Writing S-Functions

Example - Discrete State S-Function

Simulink includes a function called dsfunc.m, which is an example of a discrete state system modeled in an S-function. This function is similar to csfunc.m, the continuous state S-function example. The only difference is that mdlUpdate is called instead of mdlDerivative. mdlUpdate updates the discrete states when the flag = 2. Note that for a single-rate discrete S-function, Simulink calls the mdlUpdate, mdlOutput, and mdlGetTimeOfNextVarHit (if needed) routines only on sample hits. Here is the code for the M-file S-function.

function [sys,x0,str,ts] = dsfunc(t,x,u,flag)
% An example M-file S-function for defining a discrete system.
% This S-function implements discrete equations in this form:
%      x(n+1) = Ax(n) + Bu(n)
%      y(n)   = Cx(n) + Du(n)
% 
% Generate a discrete linear system:
A=[-1.3839 -0.5097
    1.0000         0];
B=[-2.5559         0
         0    4.2382];
C=[      0    2.0761
         0    7.7891];
D=[   -0.8141   -2.9334
       1.2426         0];

switch flag,
  case 0
    sys = mdlInitializeSizes(A,B,C,D); % Initialization

  case 2
    sys = mdlUpdate(t,x,u,A,B,C,D); % Update discrete states

  case 3
    sys = mdlOutputs(t,x,u,A,B,C,D); % Calculate outputs

  case {1, 4, 9} % Unused flags
    sys = [];

  otherwise
    error(['unhandled flag = ',num2str(flag)]); % Error handling
end
% End of dsfunc.

%==============================================================
% Initialization
%==============================================================

function [sys,x0,str,ts] = mdlInitializeSizes(A,B,C,D)

% Call simsizes for a sizes structure, fill it in, and convert it 
% to a sizes array.

sizes = simsizes;
sizes.NumContStates  = 0;
sizes.NumDiscStates  = 2;
sizes.NumOutputs     = 2;
sizes.NumInputs      = 2;
sizes.DirFeedthrough = 1; % Matrix D is non-empty.
sizes.NumSampleTimes = 1;
sys = simsizes(sizes); 
x0  = ones(2,1);   % Initialize the discrete states.
str = [];          % Set str to an empty matrix.
ts  = [1 0];       % sample time: [period, offset]
% End of mdlInitializeSizes.

%==============================================================
% Update the discrete states
%==============================================================
function sys = mdlUpdates(t,x,u,A,B,C,D)
sys = A*x + B*u;
% End of mdlUpdate.

%==============================================================
% Calculate outputs
%==============================================================
function sys = mdlOutputs(t,x,u,A,B,C,D)
sys = C*x + D*u;
% End of mdlOutputs.

The above example conforms to the simulation stages discussed earlier in chapter 1. The system discrete state equations are of the form

x(n+1) = Ax(n) + Bu(n)
y(n)   = Cx(n) + Du(n)

so that very general sets of difference equations can be modeled using dsfunc.m. This is similar to the built-in Discrete State-Space block. You can use dsfunc.m as a starting point for modeling discrete state-space systems with time-varying coefficients.

Examples of M-File S-Functions

Example - Hybrid System S-Functions