Minimum value over entire simulation - modeling

Question

In a continuous model, how do I save the minimum value of a variable during the simulation?
When a simulation has finished I want to display a variable T_min with a graphical annotation that shows me the lowest value of a temperature T during the simulation.
For example, if the simulated temperature T was a sine function, the desired result for the value of T_min would be:
In discrete code this would look something like this:
T_min := Modelica.Constants.inf "Start value";
if T < T_min then
T_min := T;
else
T_min := T_min;
end if;
... but I would like a continuous implementation to avoid sampling, high number of events etc.

Answer 1

I'm not sure if Renes solution is optimal. The solution generates many state events generated by the two if conditions. Embedded in the following model:
model globalMinimum2
Real T, T_min;
Boolean is_true;
initial equation
T_min = T;
equation
T =time/10*sin(time);
// if statement ensures that 'T_min' doesn't integrate downwards...
// ... whenever der(T) is negative;
if T < T_min then
der(T_min) = min(0, der(T));
is_true=true;
else
der(T_min) = 0;
is_true=false;
end if;
end globalMinimum2;
The simulation log is the following:
Integration started at T = 0 using integration method DASSL
(DAE multi-step solver (dassl/dasslrt of Petzold modified by Dynasim))
Integration terminated successfully at T = 50
WARNING: You have many state events. It might be due to chattering.
Enable logging of event in Simulation/Setup/Debug/Events during simulation
CPU-time for integration : 0.077 seconds
CPU-time for one GRID interval: 0.154 milli-seconds
Number of result points : 3801
Number of GRID points : 501
Number of (successful) steps : 2519
Number of F-evaluations : 4799
Number of H-evaluations : 18822
Number of Jacobian-evaluations: 2121
Number of (model) time events : 0
Number of (U) time events : 0
Number of state events : 1650
Number of step events : 0
Minimum integration stepsize : 1.44e-005
Maximum integration stepsize : 5.61
Maximum integration order : 3
Perhaps it is better to detect two events as given in the following example:
model unnamed_2
Real T;
Real hold;
Real T_min;
Boolean take_signal;
initial equation
hold=T;
equation
T = time/10*sin(time);
when (T < pre(hold)) then
take_signal = true;
hold = T;
elsewhen (der(T) >=0) then
take_signal = false;
hold = T;
end when;
if (take_signal) then
T_min = T;
else
T_min = hold;
end if;
end unnamed_2;
The simulation log shows that this solutions is more efficient:
Log-file of program ./dymosim
(generated: Tue May 24 14:13:38 2016)
dymosim started
... "dsin.txt" loading (dymosim input file)
... "unnamed_2.mat" creating (simulation result file)
Integration started at T = 0 using integration method DASSL
(DAE multi-step solver (dassl/dasslrt of Petzold modified by Dynasim))
Integration terminated successfully at T = 50
CPU-time for integration : 0.011 seconds
CPU-time for one GRID interval: 0.022 milli-seconds
Number of result points : 549
Number of GRID points : 501
Number of (successful) steps : 398
Number of F-evaluations : 771
Number of H-evaluations : 1238
Number of Jacobian-evaluations: 373
Number of (model) time events : 0
Number of (U) time events : 0
Number of state events : 32
Number of step events : 0
Minimum integration stepsize : 4.65e-006
Maximum integration stepsize : 3.14
Maximum integration order : 1
Calling terminal section
... "dsfinal.txt" creating (final states)

Answer 2

It seems I was able to finde an answer to my own question simply by looking at the figure above
The code is quite simple:
model globalMinimum
Modelica.SIunits.Temperature T, T_min;
initial equation
T_min = T;
equation
// if statement ensures that 'T_min' doesn't integrate downwards...
// ... whenever der(T) is negative;
der(T_min) = if T < T_min then min(0, der(T)) else 0;
end globalMinimum;