## Generate Simscape Equations from Symbolic Expressions

Simscape™ software extends the Simulink® product line with tools for modeling and simulating multidomain physical systems, such as those with mechanical, hydraulic, pneumatic, thermal, and electrical components. Unlike other Simulink blocks, which represent mathematical operations or operate on signals, Simscape blocks represent physical components or relationships directly. With Simscape blocks, you build a model of a system just as you would assemble a physical system. For more information about Simscape software see Simscape.

You can extend the Simscape modeling environment by creating custom components. When you define a component, use the equation section of the component file to establish the mathematical relationships among a component's variables, parameters, inputs, outputs, time, and the time derivatives of each of these entities. The Symbolic Math Toolbox™ and Simscape software let you perform symbolic computations and use the results of these computations in the equation section. The simscapeEquation function translates the results of symbolic computations to Simscape language equations.

### Convert Algebraic and Differential Equations

Suppose, you want to generate a Simscape equation from the solution of the following ordinary differential equation. As a first step, use the dsolve function to solve the equation:

syms a y(t)
Dy = diff(y);
s = dsolve(diff(y, 2) == -a^2*y, y(0) == 1, Dy(pi/a) == 0);
s = simplify(s)

The solution is:

s =
cos(a*t)

Then, use the simscapeEquation function to rewrite the solution in the Simscape language:

simscapeEquation(s)

simscapeEquation generates the following code:

ans =
's == cos(a*time);'

The variable time replaces all instances of the variable t except for derivatives with respect to t. To use the generated equation, copy the equation and paste it to the equation section of the Simscape component file. Do not copy the automatically generated variable ans and the equal sign that follows it.

simscapeEquation converts any derivative with respect to the variable t to the Simscape notation, X.der, where X is the time-dependent variable. For example, convert the following differential equation to a Simscape equation. Also, here you explicitly specify the left and the right sides of the equation by using the syntax simscapeEquation(LHS, RHS):

syms a x(t)
simscapeEquation(diff(x), -a^2*x)
ans =
'x.der == -a^2*x;'

simscapeEquation also translates piecewise expressions to the Simscape language. For example, the result of the following Fourier transform is a piecewise function:

syms v u x
assume(x, 'real')
f = exp(-x^2*abs(v))*sin(v)/v;
s = fourier(f, v, u)
s =
piecewise(x ~= 0, atan((u + 1)/x^2) - atan((u - 1)/x^2))

From this symbolic piecewise equation, simscapeEquation generates valid code for the equation section of a Simscape component file:

simscapeEquation(s)
ans =
'if (x ~= 0.0)
s == -atan(1.0/x^2*(u-1.0))+atan(1.0/x^2*(u+1.0));
else
s == NaN;
end'

Clear the assumption that x is real by recreating it using syms:

syms x

### Limitations

The equation section of a Simscape component file supports a limited number of functions. For details and the list of supported functions, see Simscape equations (Simscape). If a symbolic expression contains functions that are not supported by Simscape, then simscapeEquation cannot represent the symbolic expression as a Simscape equation and issues a warning instead. Always verify the conversion result. Expressions with infinities are prone to invalid conversion.