Scotland issue

Scottland issue

The system is created composing crazy river (easy version) with a stormy weather. The stormy weather is described as a an automaton wich models a sawtooth or a sinusoidal function.

Here a graphical representation

Tanks

Tanks automaton presents 2 tanks wich can overflow indipendently. If the first tank overflow water, the excedeed water go on tank number 2. If tank number 2 goes in overflow the excedeed water is lost. There is a third tank wich takes a costant flow from each of 2 tanks and purify it. It must garantee a minimal level of water to purify water.

State description

$S_0$ := overflow nowhere $S_1$ := overflow only on first tank $S_2$ := overflow only on second tank $S_3$ := overflow only on third tank $S_4$ := overflow on first and second tank $S_5$ := overflow on first and third tank $S_6$ := overflow on second and third tank $S_7$ := overflow on every tank

Transition table:

	S0	S1	S2	S3	S4	S5	S6	S7
a := $z_1>H_1$	S1	-	S4	S5	-	-	S7	-
b := $z_2>H_2$	S2	S4	-	S6	-	S7	-	-
c := $z_3>H_3$	S3	S5	S6	-	S7	-	-	-
d := $ \beta_1 * a + \alpha_1 * z_1 < 0 $	-	S0	-	-	S2	S3	-	S6
e := $ \beta_2 * a + \alpha_2 * z_2 < 0 $	-	-	S0	-	S1	-	S3	S5
f := $ \beta_3 * a + \alpha_3 * z_3 < 0 $	-	-	-	S0	-	S1	S2	S4

Controller

The controller check if one of a water level of the 3 tank in overflow is lower or greater than $ h_{min} $ or $ h_{max} $ respectively.

Valve

The valve has a variable (a) wich describes opening and closing states used by controller.