What is the meaning of "Algebraic loop involving integers or booleans" in the error message - modelica

Question

I'm making the PI controller using the Dymola Platform and i met the error message like below
And here's some of my code that consist of valve which calculate the disp and PI controller which control the amount of the disp.
They are communicating each other using the flag
//PI controller///
if flag_input==1 then //flag_input==1 : Stop control / flag_input==0 : Restart control//
control:=0;
else
control:=(P_term+I_term)/unit;
end if;
if error<0 then // error<0 : flag to Valve to restart calculating the disp//
flag_output:=1;
else
flag_output:=0;
end if;
//Valve//
if (26/5)*(thetta/(2*pi))*0.001>0.026 and flag_input==0 then
//restart calculating the disp when received flag==1 from the PI controller//
disp:=0.026;
flag:=1;
elseif (26/5)*(thetta/(2*pi))*0.001<0 and flag_input==0 then
disp:=0;
flag:=1;
else
disp:=(26/5)*(thetta/(2*pi))*0.001;
flag:=0;
end if;
Can someone tell me what is the meaning of algebraic loop error and figure out the problem?

Answer 1

From your code snippet it's hard to tell where exactly the problem is.
Dymola tells you that you created a large algebraic loop over all the variables listed at the top under Unknowns and the equations listed below in the section Equations.
This can happen easily when you create if statements with variables which depend on each other. Often you just have to use pre() at the right place to break the loop.
Let`s use another small example to explain the problem.
For some reason we try to count the full milliseconds, which have passed in the current simulation and stop, once we reach 100.
model count_ms
Integer y(start=0);
equation
if y >= 100 then
y = 100;
else
y = integer(1000*time);
end if;
end count_ms;
This code will produce a similar error as yours:
An algebraic loop involving Integers or Booleans has been detected.
Unknowns: y
Equations: y = (if y >= 100 then 100 else integer(1000*time));
From the error message we see that y can not be solved, due to the equation resulting from the if statement. The equation is not solvable, as y depends on itself. To solve such problems pre was introduced, which gives you access to the value of a variable had when the event was triggered.
To fix the code above, we simply have to use pre when we check for y
if pre(y) >= 100 then
and the model simulates as expected.