Parametric Modeling and Simulations with Modelica

Constraints have certain reserved keywords. They are

• der - Derivative, e.g. der(x)
• sin - Sine of radian
• cos - Cosine of radian
• tan - Tangent of radian
• min - Minimum, e.g. min(1,2,4) = 1
• max - Maximum, e.g. max(1,2,4) = 4

Common Built-in Variables can be modified in the 'Edit Constraint Block'. Click the 'Edit Built-in Variable' button. If you have more than one then separate them with a ','. Recommend to add:

• time

• Create a package where you want to do your parametric modeling. I've kept it simple and called it 'Modeling'

• Create a block diagram for this package

• Inside the BDD insert a Block and give it the name of your parametric model. I've called it 'Water_Quality_Model'

• Add to the package relevant Constraint Blocks. Add part association relationships between constraint blocks (source) to the model block (target).

• Add equations to your Constrain Blocks. If you will use an equation more than once (e.g. Inversion: a = 1/b) add another part association relationship between the Constraint Block and the Model Block. Don't forget to add a name to the additional usage to avoid confusion later.
• You can't just have equations, you need inputs and outputs. Add to the BDD relevant Blocks that holds these inputs and outputs. Add a reference association relationship between these blocks and the Model Block

• With the building blocks ready for your parametric model you need to actually create the parametric relationships between the inputs, outputs and equation variables. Right click the Model Block → Add Child Diagram… → Parametric Diagram
• In the PAR diagram make sure to use the Binding Connector between variables. If you have a variable that doesn't have a connection it may suggest that you've missed something

• Making PAR diagrams look presentable is hard and probably takes as long if not longer than making all the connections. If you have a coffee break and looking for something to do then get to making your parametric model look presentable. Welcome to the churn!

The below is largely based on Creating a Parametric Model: Simulation Functions by Sparx Enterprise Architect which can be found here.

• Modelica supports a limited number of mathematical functions, like 'min()' to return minimum value of a set, out of the box. If you want to create a function, say range() then that's where you come in. Note the below created function is obsolete as min() already exists (at the time of writing this function I didn't know that…)
• Insert a Constraint Block, call it 'Minimum' (it doesn't have to be the same name of your function).
• Add an Operation (right click → Features → Operations…). Click 'New Operation…'
• Give it the same name as your intended function (here I've given it 'min').
• In Parameters give each parameter a name, type and direction.

• The Return Type is the same as the output. I've always kept Scope Public.
• In Stereotype if you can't find 'SimFunction' then just create it
• With the Features window still visible right click your newly minted operation and choose Properties…
• In the code section add the following code and save it.

min_output := 

if min_input_1 <= min_input_2 then 
	min_input_1
else 
	min_input_2;

• Now that the min() operation has been defined you can use it in your equations.
• In the Constrain Block define an equation using your function, e.g. a=min(b,c)

• If you are getting a 'parameter x of constrain y does not have an input or output relationship' when it appears to be then check the model tree. It has been known that parameters are replicated (so it looks like you have 2 parameter x where only one should be)
• Likewise if you are getting 'Too many equations, over-determined system' you have unwittingly binded the replicated parameters to form more equations then you actually need.
• As of the time of writing parameters are replicated if you removed a property from the parametric diagram and reintroduced the same property
• Are your blocks in a different namespace to the package that contains your simulation artifact? If so then add a package import relationship to the namespace that contains these blocks
• Always use Binding Connector to connect parameters
• Models, parameters, constraints and blocks name can not have any special characters, including space