Ｓ－Ｆｕｎｃｔｉｏｎ　使用及应用举例
【说明】近来在论坛中很多朋友问及 Simulink 下的S-函数的编写及使用方法，在西安交大 BBS 上，hii_yzf网友发表了有关S-函数使用的文章，举例比较详尽，相信对关心S-函数的网友会有很大帮助。
发信人: hii_yzf (叶子), 信区: MathTools
标题: S-FUNCTIONS的书写之一
发信站: 交通大学思源BBS站 (Mon Apr 16 16:35:09 2001) , 站内信件
S-FUNCTIONS的书写之一
s-function也就是system-function的缩写。说得简单，s-function就是用MATLAB所提供的模型不能完全满足用户，而提供给用户自己编写程序来满足自己要求模型的接口。要了解s-function，必须了解以下知识：
（1）direct feedthrough
（2）dynamically sized inputs
（3）setting sample times and offsets
[由于我也不知道怎么把上面三句话精确的翻译成中文，因此在此不加翻译，大家自己理解，也许更好]由于上面三部分的重要性，在此详细进行分析。
一.direct feedthrough
direct feedthrough意思是说系统的输出或可变采样时间是否受到输入的控制。大家清楚有的系统是受到输入控制如：
y=k*u (u是输入，k是放大因子，y是输出）
而有的系统输出是不受到输入影响，如：
输出：y=x
dx=u
x表示状态
二.dynamically sized inputs
主要是给出：输入连续状态数目（size.NumContStates)，离散状态数目（size.NumDiscStates)
，输出数目（size.NumOutputs)，输入数目(size.NumInputs),Direct Feedthrough(size.Dir Feedthrough)。
三.setting sample times and offsets
setting smaple times and offsets主要设置采样时间 MATLAB为了用户方便，已经书写了S-FUNCTIONS模板函数sfuntmpl.m。为了更好的写S-FUNCTIONS，大家来看一下，该函数sfuntmpl.m内容如下：（我通过在该内容加注释来说明，以$开头）
function [sys,x0,str,ts] = sfuntmpl(t,x,u,flag)
$输出变量就此四个，大家必须注意它的顺序。$输入变量可以为t,x,u,flag,p1,...,pn等，但是前面的四个变量不能变，特此说明。
%SFUNTMPL General M-file S-function template
%  With M-file 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.
%
$上面是其功能
%  The general form of an M-File S-function syntax is:
%      [SYS,X0,STR,TS] = SFUNC(T,X,U,FLAG,P1,...,Pn)
%
$调用格式
%  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.
$具体怎样实现，大家参看后面的函数mdlInitializeSizes
%  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=[].
%
$参看后面相应函数
%
%  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. %
$需要说明的是sys的顺序不能乱
%
%      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 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].
%  Copyright (c) 1990-1998 by The MathWorks, Inc. All Rights Reserved. %  $Revision: 1.12 $
%
% The following outlines the general structure of an S-function.
%
switch flag,
%%%%%%%%%%%%%%%%%%
% Initialization %
%%%%%%%%%%%%%%%%%%
case 0,[sys,x0,str,ts]=mdlInitializeSizes;
$大家是不是觉得此函数名太长，当然可以根据自己的爱好加以改变，不过后面的相应改。
%%%%%%%%%%%%%%%
% Derivatives %
%%%%%%%%%%%%%%%
case 1,sys=mdlDerivatives(t,x,u);
%%%%%%%%%%
% Update %
%%%%%%%%%%
case 2,sys=mdlUpdate(t,x,u);
%%%%%%%%%%%
% Outputs %
%%%%%%%%%%%
case 3,sys=mdlOutputs(t,x,u);
%%%%%%%%%%%%%%%%%%%%%%%
% GetTimeOfNextVarHit %
%%%%%%%%%%%%%%%%%%%%%%%
case 4,sys=mdlGetTimeOfNextVarHit(t,x,u);
%%%%%%%%%%%%%
% Terminate %
%%%%%%%%%%%%%
case 9,sys=mdlTerminate(t,x,u);
%%%%%%%%%%%%%%%%%%%%
% Unexpected flags %
%%%%%%%%%%%%%%%%%%%%
otherwise, error(['Unhandled flag = ',num2str(flag)]);
end
% end sfuntmpl
%
%============================================================================= % mdlInitializeSizes
% Return the sizes, initial conditions, and sample times for the S-function.
%============================================================================= %
function [sys,x0,str,ts]=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.
%
$关于函数simsizes大家必须遵循，因为把是内部函数，不得随便改变，其作用是返回未初始化的size结构。sizes = simsizes;
$number of continuous states
switch函数用法举例sizes.NumContStates  = 0;
$number of discrete states
sizes.NumDiscStates  = 0;
$number of outputs
sizes.NumOutputs    = 0;
$ number of inputs
sizes.NumInputs      = 0;
$Flag for direct feedthrough
sizes.DirFeedthrough = 1;
$number of sample times
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  = [0 0];
% end mdlInitializeSizes
%
%=============================================================================
% mdlDerivatives
% Return the derivatives for the continuous states.
%=============================================================================
%
function sys=mdlDerivatives(t,x,u)
sys = []; % end mdlDerivatives

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