Clocked thermostat

Model

using ReachabilityAnalysis, ModelingToolkit

const A1 = 40.0
const A2 = 30.0
const B = 0.5
const t1 = 75
const t2 = 65

const var′ = @variables t t′

function thermostat_on′()
    invariant = HalfSpace(t <= t1, var′)
    @system(x' = [-B 0; 0 0] * x + [A1, 1], x ∈ invariant)
end

function thermostat_off′()
    invariant = HalfSpace(t >= t2, var′)
    @system(x' = [-B 0; 0 0] * x + [A2, 1], x ∈ invariant)
end

function thermostat_hybrid′()
    automaton = GraphAutomaton(2)
    add_transition!(automaton, 1, 2, 1)
    add_transition!(automaton, 2, 1, 2)

    mode1 = thermostat_on′()
    mode2 = thermostat_off′()
    modes = [mode1, mode2]

    # transition on -> off
    guard = HalfSpace(t >= t1, var′)
    trans1 = ConstrainedIdentityMap(1, guard)
    # transition off -> on
    guard = HalfSpace(t <= t2, var′)
    trans2 = ConstrainedIdentityMap(1, guard)
    resetmaps = [trans1, trans2]

    return HybridSystems.HybridSystem(automaton, modes, resetmaps, [AutonomousSwitching()])
end

function model(X0)
    H = thermostat_hybrid′()
    return IVP(H, X0)
end

model (generic function with 1 method)

References