Assume I have a large connector involving all kinds of base types (Real, Integer, String, Boolean). How can I switch connections based on state events?
I would like to do something like this:
model switch
input ComplicatedConnector icon[2];
output ComplicatedConnector ocon;
input Real x;
equation
if x >= 0 then
connect(ocon, icon[1]);
else
connect(ocon, icon[2]);
end if;
end switch;
This does not work. How can it be properly expressed in Modelica?
Answer based on comment by Adrian Pop.
model switch
input ComplicatedConnector icon[2];
output ComplicatedConnector ocon;
input Real x;
ComplicatedConnector con;
initial equation
con = icon[1];
equation
connect(ocon, con);
when x >= 0 then
con := icon[1];
end when;
when x < 0 then
con := icon[2];
end when;
end switch;
Update: The model above is wrong because ocon outputs the initial value of icon[1] forever if no event occurs which is not what you would expect from a switch. Note that this is not due to a wrong answer but due to my false interpretation of the answer. The following model is based on the answer by Michael Tiller.
model switch
input ComplicatedConnector icon[2];
output ComplicatedConnector ocon;
input Real x;
Integer k;
initial equation
k = 1;
equation
ocon = icon[k];
when x >= 0 then
k := 1;
elsewhen x < 0 then
k := 2;
end when;
end switch;
Is not possible. You can only switch them based on a parameter known at compile time (also known as structural parameter). The condition in the if equation containing connects needs to be a parameter expression.
Note that connect statements are equations. You can expand them out yourself. They exist mainly to avoid "bookkeeping" errors for generating boilerplate equations. So what I suggest you do is simply take your switch model and expand each connect into equations. The it should work.
Related
The following model in Dymola gives an error,
model Test1
Real outvar;
Real outvarc;
Real internal;
parameter Real Tp=0.1;
equation
when Clock(Tp) then
internal = time;
end when;
outvar = hold(outvarc);
algorithm
if (firstTick(internal)) then
outvarc := 1;
else
outvarc := previous(outvarc);
outvarc := outvarc + 1;
end if;
end Test1;
If I modify the variable internal as follows then the model works.
model Test2
Real outvar;
Real outvarc;
Boolean internal(start=true);
parameter Real Tp=0.1;
equation
when Clock(Tp) then
internal = false;
end when;
outvar = hold(outvarc);
algorithm
if (firstTick(internal)) then
outvarc := 1;
else
outvarc := previous(outvarc);
outvarc := outvarc + 1;
end if;
end Test2;
Is there any explanation why model Test1 is giving an error?
It fails in Dymola 2022x and earlier.
In Dymola 2023 and later it gives the warning:
The sub clock, BaseClock_0.SubClock_1, includes pre, time, or
non-clocked when, but no solver method is specified. This is not
correct according to the specification and it could indicate that it
was clocked by mistake. The warning can be disabled by setting
Advanced.Translation.WarnForMissingSolverMethod=false;
That suggests that the simplest solution would be:
when Clock(Tp) then
internal = sample(time);
end when;
Basically time is not a clocked variable. (Yes, I'm aware that time in clocked partitions is messier than this suggests.)
Here is a suggestion for a little more compact code of the overall model. It gives a bit different results as it uses the "discrete time" internal to make equations discrete/clocked automatically, but I guess the would be the use-case anyways (otherwise sampling time does not make a lot of sense).
model Test3
parameter Real Tp=0.1;
discrete Real internal; // "discrete" is optional in Dymola, but helps understanding
discrete Real outvarc(start=1, fixed=true); // setting an initial value
Real outvar;
equation
internal = sample(time, Clock(Tp)); // sampling time with a locally defined clock and store it to "internal"
outvarc = previous(outvarc)+internal; // using a sampled/clocked variable (internal) makes the equation discrete
outvar = hold(outvarc); // converting to a continuous variable from a clocked one
end Test3;
Suggestions for further improvements welcome...
I have a contrived Modelica model in which a have a state machine variable manipulated by multiple when statements:
model WhenExample
type State = enumeration(first, second, third);
State state;
initial equation
state = State.first;
equation
when sample(0, 1) then
state = State.second;
end when;
when sample(0, 3) then
state = State.third;
end when;
end WhenExample;
When compiling under OpenModelica OMC, I get the following error:
[1] 16:46:39 Symbolic Error
Too many equations, over-determined system. The model has 2 equation(s) and 1 variable(s).
This kinda makes sense as I do have two equations for my single state variable. However, those equations only apply at discrete points in time, right?
Do I need to make sure all "manipulations" of a particular variable happen only in a single when statement?
See Modelica Spec, section 8.5 Events and Synchronization:
https://www.modelica.org/documents/ModelicaSpec33Revision1.pdf
Just before section 8.6 there is an example that should help you.
Some code based on that is given below:
model WhenExample
parameter Integer multiplySample = 3;
Boolean fastSample, slowSample;
Integer ticks(start=0);
type State = enumeration(first, second, third);
State state(start = State.first);
equation
fastSample = sample(0,1);
algorithm
when fastSample then
ticks := if pre(ticks) < multiplySample then pre(ticks)+1 else 0;
slowSample := pre(ticks) == 0;
state := State.second;
end when;
when slowSample then
state := State.third;
end when;
end WhenExample;
I'm trying to create a model where one Modelica variable is a triangular wave of another variable. First I tried the floor() function as below:
model test1
final constant Real pi=2*Modelica.Math.asin(1.0);
parameter Real b = 1;
parameter Real a = 1;
Real x,p,u;
equation
if sign(sin(x*pi/b))>=0 then
p=a*(x-b*floor(x/b));
else
p=a*(b-(x-b*floor(x/b)));
end if;
x=time;
u = floor(x/b);
end test1
(x=time; is arbitrary so the model compiles)
but the result is weird, as you can see below
zoom in:
somehow 0.005 seconds before the next step floor function behaves unexpectedly and becomes a linear function ending by the next value.
then I tried the ceil() function. everything seemed right till I realised the same problem happens with ceil() function at other values (e.g. x=13)
I would appreciate if you could:
help me understand why this "glitch" happens and if it is intentional by design or a bug?
how I can fix this?
are there any alternatives to create a triangular wave function?
P.S. I am using this "wave function" to model the interaction between two jagged bodies"
If you are allowed to utilize the Modelica Standard Library, you can build up a parametrized, time-based zigzag signal using the CombiTimeTable block with linear interpolation and periodic extrapolation. For example,
model Test4
parameter Real a=2 "Amplitude";
parameter Real b=3 "Period";
Real y=zigzag.y[1] "Zigzag";
Modelica.Blocks.Sources.CombiTimeTable zigzag(
table=[0,0;b/4,a;b/4,a;b/2,0;b/2,0;3*b/4,-a;3*b/4,-a;b,0],
extrapolation=Modelica.Blocks.Types.Extrapolation.Periodic)
annotation(Placement(transformation(extent={{-80,60},{-60,80}})));
Modelica.Blocks.Sources.Trapezoid trapezoid(
amplitude=2*a,
rising=b/2,
width=0,
falling=b/2,
period=b,
offset=-a)
annotation(Placement(transformation(extent={{-80,25},{-60,45}})));
annotation(uses(Modelica(version="3.2.2")));
end Test4;
I don't have an explanation for the glitches in your simulation.
However, I would take another approach to the sawtooth function: I see it as an integrator integrating +1 and -1 upwards and downwards. The integration time determines the amplitude and period of the sawtooth function.
The pictures below show an implementation using MSL blocks and one using code. The simulation results below are the same for both implementations.
Best regards,
Rene Just Nielsen
Block diagram:
Code:
model test3
parameter Real a=2 "amplitude";
parameter Real b=3 "period";
Real u, y;
initial equation
u = 1;
y = 0;
equation
4*a/b*u = der(y);
when y > a then
u = -1;
elsewhen y < -a then
u = 1;
end when;
end test3;
Simulation result:
The problem I guess is due to floating point representation and events not occurring at exact times.
Consider x-floor(x) and 1-(x-floor(x)) at time=0.99, they are 0.99 and 0.01; at time=1.00 they are 0.0 and 1.0, which causes your problems.
For a=b=1, you can use the following equation for p:
p=min(mod(x,2),2-mod(x,2));. You can even add noEvent to it, and you can consider the signal continuous (but not differentiable).
model test
parameter Real b = 1;
parameter Real a = 3;
Real x, p;
equation
p = 2*a*min(1 / b * mod(x, b ),1 - 1/b * mod(x, b));
x = time;
end test;
My first advise would be to remove the sign-function, since there is no benefit of doing sign(foo)>=0 compared to foo>=0.
Interesting enough that seems to fix the problem in Dymola - and I assume also in OpenModelica:
model test1 "almost original"
final constant Real pi=2*Modelica.Math.asin(1.0);
parameter Real b = 1;
parameter Real a = 1;
Real x,p,u;
equation
if sin(x*pi/b)>=0 then
p=a*(x-b*floor(x/b));
else
p=a*(b-(x-b*floor(x/b)));
end if;
x=time;
u = floor(x/b);
end test1;
Now I only have to explain that - and the reason is that sin(x*pi/b) is slightly out of sync with the floor-function, but if you use sin(x*pi/b)>=0 that is within the root-finding epsilon and nothing strange happen.
When you use sign(sin(x*pi/b))>=0 that is no longer possible, instead of having sin(x*pi/b) an epsilon below zero it is now -1, and instead of epsilon above zero it is 1.
The real solution is thus slightly more complicated:
model test2 "working"
parameter Real b = 1;
parameter Real a = 1;
Real x,p,u;
Real phase=mod(x,b*2);
equation
if phase<b then
p=a/b*phase;
else
p=a-a/b*(phase-b);
end if;
x=time;
u = floor(x/b);
end test2;
which was improved based on a suggested solution:
model test3 "almost working"
parameter Real b = 1;
parameter Real a = 1;
Real x,p,u;
equation
if mod(x,2*b)<b then
p=a/b*mod(x,b);
else
p=a-a/b*mod(x,b);
end if;
x=time;
u = floor(x/b);
end test3;
The key point in this solution, test2, is that there is only one problematic event generating expression mod(x,2*b) - and the < will not get out of sync with this.
In practice test3 will almost certainly also work, but in unlikely cases the event generation might get out of sync between mod(x,2*b) and mod(x,b); with unknown consequences.
Note that all three examples are now modified to generate output that looks similar.
I would like to ask a Modelica question about when function, and the following source code cannot be properly functioned. The variable Pstart_CONV is an initial condition for der(x_calc) in the if statement, and the Pstart_CONV value is given by x when the "when statement" becomes true. Because x is a step function, I want to assign an initial condition for der(x_calc) so x can be continued for the whole domain.
Thank you very much,
Source:
model Unnamed4
Real Pstart_CONV;
Real P_crit_ratio;
parameter Real P_crit_ratio_criteria = 2.00;
Real x;
Real x_calc(start=0);
equation
P_crit_ratio = 10-time;
when P_crit_ratio <= P_crit_ratio_criteria then
Pstart_CONV = x;
end when;
if P_crit_ratio >= P_crit_ratio_criteria then
x = time^2;
x_calc = 0;
else
der(x_calc) = time * 5;
x = x_calc + Pstart_CONV;
end if;
end Unnamed4;
There are two issues I see with this code. The main one has to do with the fact that this is what is called a "variable index" problem. I'll address that. But first, I want to point out that your if and when clauses are not properly synchronized. What I mean by that is that the change in behavior represented by your if statement will not necessarily occur at the same instant that the when clause is activated.
To address this, you can easily refactor your model to look like this:
model Model1
Real Pstart_CONV;
Real P_crit_ratio;
parameter Real P_crit_ratio_criteria=2.00;
Real x;
Real x_calc(start=0);
Boolean trigger(start=false);
equation
P_crit_ratio = 10-time;
when P_crit_ratio <= P_crit_ratio_criteria then
Pstart_CONV = x;
trigger = true;
end when;
if trigger then
der(x_calc) = time * 5;
x = x_calc + Pstart_CONV;
else
x_calc = 0;
x = time^2;
end if;
end Model1;
Now, both the if and when clauses are tied to the trigger variable. Now we can address your main problem which is that on one side of your if statement you have:
der(x_calc) = time * 5;
...and on the other side you have:
x_calc = 0;
In practice, what this means is that for part of the simulation you solve x_calc using a differential equation while during the other part of the simulation you solve x_calc using an algebraic equation. This leads to the "variable index" problem because the "index" of the DAE changes depending on whether the value of trigger is true or false.
One approach to this is to modify the equations slightly. Instead of using the equation x_calc = 0 we specify an initial condition of 0 for x_calc and then enforce a differential equation that says the value of x_calc doesn't change, i.e., der(x_calc) = 0. In other words, get the same behavior by removing an algebraic equation settings x_calc to a constant and replacing it with an equation where we set the initial value of x_calc to be the desired value and then add a differential equation that, in effect, simply says the value of x_calc doesn't change.
Making such a change in your case leads to the following model:
model Model2
Real Pstart_CONV;
Real P_crit_ratio;
parameter Real P_crit_ratio_criteria=2.0;
Real x;
Real x_calc(start=0);
Boolean trigger(start=false);
initial equation
x_calc = 0;
equation
P_crit_ratio = 10-time;
when P_crit_ratio <= P_crit_ratio_criteria then
Pstart_CONV = x;
trigger = true;
end when;
if trigger then
der(x_calc) = time * 5;
x = x_calc + Pstart_CONV;
else
der(x_calc) = 0;
x = time^2;
end if;
end Model2;
I tested it, and this model ran using SystemModeler (although I don't know enough about your problem or the expected results to truly validate the results).
I hope that helps.
I try to compile the following code with Dymola:
class abc
import Modelica.SIunits;
parameter SIunits.Time delta_t=0.5;
constant Real a[:]={4,2,6,-1,3,5,7,4,-3,-6};
Real x;
Integer j(start=1);
Integer k=size(a, 1);
algorithm
when {(sample(0, delta_t) and j < k),j == 1} then
x := a[j];
j := j + 1;
end when;
end abc;
and for time = 0 the variable j starts with 2. But it should start with j = 1.
Does anybody have an idea for this problem?
Keep in mind that sample(x,y) means that sample is true at x+i*y where i starts at zero. Which is to say that sample(0, ...) becomes true at time=0.
Since j starts at 1 and k is presumably more than 1, it doesn't seem unexpected to me that sample(0, delta_t) and j<k should become true at the start of the simulation.
I suspect what you want is:
class abc
import Modelica.SIunits;
parameter SIunits.Time delta_t=0.5;
constant Real a[:]={4,2,6,-1,3,5,7,4,-3,-6};
Real x;
Integer j(start=1);
Integer k=size(a, 1);
algorithm
when {(sample(delta_t, delta_t) and j < k),j == 1} then
x := a[pre(j)];
j := pre(j) + 1;
end when;
end abc;
I don't really see the point of the j==1 condition. It is true at the outset which means it doesn't "become" true then. And since j is never decremented, I don't see why it should ever return to the value 1 once it increments for the first time.
Note that I added a pre around the right-hand side values for j. If this were in an
equation section, I'm pretty sure the pre would be required. Since it is an algorithm section, it is mainly to document the intent of the code. It also makes the code robust to switching from equation to algorithm section.
Of course, there is an event at time = 0 triggered by the expression sample(0, delta_t) and j<k which becomes true.
But in older versions of Dymola there is an bug with the initialization of discrete variables. For instance even if you remove sample(0.0, delta_t) and j<k in dymola74, j will become 2 at time=0. The issue was that the pre values of when clauses, where not initialized correct. As far as I know this is corrected at least in the version FD1 2013.