S-functions

In SIMULINK's 'Nonlinear' menu is a block called an 'S-Function'. It allows the input of a user-defined set of differential equations for simulation purposes. However, the file which is entered into the 'S-Function' block is required to have a special syntax, as seen below: (comment lines are preceeded by a %, the comment character for MATLAB)




function [sys, x0] = functionname(t,x,u,flag)

if abs(flag)==1

%  Constants and algebraic equations are defined here.
%  All lines must be followed by a ';'.
%  States of your system are given by x(n), where n represents
%     the number of the state, starting from 1.
%  The inputs of the system are given by u(n), where u is the
%     number of the input to the S-Function, starting with 1.

    q=x(1)*u(1);
    A=25.0;

%  Below the algebraic equations and constants go the differential
%     equations, in the following form (dx/dt = f(x,u)):

    dx(1) = A * x(1) + x(2) * u(2);
    
    dx(2) = q * x(2) - u(1);
    
%  The 'sys' below defines the system of differential equations being simulated.

    sys=[dx(1);dx(2)];
elseif flag == 0

%  The simulation is defined below by 'sys'.  The numbers in the vector are
%     explained below:

%  sys=[(# of continuous states) (# of discrete states) (# of outputs)...
%       (# of inputs) (# of roots in the system) (set to 1 if the system
%        has direct feed through of its inputs)];

    sys = [2 0 3 2 0 0];
    
%  These are the initial conditions of the states, starting from 1.     

    x0 = [0.0;0.0];

elseif flag == 3

%  This is the output portion of the S-Function.  Outputs are given by
%     'sys', below.  This case outputs the two states, and the product
%     of those states.

    sys = [x(1);
           x(2);
           x(2)*x(1)];

%  This could also be written:  sys=[x(1);x(2);x(2)*x(1)];

else
    sys = [];
end
% End of S-Function.

For more information, type 'help sfunc' at the MATLAB prompt.