How to initialize Sympy python function in Simulink

Hello,

I want to solve ODE in Simulink with python function (derived in Sympy). This is just example, real Sympy equations will be larger.

Python function called Pyfun.py:

from sympy import lambdify, Matrix, symbols
t,x1,x2 = symbols('t x1 x2')
def create_symbolic_expression():

    expr = Matrix([[x2], [(1-x1**2)*x2-x1]]);
    return expr

def lambdify_expression(expr):
    return(lambdify([t,x1,x2],expr, modules='numpy'))
    

Then I have MATLAB Function in Simulink that looks like this

function y = fcn(t,u)
y = [0;0];
coder.extrinsic('py.Pyfun.create_symbolic_expression')
coder.extrinsic('py.Pyfun.lambdify_expression')
expr = py.Pyfun.create_symbolic_expression();
myfunc = py.Pyfun.lambdify_expression(expr);

y = double(myfunc(t,u(1),u(2)));

Output of this function is integrated and going back as input, as it should. Everything here works well and gives right results.

My problem is, that the MATLAB Function is calling the "create" and "lambdify" symbolic expression every iteration and it makes the calculation very slow. The question is, if there is a way to initialize the python code before the Simulink simulation and only calculate with "myfunc" expression/function. I tried to call this in InitFcn in Callbacks like this

coder.extrinsic('py.Pyfun.create_symbolic_expression')
coder.extrinsic('py.Pyfun.lambdify_expression')
expr = py.Pyfun.create_symbolic_expression();
myfunc = py.Pyfun.lambdify_expression(expr);

and run MATLAB Function only like this

function y = fcn(t,u)
y = [0;0];
y = double(myfunc(t,u(1),u(2)));

but it says "Undefined function or variable 'myfunc'.". Thank you.

Answer 1

[Ayush Aniket]

Hi Ondrej,

To avoid the repeated initialization of your Python function within the Simulink model, you can use persistent variables in your MATLAB Function block to store the function handle across function calls. The persistent variable will be initialized only once when the model starts running. Refer to the documentation below to read more about it:

https://www.mathworks.com/help/simulink/ug/initialize-persistent-variables.html

You can modify your MATLAB Function block as shown below:

function y = fcn(t,u)
    y = [0;0];
    coder.extrinsic('py.Pyfun.create_symbolic_expression')
    coder.extrinsic('py.Pyfun.lambdify_expression')

    persistent myfunc
    if isempty(myfunc)

        expr = py.Pyfun.create_symbolic_expression();
        myfunc = py.Pyfun.lambdify_expression(expr);
    end
    y = double(myfunc(t,u(1),u(2)));
end

In the code above, 'myfunc' is declared as a persistent variable, which means that its value is retained in memory between calls to the function. The check 'isempty(myfunc)' ensures that the Python function is only created and lambdified once, when 'myfunc' is not yet initialized (i.e., during the first function call).

The InitFcn callback in the model's Callbacks is not suitable for initializing variables used within the MATLAB Function block because the scope of variables defined in the InitFcn is not shared with the MATLAB Function block.

[Ondrej Zoufaly]

Thank you, it works much faster. The only problem now is that you can only simulate the block with the discrete sample time, do you know if there is a way to use continuous time with coder.extrinsic ? Thank you.