I am creating a Max Per Interval block in Wolfram System Modeler.
To make it easy for me to explain, I just set the Max value to 10.
block HighWaterMarkPerInterval
extends Modelica.Blocks.Interfaces.SISO;
protected
Integer index;
Real currentMax;
Real endTimes[1, 45] = [30812532.2, 32037805, 33265581.8, 34493233.8, 35720861.5, 36948483, 38176307.7, 39426940.6, 40654485.4, 41882212.1, 43109672.7, 44337076, 45564265.7, 46793039.6, 48045130.9, 50749960.3, 52040090.6, 53558507.7, 54814537.3, 56331978.2, 57587753.3, 59105952.9, 60362517.8, 61879307.8, 63136031.5, 64363411.4, 65590464.3, 67738027.40000001, 84725789.8, 87831338.09999999, 89030965.40000001, 90258821.8, 91486663.5, 92714210.3, 93941727.7, 95166770.3, 97283519, 99434222.90000001, 100658067.1, 102807019, 104030032.7, 106179193, 107402090, 109550214.2, 110771545.3];
algorithm
if endTimes[1, index] < time then
index := pre(index) + 1;
currentMax := 0;
else
currentMax := 10; // Constant to until I get logic working
end if;
initial algorithm
index := 0;
equation
y = currentMax;
end HighWaterMarkPerInterval;
When ran, index increments to infinity right off the bat. I figure there is something wrong with my logic, but I can't figure it.
The code is supposed to check to see if we are still in the interval time, and when we cross over into the next interval time it sets the "currentMax" value to zero. Which will reset the Max value I've implemented in another block.
Any help would be appreciated. Thanks.
EDIT: Code section form example.
model HighWaterMarkPerInterval
annotation(Diagram(coordinateSystem(extent = {{-148.5, -105}, {148.5, 105}}, preserveAspectRatio = true, initialScale = 0.1, grid = {5, 5})));
extends Modelica.Blocks.Interfaces.SISO;
Modelica.Blocks.Math.Max maxblock(u1 = currentMax, u2 = u);
Real flybyEnds[1, 45] = [30813151,32038322,33266015, truncated for space saving...];
Integer index;
Real currentMax;
initial equation
index = 1;
currentMax = 0;
algorithm
// When we are in the interval continually grab max block output and output currentMax
when {time>=flybyEnds[1, index-1], time <=flybyEnds[1,index]} then
currentMax := pre(maxblock.y);
y := currentMax;
end when;
// When we move to the next interval reset current max and move to the next interval
when time > flybyEnds[1, index] then
currentMax := 0;
index := pre(index) + 1;
end when;
end HighWaterMarkPerInterval;
You need to use when, not if. You can find a discussion about both and the differences between them in Modelica by Example.
This issue has also been discussed on SO both here and here.
Here is an example (completely untested, but it shows the basic idea):
model HighWaterMarkPerInterval
extends Modelica.Blocks.Interfaces.SISO;
parameter Modelica.SIunits.Time sample_rate=3600;
Real flybyEnds[45] = {30813151,32038322,33266015,...};
Integer index;
Real currentMax;
initial algorithm
// Specify the first time we are interested in...
index := 1;
algorithm
// At the start of the simulation, the initial max for the current
// interval [0,30813151] is whatever u is. The initial output value
// is also the initial value for u
when initial() then
currentMax := u
y := u;
end when;
// Check at some sample rate (faster than the flyby interval!)
// if u > currentMax...
when sample(sample_rate, sample_rate) then
// New currentMax is the larger of either currentMax or u
// when the sample took place
currentMax := max(pre(currentMax), pre(u));
end when;
// At the end of the "flyby", record the maximum found since
// the last flyby and specify the next flyby index.
when time>=flybyEnd[index] then
// New output is the value of currentMax from this interval
y := pre(currentMax);
// Now reset currentMax
currentMax := pre(u);
// Increment index up to the length of flybyEnd
index := min(pre(index)+1, size(flybyEnd,1));
end when;
end HighWaterMarkPerInterval;
Related
I've created what is a fairly simple MATLAB script to simulate the behaviour discussed in this question over on Maths SE.
clearvars;
samples = 1000;
x = 256;
r=exprnd(1/20e6,1,samples); % Generate exponentially distributed randoms.
endTime = sum(r);
quickMean=sum(r(1:x))/x; % Quick calc the mean and median.
quickMedian=0.693 * quickMean;
p = cumsum(r); % Convert event deltas into timestamps
bitstream = false(1,samples);
time = 0;
lastTime = 0;
for i = 1:samples
lastTime = time;
time = time + quickMedian;
if (numel(p(p < time & p > lastTime)) > 0)
bitstream(i) = true;
end
if (time > p(end))
break
end
end
ratio = sum(bitstream)/samples;
The script seems to work, however, if I use a large number of samples (say a million), which would be beneficial, it really crawls.
I'm assuming that the problematic statement is this one:
p(p < time & p > lastTime)
Is there a more efficient way to check if any elements in an array fall between two values?
As I mentioned in my comment, we can use the fact that p is monotonically increasing and ignore values less than lastTime. If we find the last value for which p < time, only the values to the right can be greater than* time on the next iteration (lastTime).
clearvars;
samples = 1000;
x = 256;
r=exprnd(1/20e6,1,samples); % Generate exponentially distributed randoms.
endTime = sum(r);
quickMean=sum(r(1:x))/x; % Quick calc the mean and median.
quickMedian=0.693 * quickMean;
p = cumsum(r); % Convert event deltas into timestamps
bitstream = false(1,samples);
time = 0;
lastTime = 0;
% code is the same up to here ---
lastTimeIdx = 1; % index of (last value < lastTime) + 1
for i = 1:samples
lastTime = time;
time = time + quickMedian;
valsInRange = p(lastTimeIdx:end) < time; % p > lastTime & p < time
timeIdx = find(valsInRange, 1, 'last'); % returns [] or index
if ~isempty(timeIdx)
bitstream(i) = true;
lastTimeIdx = lastTimeIdx + timeIdx; % update start of next search
end
if (time > p(end))
break
end
end
ratio = sum(bitstream)/samples;
*Actually, this is "greater than or equal to", but since the values of p are unique, they are the same thing.
Okay, I just tried histc in Octave. I'm embarrassed to say that it's ridiculously fast. Like 4 orders of magnitude faster. Here's the code I used, but histc is deprecated in MATLAB, and the binning for histcounts is different, so you may have to play with it a bit.
bitstream_hist = histc(p, [0:samples]*quickMedian) > 0;
bitstream_hist = bitstream_hist(1:samples);
One million samples finishes in a fraction of a second. Sorry I didn't think of this sooner.
Let’s examine that whole expression:
numel(p(p < time & p > lastTime)) > 0
We can separate that out for clarity:
I = p < time & p > lastTime;
tmp = p(I);
n = numel(tmp);
n > 0
Here, the creation of tmp is pretty expensive: it looks at where I is true, and it copies those elements over to a new array. But the only thing you do with this array is seeing how many elements it has. Logically n will be equal to the number of true elements in I. And you don’t really need this number, you just need to know if it’s larger than 0. That is, you want to know if any of the elements in I is true. You can do so with any:
any(p < time & p > lastTime)
I'm trying to implement a DFT on my own because the FFT example in OpenModelica is not working for me and I can't figure out why.
But I'm already stuck sampling a sine function and assigning the sampled values to a buffer array.
This is why I tried to make it even simpler and just assign a counter variable "iTick" to the array which still doesn't work.
See the basic example.
Can anyone tell me why this is not working and how I can actually assign a value to the array when using the sample() function ??
block DFT
import Modelica.Constants.pi;
parameter Integer N = 360 "Total number of samples";
Integer iTick;
Real y_buf[N];
algorithm
when sample(0, 0.1) then
iTick :=iTick + 1;
if iTick >= 1 and iTick <= N then
y_buf[iTick] := iTick;
end if;
end when;
end DFT;
[358] 14:56:15 Symbolisch Warnung
The linear system:
1 : $PRE.y_buf[2] = y_buf[2]
2 : y_buf[2] = $PRE.y_buf[2]
[
-1.0 , 1.0 ;
1.0 , -1.0
]
*
[
y_buf[2] ;
$PRE.y_buf[2]
]
=
[
0.0 ;
0.0
]
might be structurally or numerically singular for variable $PRE.y_buf[2] since U(2,2) = 0.0. It might be hard to solve. Compilation continues anyway.
[359] 14:56:15 Symbolisch Warnung
The linear system:
1 : $PRE.y_buf[1] = y_buf[1]
2 : y_buf[1] = $PRE.y_buf[1]
[
-1.0 , 1.0 ;
1.0 , -1.0
]
*
[
y_buf[1] ;
$PRE.y_buf[1]
]
=
[
0.0 ;
0.0
]
might be structurally or numerically singular for variable $PRE.y_buf[1] since U(2,2) = 0.0. It might be hard to solve. Compilation continues anyway.
[360] 14:56:15 Übersetzung Warnung
Assuming fixed start value for the following 2 variables:
y_buf[360]:DISCRETE(fixed = false ) type: Real [360]
iTick:DISCRETE(fixed = false ) type: Integer
After a long search and try and error I found out that the magic word "discrete" solves my problem! I can't yet explain why, but see below the working example:
model Test
import Modelica.Constants.pi;
parameter Integer N = 360 "Total number of samples";
Integer iTick(start=0, fixed=true);
discrete Real y_buf[N](start=fill(0,N), fixed=fill(true, N));
algorithm
when sample(0, 0.1) then
iTick :=iTick + 1;
if iTick >= 1 and iTick <= N then
y_buf[iTick] := iTick;
end if;
end when;
end Test;
Hopefully this is a help to someone!
Your "Symbolisch Warnung" disappears once you initialize iTick and y_buf. However, the code still does not work. OpenModelica simulates it, but the items of y_buf are never updated.
This issue might be related to this question where the delay operator is not working in algorithm sections. Therefore, I suggest a similar workaround: Try to avoid the algorithm section. With an equation section and proper initialization, your minimal example could look as follows:
block DFT
import Modelica.Constants.pi;
parameter Integer N = 360 "Total number of samples";
Integer iTick(start=0, fixed=true);
Real y_buf[N](start=fill(0, N), fixed=fill(true, N));
equation
when sample(0, 0.1) then
iTick = pre(iTick) + 1;
end when;
for i in 1:N loop
when iTick >= i then
y_buf[i] = iTick;
end when;
end for;
end DFT;
I'm trying to simulate Coulomb friction in Modelica. The basic concept is to check if relative velocity speed between to surfaces is less than a constant and the external force which tried to slid surfaces against each other is less than maximum static friction force (normalForce * staticFrictionCoefficient) then the friction force is equal to negative of the external shear force. otherwise, the friction force is equal to the kinetic friction force (normalForce * kineticFrictionCoefficient)in the opposite direction of the sliding direction.
I implemented this concept in Modelica as below:
function coulombFriction
input Real relVel;
input Real shearForce;
input Real normalForce;
input Real statfricco;
input Real kinfricco;
output Real fricForce;
algorithm
if relVel==0 and abs(shearForce)<statfricco*normalForce then
fricForce:=shearForce;
else
fricForce:=kinfricco*normalForce*sign(relVel);
end if;
end coulombFriction;
but when I call this function from a model as below:
model fricexample_1
extends coulombFriction;
//parameters
parameter Real kco=0.3;
parameter Real sco=0.4;
parameter Real nfo=1.0;
Real sfo;
Real ffo;
Real x;
Real v;
initial equation
x=0;
v=0;
equation
v=der(x);
der(v)=sfo-ffo;
sfo=time;
ffo=coulombFriction(relVel=v, shearForce=sfo, normalForce=nfo, statfricco=sco, kinfricco=kco);
end fricexample_1;
I see the error:
Translation Error
post-optimization module findZeroCrossings (simulation) failed.
If I remove the abs function from the defined function, it solves the compiling problem, but the model is wrong! I would appreciate if you could help me know:
how can I solve this problem?
how to model friction otherwise?
You can use noEvent on the conditions that might generate events in the function. Note that you don't need to extend the model with the function.
It should actually not work (to extend a model from a function), but it seems we don't check for it.
The model that compiles for me is below:
package Friction
function coulombFriction
input Real relVel;
input Real shearForce;
input Real normalForce;
input Real statfricco;
input Real kinfricco;
output Real fricForce;
algorithm
if noEvent(relVel==0) and noEvent(abs(shearForce)<statfricco*normalForce) then
fricForce:=shearForce;
else
fricForce:=kinfricco*normalForce*sign(relVel);
end if;
end coulombFriction;
model fricexample_1
//parameters
parameter Real kco=0.3;
parameter Real sco=0.4;
parameter Real nfo=1.0;
Real sfo;
Real ffo;
Real x;
Real v;
initial equation
x = 0;
v = 0;
equation
v = der(x);
der(v) = sfo-ffo;
sfo = time;
ffo = coulombFriction(relVel=v, shearForce=sfo, normalForce=nfo, statfricco=sco, kinfricco=kco);
end fricexample_1;
end Friction;
Your model does work with the 1.11 release. The issue is the extends coulombFriction; statement. Once you removed it, it should work fine even without the noEvent calls:
package Friction
function coulombFriction
input Real relVel;
input Real shearForce;
input Real normalForce;
input Real statfricco;
input Real kinfricco;
output Real fricForce;
algorithm
if relVel==0 and abs(shearForce)<statfricco*normalForce then
fricForce:=shearForce;
else
fricForce:=kinfricco*normalForce*sign(relVel);
end if;
end coulombFriction;
model fricexample_1
parameter Real kco=0.3;
parameter Real sco=0.4;
parameter Real nfo=1.0;
Real sfo;
Real ffo;
Real x;
Real v;
initial equation
x = 0;
v = 0;
equation
v = der(x);
der(v) = sfo-ffo;
sfo = time;
ffo = coulombFriction(relVel=v, shearForce=sfo, normalForce=nfo, statfricco=sco, kinfricco=kco);
end fricexample_1;
end Friction;
I'd recommend to reuse the friction state machine available in the Modelica Standard Library. An example, that works in OpenModelica and other tools, is given by https://github.com/dzimmer/ZimmersModelicaTutorial/blob/master/Tutorial2015/BaseComponents/Friction/IdealDryFriction.mo.
Actually, the model I have developed above for Columb friction is wrong. Thanks to this post I could find the correct version:
package friction1D
final constant Real eps=1.e-15 "Biggest number such that 1.0 + eps = 1.0";
function sgn
input Real inputVar;
output Real outputVar;
algorithm
if noEvent(inputVar < 0) then
outputVar := -1;
else
outputVar := 1;
end if;
end sgn;
function coulombFriction
input Real relVel;
input Real shearForce;
input Real normalForce;
input Real statfricco;
input Real kinfricco;
output Real fricForce;
algorithm
if noEvent(abs(relVel) < eps) and noEvent(abs(shearForce) < statfricco * normalForce) then
fricForce := shearForce;
else
fricForce := kinfricco * normalForce * sgn(relVel);
end if;
end coulombFriction;
model fricexample_1
//parameters
parameter Real kco = 0.3;
parameter Real sco = 0.4;
parameter Real nfo = 1.0;
parameter Real mass = 1.0;
Real sfo;
Real ffo;
Real x;
Real v;
initial equation
x = 0;
v = 0;
algorithm
sfo := 0.7 * sin(time);
ffo := coulombFriction(relVel = v, shearForce = sfo, normalForce = nfo, statfricco = sco, kinfricco = kco);
equation
v = der(x);
mass * der(v) = sfo - ffo;
annotation(
experiment(StartTime = 0, StopTime = 10, Tolerance = 1e-8, Interval = 0.02),
__OpenModelica_simulationFlags(lv = "LOG_STATS", outputFormat = "mat", s = "dassl"));
end fricexample_1;
end friction1D;
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.