StaticSystems

Basic Operation of StaticSystems

Static systems are the systems whose output y at time t depends on the current time t and the value of their inputs u. The input-output relation of static systems are represented by their output function outputfunc which is of the form

where g is the output function outputfunc. Note that outputfunc is expected to have two inputs, the value u of the input and the current time t. The simulation in Jusdl is a clocked-simulation, that is the data flowing through the input and output connections of components is actually sampled at time t. Therefore, for example, the system modelled by

is actually sampled at clock ticks t which is generated by a Clock. Therefore the sampled system corresponds to

where $k$ is $k_i T_s$ where $k_i$ is an integer number, $T_s$ is the sampling interval. $T_s$ corresponds to sampling time dt of Clock. Thus, the system given above is coded like

function g(u, t)
    # Define the relation `y = g(u, t)`
end

For further clarity, let us continue with a case study. Consider the following static system,

Note that the number of inputs is 2 and the number of outputs of is 3. To define such a system, the output function is written as

julia> g(u, t) = [t * u[1], sin(u[1]), cos(u[2])]
g (generic function with 1 method)

Note that the function g is defined such a way that the input value u is sampled, which implies u is not vector of function but is a vector of real. Having defined output function outputfunc, the system can be constructed.

julia> ss = StaticSystem(Bus(2), Bus(3), g)
StaticSystem(outputfunc:g, input:Bus(nlinks:2, eltype:Link{Float64}, isreadable:false, iswritable:false), output:Bus(nlinks:3, eltype:Link{Float64}, isreadable:false, iswritable:false))

Note the construction of input bus Bus(2) and output bus Bus(3) by recalling that the number of input is 2 and the number of output is 3.

A StaticSystem operates by being triggered from its trigger link. When triggered from its trigger link, a StaticSystem read the current time t from its trigger link and computes its output y according to its output function outputfunc and writes its output t to its output bus (If output bus exists since output bus may not have depending on the relation defined by outputfunc. When constructed, a StaticSystem is not ready to be triggered since its trigger link is not writeable.

julia> ss.trigger
Link(state:open, eltype:Float64, hasmaster:false, numslaves:0, isreadable:false, iswritable:false)

To make ss drivable, we need to launch ss.

julia> task = launch(ss)
(Task (runnable) @0x00007fd8d851e980, Task (runnable) @0x00007fd8d85189d0)

Now, ss is drivable from its trigger link.

julia> ss.trigger
Link(state:open, eltype:Float64, hasmaster:false, numslaves:0, isreadable:false, iswritable:true)

Now let us drive ss.

julia> put!(ss.trigger, 1.)
1.0

As this point ss wait for its to be written. Let us write some data to input of ss.

julia> put!(ss.input, [10., 10.])
2-element Array{Float64,1}:
 10.0
 10.0

ss read the value u of its input , read the current time t, and computed its output value y and wrote it its output. To signal that it succeeded to be take the step, it put a true to its handshake which needs to be taken.

julia> ss.handshake
Link(state:open, eltype:Bool, hasmaster:false, numslaves:0, isreadable:true, iswritable:false)

julia> take!(ss.handshake)
true

We can see the current data in the output of ss.

julia> println(ss.output[1].buffer.data)
[10.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

Let us further drive ss.

julia> for t in 2. : 10.
           put!(ss.trigger, t)
           put!(ss.input, [10 * t, 20 * t])
           take!(ss.handshake)
       end

The data written to the output of ss is also written to the internal buffers of output.

julia> println(ss.output[1].buffer.data)
[10.0, 40.0, 90.0, 160.0, 250.0, 360.0, 490.0, 640.0, 810.0, 1000.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

Full API

StaticSystem(input, output, outputfunc)

julia> g(u, t) = [u[1] + u[2], sin(u[2]), cos([1])]  # The system has 2 inputs and 3 outputs.
g (generic function with 1 method)

julia> ss = StaticSystem(Bus(2), Bus(3), g)
StaticSystem(outputfunc:g, input:Bus(nlinks:2, eltype:Link{Float64}, isreadable:false, iswritable:false), output:Bus(nlinks:3, eltype:Link{Float64}, isreadable:false, iswritable:false))

julia> g2(u, t) = t  # The system does not have any input.
g2 (generic function with 1 method)

julia> ss2 = StaticSystem(nothing, Bus(), g2)
StaticSystem(outputfunc:g2, input:nothing, output:Bus(nlinks:1, eltype:Link{Float64}, isreadable:false, iswritable:false))

Adder(input::Bus[, signs])

julia> adder = Adder(Bus(3), (+, +, -));

julia> adder.outputfunc([3, 4, 5], 0.) == 3 + 4 - 5
true

Multiplier(input::Bus[, ops])

julia> mlt = Multiplier(Bus(3), (*, *, /));

julia> mlt.outputfunc([3, 4, 5], 0.) == 3 * 4 / 5
true

Gain(input; gain=1.)

julia> K = [1. 2.; 3. 4.];

julia> g = Gain(Bus(2), gain=K);

julia> g.outputfunc([1., 2.], 0.) == K * [1., 2.]
true

Terminator(input::Bus)

Memory(input::Bus{Union{Missing, T}}, numdelay::Int; initial=Vector{T}(undef, length(input)))

Coupler(conmat::AbstractMatrix, cplmat::AbstractMatrix)