end

function BreakingPendulum()
x = Unknown(cos(pi/4), "x")
y = Unknown(-cos(pi/4), "y")
vx = Unknown()
vy = Unknown()
{
StructuralEvent(MTime - 5.0, # when time hits 5 sec, switch to FreeFall
Pendulum(x,y,vx,vy),
() -> FreeFall(x,y,vx,vy))
}
Equation[
StructuralEvent(MTime - 5.0, # when time hits 5 sec, switch to FreeFall
Pendulum(x,y,vx,vy),
() -> FreeFall(x,y,vx,vy))
]
end

p = BreakingPendulum()
Expand Down
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