Decouples Signal sources from their smooth wave shapes

src/Blocks/Blocks.jl

@@ -13,6 +13,7 @@ where `u` are inputs, `x` are state variables and `y` are outputs. `x,u,y` are a
 """
 module Blocks
 using ModelingToolkit, Symbolics, IfElse, OrdinaryDiffEq
+using ModelingToolkit: @register
 
 @parameters t
 Dₜ = Differential(t)
@@ -26,4 +27,8 @@ include("nonlinear.jl")
 export Constant, Integrator, Derivative, FirstOrder, SecondOrder, PID, StateSpace
 include("continuous.jl")
 
+export ConstantFunction, SmoothCosineFunction, SmoothDampedSineFunction, SmoothRampFunction,
+       SmoothSineFunction, SmoothSquareFunction, SmoothStepFunction, SmoothTriangularFunction
+include("wave_functions.jl")
+
 end

src/Blocks/wave_functions.jl

@@ -0,0 +1,131 @@
+# Define and register smooth functions
+using ModelingToolkit, Symbolics
+_constant(K) = K
+_cos_wave(x, f, A, st, ϕ) = A*cos(2*π*f*(x-st) + ϕ)
+_damped_sine_wave(x, f, A, st, ϕ, d) = exp((st-x)*d)*A*sin(2*π*f*(x-st) + ϕ)
+_ramp(x, δ, st, et, h) = h/(et-st)*(_xH(x, δ, st) - _xH(x, δ, et))
+_sine(x, f, A, st, ϕ) = A*sin(2*π*f*(x - st) + ϕ)
+_square_wave(x, δ, f, A, st) = A*2atan(sin(2π*(x-st)*f)/δ)/π
+_step(x, δ, h, a) = h*(atan((x-a)/δ)/π + 1//2)
+_triangular_wave(x, δ, f, A, st) = A*(1-2acos((1 - δ)sin(2π*(x-st)*f))/π)
+_xH(x, δ, tₒ) = (x-tₒ)*(1+((x-tₒ)/sqrt((x-tₒ)^2+δ^2)))/2
+
+
+@register _constant(K)
+@register _cos_wave(x, f, A, st, ϕ)
+@register _damped_sine_wave(x, f, A, st, ϕ, damping)
+@register _ramp(x, δ, st, et, h)
+@register _sine(x, f, A, st, ϕ)
+@register _square_wave(x, δ, f, A, st)
+@register _step(x, δ, h, a)
+@register _triangular_wave(x, δ, f, A, st)
+
+function ConstantFunction(;name, K=1.0)
+    val = K
+    @info val
+    @parameters K
+    @variables y(t) [output=true]
+
+    eqs = [
+        y ~ val
+    ]
+
+    ODESystem(eqs, t, [y], [K], defaults=Dict(K => val), name=name)
+end
+
+function SmoothCosineFunction(;name, offset=0.0, amplitude=1.0, frequency=1.0, starttime=0.0, phase=0.0)
+    o, A, f, st, ϕ = offset, amplitude, frequency, starttime, phase
+    δ = 0.00001
+
+    @parameters offset amplitude frequency starttime phase
+    @variables y(t) [output=true]
+
+    eqs = [
+           y ~ _cos_wave(t, f, A, st, ϕ) * _step(t, δ, 1.0, st) + offset
+          ]
+    defaults = Dict(zip((offset, amplitude, frequency, starttime, phase), (o, A, f, st, ϕ)))
+    ODESystem(eqs, t, [y], [offset, amplitude, frequency, starttime, phase], defaults=defaults, name=name)
+end
+
+function SmoothDampedSineFunction(;name, offset=0.0, amplitude=1.0, frequency=1.0, starttime=0.0, phase=0.0, damping_coef=0.0)
+    o, A, f, st, ϕ, d = offset, amplitude, frequency, starttime, phase, damping_coef
+    δ = 0.0001
+
+    @parameters offset amplitude frequency starttime phase damping_coef
+    @variables y(t) [output=true]
+
+    eqs = [
+           y ~ _step(t, δ, o, 0.0) + _damped_sine_wave(t, f, A, st, ϕ, d) * _step(t, δ, 1.0, st)
+          ]
+    defaults = Dict(zip((offset, amplitude, frequency, starttime, phase, damping_coef), (o, A, f, st, ϕ, d)))
+    ODESystem(eqs, t, [y], [offset, amplitude, frequency, starttime, phase, damping_coef], defaults=defaults, name=name)
+end
+
+function SmoothRampFunction(;name, offset=0.0, starttime=0.0, endtime=1.0, height=1.0)
+    o, st, et, h = offset, starttime, endtime, height
+    δ = 0.0001
+
+    @parameters offset starttime endtime height
+    @variables y(t) [output=true]
+
+    eqs = [
+           y ~ offset + _ramp(t, δ, st, et, h)
+          ]
+    defaults = Dict(zip((offset, starttime, endtime, height), (o, st, et, h)))
+    ODESystem(eqs, t, [y], [offset, starttime, endtime, height], defaults=defaults, name=name)
+end
+
+function SmoothSineFunction(;name, offset=0.0, amplitude=1.0, frequency=1.0, starttime=0.0, phase=0.0)
+    o, A, f, st, ϕ = offset, amplitude, frequency, starttime, phase
+
+    @parameters offset amplitude frequency starttime phase
+    @variables y(t) [output=true]
+
+    eqs = [
+           y ~ offset + (t > st) * _sine(x, f, A, st, ϕ)
+          ]
+    defaults = Dict(zip((offset, amplitude, frequency, starttime, phase), (o, A, f, st, ϕ)))
+    ODESystem(eqs, t, [y], [offset, amplitude, frequency, starttime, phase], defaults=defaults, name=name)
+end
+
+function SmoothSquareFunction(; name, offset=0.0, amplitude=1.0, frequency=1.0, starttime=0.0)
+    o, A, f, st  = offset, amplitude, frequency, starttime
+    δ = 0.0001
+
+    @parameters offset amplitude frequency starttime
+    @variables y(t) [output=true]
+
+    eqs = [
+        y ~ o + _square_wave(t, δ, f, A, st) * (t > st)
+        ]
+    defaults = Dict(zip((offset, amplitude, frequency, starttime), (o, A, f, st)))
+    ODESystem(eqs, t, [y], [offset, amplitude, frequency, starttime], defaults=defaults, name=name)
+end
+
+function SmoothStepFunction(;name, offset=0.0, starttime=0.0, height=1.0)
+    o, st, h = offset, starttime, height
+    δ = 0.0001
+
+    @parameters offset starttime height
+    @variables y(t)
+
+    eqs = [
+           y ~ offset + _step(t, δ, h, st)
+          ]
+    defaults = Dict(zip((offset, starttime, height), (o, st, h)))
+    ODESystem(eqs, t, [y], [offset, starttime, height], defaults=defaults, name=name)
+end
+
+function SmoothTriangularFunction(; name, offset=0.0, amplitude=1.0, frequency=1.0, starttime=0.0)
+    o, A, f, st  = offset, amplitude, frequency, starttime
+    δ = 0.0001
+
+    @parameters offset amplitude frequency starttime
+    @variables y(t) [output=true]
+
+    eqs = [
+        y ~ offset + (t>st) * _triangular_wave(t, δ, f, A, st)
+    ]
+    defaults = Dict(zip((offset, amplitude, frequency, starttime), (o, A, f, st)))
+    ODESystem(eqs, t, [y], [offset, amplitude, frequency, starttime], defaults=defaults, name=name)
+end