Consider the above figure depicting a system comprising two tanks containing water. Each tank is leaking at a constant rate. Water is added at a constant rate to the system through a hose, which at any point in time is filling either one tank or the other. It is assumed that the hose can switch between the tanks instantaneously. For {1,2}, let _i denote the volume of water in Tank i and

_i > 0 denote the constant flow of water out of Tank i. Let w denote the constant flow of water into the system. The objective is to keep the water volumes above ₁ and _$, respectively, assuming that the water volumes are above ₁ and _$ initially. This is to be achieved by a controller that switches the inflow to Tank 1 whenever ₁() ₁() and to Tank 2 whenever _$()

_$()

The hybrid automaton representing this two-tank system is given below figure

Construct a model of this hybrid automaton in Ptolemy II . Use the following parameter values: ₁ = _$ = 0, ₁ = _$ = 0.5, and = 0.75. Set the initial state to be (₁; (0; 1)). (That is, initial value ₁ is 0 and _$ is 1.) Simulate your model for 100 seconds and plot how ₁ and _$ vary as a function of time t.

Please provide your model files, your Plot, and a document

x1(0)r1x2(0)r2x1(t)=wv1x2(t)=v2x1(0)r1x2(0)r2