MATLABS-Function s函数简单应用

什么叫S函数

• s函数是系统函数（System Function）的简称，是指采用一种程序设计语言描述的一个功能模块。
• 用户可以采用MATLAB语言，也可以采用C、C++或FORTRAN等语言来编写S函数。
• S函数有自己特定的语法构成规则，可以用来描述并实现连续系统、离散系统以及复合系统。
• S函数能够接收来自Simulink求解算法的相关信息，并对求解算法发出的命令做出适当的响应，这种交互作用类似于Simulink系统模块与求解算法的相互作用。

用MATLAB语言编写S函数

在MATLAB命令行窗囗输入命令，打开模板文件。

>> edit sfuntmpl.m

模板文件sfuntmpl.m包括：

• 1个主函数
• 6个子函数

(1)主函数

主函数的引导语句为:
function [sys,x0,str,ts]=fname(t,x,u,flag)

• fmame是S函数的函数名.
• 输入形参t、x、u、flag分别为仿真时间、状态向量、输入向量和子函数调用标志.
• 输出形参sys代表一种返回参数;×0是初始状态值;对于M文件S函数,str将被置成一个空阵;ts是一个两列矩阵(一列是各状态变量的采样周期，一列是相应的采样时间的偏移量).TS = [0 0] 连续采样 ；TS =[-1 0]继承被连接模块的采样时间

(2)子函数

S函数共有6个子函数,这些子函数的前辍为mdl,由flag的值来控制在仿真的各阶段调用S函数的哪一个子函数.

• flag取0:调用初始化子函数mdllnitializeSizes.
• flag取1:调用子函数mdlDerivatives实现连续状态的更新.
• flag取2:调用子函数mdlUpdate实现离散状态的更新.
• Flag取3:调用输出子函数mdlOutputs.
• flag取4,9的情况较少使用

S函数的应用

采用S函数实现y=kx+b.

(1)定义s函数

1.主函数

function [sys,x0,str,ts]=timekb(t,x,u,flag,k,b)
switch flag
    case 0
        [sys,x0,str,ts]=mdlInitializeSizes;%初始化
    case 3
        sys=mdlOutputs(t.x.u,k.b);%计算输出量
%该段其余代码与模板一致

end

2.初始化子函数

function [sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes
sizes=simsizes;
sizes.NumContStates=0;%无连续状态
sizes.NumDiscStates=0;%无离散状态
sizes.NumOutputs=1;%有一个输出量
sizes.NumInputs=1;%有一个输入信号
sizes.DirFeedthrough=1;%输出量中含有输入量
sizes.NumSampleTimes=1;%单个采样周期
sys=simsizes(sizes);
%给其他返回参数赋值
X0=[];%设置初始状态为零状态
str=[];%将str变量设置为空字符串
ts=[-1,0];%假定继承输入信号的采样周期

3.输出子函数

function sys=mdlOutputs(t,x,u,k,b)%t仿真时间，x状态向量，u输入向量，k,b自定义参数
sys=k*u+b;

完整代码

以下代码为在模板按照上述说明做改动，所用软件版本为matlabR2014a且成功运行

function [sys,x0,str,ts,simStateCompliance] = timeFunctionkb(t,x,u,flag,k,b)%%较模板加入k.b
%SFUNTMPL General MATLAB S-Function Template
%   With MATLAB S-functions, you can define you own ordinary differential
%   equations (ODEs), discrete system equations, and/or just about
%   any type of algorithm to be used within a Simulink block diagram.
%
%   The general form of an MATLAB S-function syntax is:
%       [SYS,X0,STR,TS,SIMSTATECOMPLIANCE] = SFUNC(T,X,U,FLAG,P1,...,Pn)
%
%   What is returned by SFUNC at a given point in time, T, depends on the
%   value of the FLAG, the current state vector, X, and the current
%   input vector, U.
%
%   FLAG   RESULT             DESCRIPTION
%   -----  ------             --------------------------------------------
%   0      [SIZES,X0,STR,TS]  Initialization, return system sizes in SYS,
%                             initial state in X0, state ordering strings
%                             in STR, and sample times in TS.
%   1      DX                 Return continuous state derivatives in SYS.
%   2      DS                 Update discrete states SYS = X(n+1)
%   3      Y                  Return outputs in SYS.
%   4      TNEXT              Return next time hit for variable step sample
%                             time in SYS.
%   5                         Reserved for future (root finding).
%   9      []                 Termination, perform any cleanup SYS=[].
%
%
%   The state vectors, X and X0 consists of continuous states followed
%   by discrete states.
%
%   Optional parameters, P1,...,Pn can be provided to the S-function and
%   used during any FLAG operation.
%
%   When SFUNC is called with FLAG = 0, the following information
%   should be returned:
%
%      SYS(1) = Number of continuous states.
%      SYS(2) = Number of discrete states.
%      SYS(3) = Number of outputs.
%      SYS(4) = Number of inputs.
%               Any of the first four elements in SYS can be specified
%               as -1 indicating that they are dynamically sized. The
%               actual length for all other flags will be equal to the
%               length of the input, U.
%      SYS(5) = Reserved for root finding. Must be zero.
%      SYS(6) = Direct feedthrough flag (1=yes, 0=no). The s-function
%               has direct feedthrough if U is used during the FLAG=3
%               call. Setting this to 0 is akin to making a promise that
%               U will not be used during FLAG=3. If you break the promise
%               then unpredictable results will occur.
%      SYS(7) = Number of sample times. This is the number of rows in TS.
%
%
%      X0     = Initial state conditions or [] if no states.
%
%      STR    = State ordering strings which is generally specified as [].
%
%      TS     = An m-by-2 matrix containing the sample time
%               (period, offset) information. Where m = number of sample
%               times. The ordering of the sample times must be:
%
%               TS = [0      0,      : Continuous sample time.
%                     0      1,      : Continuous, but fixed in minor step
%                                      sample time.
%                     PERIOD OFFSET, : Discrete sample time where
%                                      PERIOD > 0 & OFFSET < PERIOD.
%                     -2     0];     : Variable step discrete sample time
%                                      where FLAG=4 is used to get time of
%                                      next hit.
%
%               There can be more than one sample time providing
%               they are ordered such that they are monotonically
%               increasing. Only the needed sample times should be
%               specified in TS. When specifying more than one
%               sample time, you must check for sample hits explicitly by
%               seeing if
%                  abs(round((T-OFFSET)/PERIOD) - (T-OFFSET)/PERIOD)
%               is within a specified tolerance, generally 1e-8. This
%               tolerance is dependent upon your model's sampling times
%               and simulation time.
%
%               You can also specify that the sample time of the S-function
%               is inherited from the driving block. For functions which
%               change during minor steps, this is done by
%               specifying SYS(7) = 1 and TS = [-1 0]. For functions which
%               are held during minor steps, this is done by specifying
%               SYS(7) = 1 and TS = [-1 1].
%
%      SIMSTATECOMPLIANCE = Specifices how to handle this block when saving and
%                           restoring the complete simulation state of the
%                           model. The allowed values are: 'DefaultSimState',
%                           'HasNoSimState' or 'DisallowSimState'. If this value
%                           is not speficified, then the block's compliance with
%                           simState feature is set to 'UknownSimState'.
 
 
%   Copyright 1990-2010 The MathWorks, Inc.
 
%
% The following outlines the general structure of an S-function.
%
switch flag,
 
  %%%%%%%%%%%%%%%%%%
  % Initialization %
  %%%%%%%%%%%%%%%%%%
  case 0,
    [sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes;
 
  %%%%%%%%%%%%%%%
  % Derivatives %
  %%%%%%%%%%%%%%%
  case 1,
    sys=mdlDerivatives(t,x,u);
 
  %%%%%%%%%%
  % Update %
  %%%%%%%%%%
  case 2,
    sys=mdlUpdate(t,x,u);
 
  %%%%%%%%%%%
  % Outputs %
  %%%%%%%%%%%
  case 3,
    sys=mdlOutputs(t,x,u,k,b);%%%%较模板加入k.b
 
  %%%%%%%%%%%%%%%%%%%%%%%
  % GetTimeOfNextVarHit %
  %%%%%%%%%%%%%%%%%%%%%%%
  case 4,
    sys=mdlGetTimeOfNextVarHit(t,x,u);
 
  %%%%%%%%%%%%%
  % Terminate %
  %%%%%%%%%%%%%
  case 9,
    sys=mdlTerminate(t,x,u);
 
  %%%%%%%%%%%%%%%%%%%%
  % Unexpected flags %
  %%%%%%%%%%%%%%%%%%%%
  otherwise%出错处理
    DAStudio.error('Simulink:blocks:unhandledFlag', num2str(flag));
 
end
 
% end sfuntmpl
 
%
%=============================================================================
% mdlInitializeSizes
% Return the sizes, initial conditions, and sample times for the S-function.
%=============================================================================
%
function [sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes
 
%
% call simsizes for a sizes structure, fill it in and convert it to a
% sizes array.
%
% Note that in this example, the values are hard coded.  This is not a
% recommended practice as the characteristics of the block are typically
% defined by the S-function parameters.
%
sizes = simsizes;
 
sizes.NumContStates  = 0;
sizes.NumDiscStates  = 0;
sizes.NumOutputs     = 1;
sizes.NumInputs      = 1;
sizes.DirFeedthrough = 1;
sizes.NumSampleTimes = 1;   % at least one sample time is needed
 
sys = simsizes(sizes);
 
%
% initialize the initial conditions
%
x0  = [];
 
%
% str is always an empty matrix
%
str = [];
 
%
% initialize the array of sample times
%
ts  = [-1 0];
 
% Specify the block simStateCompliance. The allowed values are:
%    'UnknownSimState', < The default setting; warn and assume DefaultSimState
%    'DefaultSimState', < Same sim state as a built-in block
%    'HasNoSimState',   < No sim state
%    'DisallowSimState' < Error out when saving or restoring the model sim state
simStateCompliance = 'UnknownSimState';
 
% end mdlInitializeSizes
 
%
%=============================================================================
% mdlDerivatives
% Return the derivatives for the continuous states.
%=============================================================================
%
function sys=mdlDerivatives(t,x,u)
 
sys = [];
 
% end mdlDerivatives
 
%
%=============================================================================
% mdlUpdate
% Handle discrete state updates, sample time hits, and major time step
% requirements.
%=============================================================================
%
function sys=mdlUpdate(t,x,u)
 
sys = [];
 
% end mdlUpdate
 
%
%=============================================================================
% mdlOutputs
% Return the block outputs.
%=============================================================================
%
 
function sys=mdlOutputs(t,x,u,k,b)%%t仿真时间，x状态向量，u输入向量，k,b自定义参数
sys=k*u+b;
% end mdlOutputs
 
%
%=============================================================================
% mdlGetTimeOfNextVarHit
% Return the time of the next hit for this block.  Note that the result is
% absolute time.  Note that this function is only used when you specify a
% variable discrete-time sample time [-2 0] in the sample time array in
% mdlInitializeSizes.
%=============================================================================
%
function sys=mdlGetTimeOfNextVarHit(t,x,u)
 
sampleTime = 1;    %  Example, set the next hit to be one second later.
sys = t + sampleTime;
 
% end mdlGetTimeOfNextVarHit
 
%
%=============================================================================
% mdlTerminate
% Perform any end of simulation tasks.
%=============================================================================
%
function sys=mdlTerminate(t,x,u)
 
sys = [];
 
% end mdlTerminate

（2）在Simulink模型中使用S函数

做好了s函数后，simulink–user-defined function下拖一个S-Function到你的模型，就可以用了；在simulink——-user-defined function还有个s-Function Builder，他可以生成用c语言写的s函数；
在matlab的workspace下打sfundemos，可以看到很多演示s函数的程序




设置完之后，点击运行，再点击查看波形可得如下结果

最后

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