How to Solve nonlinear equations in simulink

Hello everyone, I want to define and solve a system of nonlinear equations in Simulink using the MATLAB Function block, but I encountered an error. I would like to ask, why is this happening?

Here is the code inside the MATLAB Function block:

function dx = fcn(x)
dx1=x(1)+1
dx2=2*x(2)
dx=[dx1;dx2]
end

[Sam Chak]

Your code for the differential equations

dx1 = x(1) + 1
dx2 = 2*x(2)

can interpreted in State-space form as

where .

More importantly, you should have noticed that state doesn't affect state , both state equations will produce unstable reqponses for and .

By the way, both state equations are linear.

If the above interpretation is incorrect, please show exact mathematical model in image form.

[guo qing]

Thank you for your reply, but the equations I want to implement are actually more complex and cannot be written in the form shown above. Here is the specific MATLAB FUNCTION Code:

function dx=fcn(x)
ks=29114
kt=233350
cs=925.8
mw=56.9
u_asterisk=100;
dx=[x(2);cs/x(5)*(x(4)-x(2))+ks/x(5)*(x(3)-x(1));x(4);cs/mw*(x(2)-x(4))+ks/mw*(x(1)-x(3))+kt/mw*u_asterisk-kt/mw*x(3);0]
end

But running it this way results in an error, and I don't know where the error is

[guo qing]

Also, if possible, I would like to ask how to remove the display of "double" in the model. Even though I have turned off port data type display, "double" still appears.

[Aquatris]

What error do you actually get? Since you have divisions by state, is it possible for one of your states to become 0 at one point?

[guo qing]

Index expression out of bounds. Attempted to access element 2. The valid range is 1-1. More information on function 'MATLAB Function' (#64.77.78), line 7, column 7: "2" Diagnostic report initiated.

Component: MATLAB Function | Category: Coder Error

Error parsing MATLAB function 'untitled/MATLAB Function'.

Component: MATLAB Function | Category: Coder Error

Due to errors in the module body or limitations of foundational analysis, Simulink cannot determine the output size and/or type of module 'untitled/MATLAB Function'. The error may not be accurate. Please fix the indicated errors or explicitly specify the size and/or type of all module outputs.

Component: MATLAB Function | Category: Coder Error

Due to errors in the module body or limitations of foundational analysis, Simulink cannot determine the output size and/or type of module 'untitled/MATLAB Function'. The error may not be accurate. Please fix the indicated errors or explicitly specify the size and/or type of all module outputs.

Component: Simulink | Category: Model Error

Error propagating data type 'double' through 'untitled/MATLAB Function'.

Component: Simulink | Category: Model Error

This is all the error reports I have.

[Aquatris]

Then the error seems trivial. The integrator block has a 'Initial condition' property, which is by default set to 0, a scalar value. However your matlab function requires 2 inputs and has 2 outputs. So change the 'Initial condition' to be 'zeros(2,1)' and your code should run fine. For your actual problem, it seems like you have 5 states, so Initial condition:'' should be 'zeros(5,1)' instead.

You can also define initial condition to be different than 0 depending on the problem you wanna solve.

[Sam Chak]

Hi @guo qing, Preliminary test shows that the dynamic equations look okay. Just make sure that the initial value for 5th state is non-zero, else you'll get a division-by-zero, leading to Inf or NaN reading.

The next step is to carry out the test in Simulink.

function dx=fcn(t, x)
    ks  = 29114;
    kt  = 233350;
    cs  = 925.8;
    mw  = 56.9;
    u_asterisk = 100;
    dx  = [x(2);
           cs/x(5)*(x(4)-x(2))+ks/x(5)*(x(3)-x(1));
           x(4);
           cs/mw*(x(2)-x(4))+ks/mw*(x(1)-x(3))+kt/mw*u_asterisk-kt/mw*x(3);
           0];
end

[t, x]  = ode45(@fcn, [0 0.2], [1; 0; 0; 0; 1]);    % x1(0) & x5(0) = 1, the rest are 0.
plot(t, x), grid on

[guo qing]

Thank you very much. I think the key to the problem lies in setting the initial value in the integrator module, just like you mentioned. As long as it is set, the problem is solved. However, it seems that when using block modular modeling, it is not necessary to set the initial value in the integrator module. This seems to be a unique aspect of the MATLAB Function block?

Answer 1

[Sam Chak]

Code for the MATLAB Function block:

function dx = fcn(x)

ks = 29114;

kt = 233350;

cs = 925.8;

mw = 56.9;

u_asterisk = 100;

dx = [x(2);

cs/x(5)*(x(4)-x(2))+ks/x(5)*(x(3)-x(1));

x(4);

cs/mw*(x(2)-x(4))+ks/mw*(x(1)-x(3))+kt/mw*u_asterisk-kt/mw*x(3);

0];

end

[guo qing]

Thank you very much. I think the key to the problem lies in setting the initial value in the integrator module, just like you mentioned. As long as it is set, the problem is solved. However, it seems that when using block modular modeling, it is not necessary to set the initial value in the integrator module. This seems to be a unique aspect of the MATLAB Function block?

[Sam Chak]

You are welcome, @guo qing. If you find the approach or solution helpful, please consider clicking 'Accept' ✔ on the Answer. Additionally, you can show your appreciation by voting 👍 for other helpful answers.

By the way, what do you mean by "block modular modeling"? If you use the S-Function block, then the Integrator block is unnessary. However, you will still need to supply the initial values in the code of the S-Function block. However, not many examples are provided for using the S-Function block to simulate the dynamic systems. Clicking the links directs users to other more links. 🤦‍♂️

[guo qing]

Thank you very much. From my understanding, modular modeling refers to constructing a system using modules such as gain, product, and multiply, among others. In the systems built with these modules, it seems that Simulink can automatically determine the dimensions, and you only need to assign an initial value of 0 to the integrator module. Of course, the S-function you mentioned is also a good suggestion.

Answer 2

[Nipun]

Hi Quo,

I understand that you want to solve a set of equations in Simulink and are encountering an error.

Without the knowledge of the exact error message, it will be difficult to the exact cause of the error encountered.

I recommend changing the "initial value" of the integrator function so that it gives exact result on the initial condition and does not cause any error. Here is the documentation to do so: https://www.mathworks.com/help/simulink/slref/integrator.html

By default, the initial value is set to 0 which may not be true depending upon the function being fed.

Refer to the following MathWorks documentation for more information on equation solving in Simulink: https://www.mathworks.com/help/symbolic/equation-solving.html

Hope this helps.

Regards,

Nipun

[guo qing]

Thank you for your reply.

Index expression out of bounds. Attempted to access element 2. The valid range is 1-1. More information on function 'MATLAB Function' (#64.77.78), line 7, column 7: "2" Diagnostic report initiated.

Component: MATLAB Function | Category: Coder Error

Error parsing MATLAB function 'untitled/MATLAB Function'.

Component: MATLAB Function | Category: Coder Error

Due to errors in the module body or limitations of foundational analysis, Simulink cannot determine the output size and/or type of module 'untitled/MATLAB Function'. The error may not be accurate. Please fix the indicated errors or explicitly specify the size and/or type of all module outputs.

Component: MATLAB Function | Category: Coder Error

Due to errors in the module body or limitations of foundational analysis, Simulink cannot determine the output size and/or type of module 'untitled/MATLAB Function'. The error may not be accurate. Please fix the indicated errors or explicitly specify the size and/or type of all module outputs.

Component: Simulink | Category: Model Error

Error propagating data type 'double' through 'untitled/MATLAB Function'.

Component: Simulink | Category: Model Error

This is all the error reports I have.