using "types";

# index-1 formulation

FlowSheet index_prob
	PARAMETERS
		e as negative;

	VARIABLES
		y1 as Real;
		y2 as Real;
		x  as Real;

	EQUATIONS
		diff(y1)*'s' = y2;
		diff(y2)*'s' = x;
		y1 - e*x = sin(time*'rad/s');

	SET
		e = -0.1; # system is unstable if e > 0, and index-3 if e = 0

	INITIAL
#		y1 = 1; # initial condition that tends to be inconsistent when e goes to zero
		y1 = 0;
		y2 = 1;

	OPTIONS
		DAESolver (File = "dasslc");
		TimeStep = 0.1;
		TimeEnd = 10;
		TimeUnit = 's';
end

# index-3 formulation

FlowSheet index_prob2
	VARIABLES
		y1 as Real;
		y2 as Real;
		x  as Real;

	EQUATIONS
		diff(y1)*'s' = y2;
		diff(y2)*'s' = x;
		y1 = sin(time*'rad/s');

	OPTIONS
		DAESolver (File = "dasslc");
		TimeStep = 0.1;
		TimeEnd = 10;
		TimeUnit = 's';
end