add on-off example (#20)

* add on-off example

* import packages

Author: baggepinnen

docs/make.jl

@@ -32,6 +32,7 @@ makedocs(;
              ],
              "Examples" => [
                 "Controlled DC motor" => "examples/dc_motor_pi.md",
+                "On-off controller" => "examples/onoffcontroller.md",
              ],
              "Library API" => "blocks.md",
          ],

docs/src/examples/onoffcontroller.md

@@ -0,0 +1,38 @@
+# On-off controller
+A common form of controller is one which can output two distinct values only, such as on/off, or 1/-1. Below, we demonstrate the usage of such a controller, the [`DiscreteOnOffController`](@ref), and let it control an unstable first-order system. The system is given by the equation
+```math
+τ \dot x = x + 10u
+```
+where ``τ = 100`` is a time constant. The controller ``u = f(x)`` is an on/off controller with a hysteresis band of 0.3 and possible output values -1 and 1. The controller runs with an update frequency of 1 Hz.
+
+
+```@example ONOFF
+using ModelingToolkit, ModelingToolkitSampledData, OrdinaryDiffEq, Plots
+using ModelingToolkit: t_nounits as t, D_nounits as D
+using ModelingToolkitStandardLibrary.Blocks
+using JuliaSimCompiler
+cl = Clock(1)
+z = ShiftIndex(cl)
+@mtkmodel OnOffModel begin
+    @components begin
+        onoff = DiscreteOnOffController(; b = 0.3, z, bool=false)
+        c = Constant(k=1)
+    end
+    @variables begin
+        x(t) = 0 
+    end
+    @equations begin
+        onoff.u ~ Sample(cl)(x)
+        connect(c.output, onoff.reference)
+        100D(x) ~ x + 10Hold(onoff.y)
+    end
+end
+@named m = OnOffModel()
+m = complete(m)
+ssys = structural_simplify(IRSystem(m))
+prob = ODEProblem(ssys, [m.onoff.y(z-1) => 0], (0.0, 40.0))
+sol = solve(prob, Tsit5(), dtmax=0.1)
+plot(sol, idxs=[m.x, m.onoff.y], title="On-off control of an unstable first-order system")
+```
+
+The parameter `b` controls the width of the hysteresis band, and the structural parameter `bool = false` indicates that this is a 1/-1 controller and not a 0/1 controller. The controller additionally takes a parameter `k` which is the gain of the controller, here we used the default `k = 1`.