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 mdlDerivatives. mdlUpdate updates the discrete states when flag = 2. Note that for a single-rate discrete S-function, Simulink calls the mdlUpdate, mdlOutputs, 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.

Simple M-File S-Function Example

Example - Hybrid System S-Function