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speed-measurement.jl
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speed-measurement.jl
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using FunctionalModels, FunctionalModels.Lib
const D = FunctionalModels.D
const t = FunctionalModels.t
export SecondOrderSystem, SecondOrderSystemUsingFunctionalModelsLib, SampleAndHold, IntervalMeasure, PulseCounting
"""
# Examples of speed measurement
These examples show several ways of measuring speed on a rotational
system. They are based on Michael's section on [Speed
Measurement](http://mbe.modelica.university/behavior/discrete/measuring/). These
examples include use of Variable variables and Events.
The system is based on the following plant:
"""
@comment
"""
Rotational example
http://mbe.modelica.university/behavior/equations/mechanical/
"""
function SecondOrderSystem(; phi1 = Unknown(name = :phi1),
phi2 = Unknown(1.0, name = :phi2),
omega1 = Unknown(name = :omega1),
omega2 = Unknown(name = :omega2),
J1 = 0.4, J2 = 1.0, c1 = 11.0, c2 = 5.0, d1 = 0.2, d2 = 1.0)
[
## Equations for inertia 1
D(phi1) ~ omega1
D(omega1) ~ (c1*(phi2 - phi1) + d1*(omega2 - omega1)) / J1
## Equations for inertia 2
D(phi2) ~ omega2
D(omega2) ~ (c1*(phi1 - phi2) + d1*(omega1 - omega2) - c2*phi2 - d2*omega2) / J2
]
end
# function SecondOrderSystem(; phi1 = Unknown(name = :phi1),
# phi2 = Unknown(1.0, name = :phi2),
# omega1 = Unknown(name = :omega1),
# omega2 = Unknown(name = :omega2),
# J1 = 0.4, J2 = 1.0, k1 = 11.0, k2 = 5.0, d1 = 0.2, d2 = 1.0)
# # @named phidiff = Unknown(default_value(phi2) - default_value(phi1)) # Used because der(phi2 - phi1) isn't supported
# @named phidiff = Unknown(default_value(phi2) - default_value(phi1)) # Used because der(phi2 - phi1) isn't supported
# [
# ## Equations for inertia 1
# phidiff ~ phi2 - phi1
# der(phi1) ~ omega1
# J1*der(omega1) - d1*der(phidiff) ~ k1*(phi2-phi1)
# ## Equations for inertia 2
# der(phi2) ~ omega2
# J2*der(omega2) + d1*der(phidiff) ~ -d2*omega2 + k1*(phi1-phi2) - k2*phi2
# ]
# end
"""
Rotational example based on components in FunctionalModels.Lib
http://mbe.modelica.university/behavior/equations/mechanical/
"""
function SecondOrderSystemUsingFunctionalModelsLib(; phi1 = Angle(0.0, name = :phi1),
phi2 = Angle(1.0, name = :phi2),
omega1 = Unknown(0.0, name = :omega1),
omega2 = Unknown(0.0, name = :omega2),
J1 = 0.4, J2 = 1.0, c1 = 11.0, c2 = 5.0, d1 = 0.2, d2 = 1.0)
[
der(phi1) ~ omega1
der(phi2) ~ omega2
:in1 => Inertia(phi1, J = J1)
:in2 => Inertia(phi2, J = J2)
:sd1 => SpringDamper(phi1, phi2, c = c1, d = d1)
:sd2 => SpringDamper(phi2, 0.0, c = c2, d = d2)
]
end
"""
Rotational example with sample-and-hold measurement
http://mbe.modelica.university/behavior/discrete/measuring/#sample-and-hold
"""
function SampleAndHold()
sample_time = 0.125
@named omega1 = Unknown()
@named omega1_measured = Unknown()
[
SecondOrderSystem(omega1 = omega1)
Event(sin(FunctionalModels.t / sample_time * 2pi) ~ 0.0,
omega1_measured ~ omega1)
der(omega1_measured) ~ 0.0
]
end
"""
Rotational example with interval measurements
http://mbe.modelica.university/behavior/discrete/measuring/#interval-measurement
"""
function IntervalMeasure()
teeth = 200
tooth_angle = 2pi / teeth
@named phi1 = Unknown()
@named omega1_measured_u = Unknown()
@named omega1_measured = Variable(0.0)
@named next_phi = Variable(default_value(phi1) + tooth_angle)
@named prev_phi = Variable(default_value(phi1) - tooth_angle)
@named last_time = Variable(0.0)
[
Event(IfElse.ifelse(phi1 > next_phi, phi1 - next_phi, prev_phi - phi1),
[
omega1_measured ~ tooth_angle / (t - last_time)
next_phi ~ phi1 + tooth_angle
prev_phi ~ phi1 - tooth_angle
last_time ~ FunctionalModels.t
])
:sos => SecondOrderSystem(phi1 = phi1)
omega1_measured_u ~ omega1_measured
]
end
"""
Rotational example with pulse counting
http://mbe.modelica.university/behavior/discrete/measuring/#pulse-counting
"""
function PulseCounting()
sample_time = 0.125
teeth = 200
tooth_angle = 2pi / teeth
@named phi1 = Unknown()
@named omega1_measured_u = Unknown()
@named omega1_measured = Variable(0.0)
@named next_phi = Variable(default_value(phi1) + tooth_angle)
@named prev_phi = Variable(default_value(phi1) - tooth_angle)
@named count = Variable(0)
[
Event(IfElse.ifelse(phi1 > next_phi, phi1 - next_phi, prev_phi - phi1) ~ 0.0,
[
next_phi ~ phi1 + tooth_angle
prev_phi ~ phi1 - tooth_angle
count ~ count + 1
])
Event(sin(t / sample_time * 2pi) ~ 0.0,
[
omega1_measured ~ count * tooth_angle / sample_time
count ~ 0
])
:sos => SecondOrderSystem(phi1 = phi1)
omega1_measured_u ~ omega1_measured
]
end