State Space Model as Simscape Thermal component

Hello, I want to include a thermal impedance model in state space representation. For this I want to create a custom simscape component in the following style:

component thermal_state_space

nodes
    input_1 = foundation.thermal.thermal; % input_1
    input_2 = foundation.thermal.thermal; % input_1
    input_3 = foundation.thermal.thermal; % input_1
    input_4 = foundation.thermal.thermal; % input_1
    
    output_1 = foundation.thermal.thermal; % output_1
    output_2 = foundation.thermal.thermal; % output_1
    output_3= foundation.thermal.thermal; % output_1
    output_4 = foundation.thermal.thermal; % output_1
    .
    .
    .
end

The dimensions of my state space matrices specify the numer of input nodes and output nodes.

Is there a predefined object I culd use for this? If not, what is the easiest representation of such a model?

Answer 1

[Shubham]

Hi Johannes,

There is no predefined object in Simulink that can directly represent a thermal impedance model in state space representation. However, you can create a custom Simulink component to represent this model using the Simulink Simscape language.

Here's an example of how you can create a custom Simscape component to represent a thermal impedance model in state space representation:

1. Create a new Simscape component in your Simulink model.
2. Define the nodes for your component. In your case, you have four input nodes and four output nodes. You can define them as follows:

nodes
    p1 = foundation.thermal.thermal;
    p2 = foundation.thermal.thermal;
    p3 = foundation.thermal.thermal;
    p4 = foundation.thermal.thermal;
    
    t1 = foundation.thermal.thermal;
    t2 = foundation.thermal.thermal;
    t3 = foundation.thermal.thermal;
    t4 = foundation.thermal.thermal;
end

3. Define the state variables for your component. In your case, you have a state space model, so you will need to define t he state variables as follows:

variables
    x = zeros(4, 1);
end

4. Define the state space matrices for your component. You can define them as follows:

parameters
    A = [-1.0, 0.5, 0.0, 0.0; 0.5, -1.0, 0.5, 0.0; 0.0, 0.5, -1.0, 0.5; 0.0, 0.0, 0.5, -1.0];
    B = [1.0, 0.0, 0.0, 0.0; 0.0, 1.0, 0.0, 0.0; 0.0, 0.0, 1.0, 0.0; 0.0, 0.0, 0.0, 1.0];
    C = [1.0, 0.0, 0.0, 0.0; 0.0, 1.0, 0.0, 0.0; 0.0, 0.0, 1.0, 0.0; 0.0, 0.0, 0.0, 1.0];
    D = [0.0, 0.0, 0.0, 0.0; 0.0, 0.0, 0.0, 0.0; 0.0, 0.0, 0.0, 0.0; 0.0, 0.0, 0.0, 0.0];
end

5. Define the equations for your component. You can define them as follows:

equations
    t1 == x(1);
    t2 == x(2);
    t3 == x(3);
    t4 == x(4);
    
    der(x) == A * x + B * [p1.p; p2.p; p3.p; p4.p];
    
    [output_1.p; output_2.p; output_3.p; output_4.p] == C * x + D * [p1.p; p2.p; p3.p; p4.p];
end

6. Connect your component to the rest of your Simulink model.

This example assumes that you have a thermal impedance model that can be represented by a state space model with four inputs and four outputs. You will need to modify the component to match the dimensions of your state space matrices and the number of input and output nodes in your model.

I hope this helps!

[Johannes Flohe]

Dear @Shubham, thank you for your help. If I try to run your code, the struct with the field ".p" in p1...p4 and output_1... output_4 is not defined. Can you also implement it direct with the inputs und outputs right away?

equations
    t1 == x(1);
    t2 == x(2);
    t3 == x(3);
    t4 == x(4);
    
    der(x) == A * x + B * [p1; p2; p3; p4];
    
    [output_1; output_2; output_3; output_4] == C * x + D * [p1; p2; p3; p4];
end

[Shubham]

Hi Johannes,

You are correct that the .p field is not defined for the foundation.thermal.thermal nodes in Simscape. Instead, you can directly use the nodes as inputs and outputs in the equations section. Here is the updated code:

component thermal_state_space
    nodes
        input_1 = foundation.thermal.thermal; % input_1
        input_2 = foundation.thermal.thermal; % input_2
        input_3 = foundation.thermal.thermal; % input_3
        input_4 = foundation.thermal.thermal; % input_4

        output_1 = foundation.thermal.thermal; % output_1
        output_2 = foundation.thermal.thermal; % output_2
        output_3 = foundation.thermal.thermal; % output_3
        output_4 = foundation.thermal.thermal; % output_4
    end

    variables
        x = zeros(4, 1);
    end

    parameters
        A = [-1.0, 0.5, 0.0, 0.0; 0.5, -1.0, 0.5, 0.0; 0.0, 0.5, -1.0, 0.5; 0.0, 0.0, 0.5, -1.0];
        B = [1.0, 0.0, 0.0, 0.0; 0.0, 1.0, 0.0, 0.0; 0.0, 0.0, 1.0, 0.0; 0.0, 0.0, 0.0, 1.0];
        C = [1.0, 0.0, 0.0, 0.0; 0.0, 1.0, 0.0, 0.0; 0.0, 0.0, 1.0, 0.0; 0.0, 0.0, 0.0, 1.0];
        D = [0.0, 0.0, 0.0, 0.0; 0.0, 0.0, 0.0, 0.0; 0.0, 0.0, 0.0, 0.0; 0.0, 0.0, 0.0, 0.0];
    end

    equations
        t1 == x(1);
        t2 == x(2);
        t3 == x(3);
        t4 == x(4);

        der(x) == A * x + B * [input_1; input_2; input_3; input_4];

        [output_1; output_2; output_3; output_4] == C * x + D * [input_1; input_2; input_3; input_4];
    end
end

In this updated code, the inputs and outputs are directly used in the equations section without the .p field. This code assumes that you have a thermal impedance model that can be represented by a state space model with four inputs and four outputs and that the state space matrices A, B, C, and D are defined. You will need to modify the component to match the dimensions of your state space matrices and the number of input and output nodes in your model.

[Johannes Flohe]

Dear @Shubham thank you again for your help. Unfortunatly, there is still some issue with your code. I get the following failure:

Failed to generate 'Thermal_SS' 

Caused by:
't1' is not defined in this scope.
   • In Thermal_SS (line 26)

Do you need to initialize t1 to t4 before using it?

Thank you for your help again!