Matlab 中S-函数的使用 sfuntmpl

function [sys,x0,str,ts,simStateCompliance] = sfuntmpl(t,x,u,flag)
%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
%   -----  ------             --------------------------------------------
%         [SIZES,X0,STR,TS]  Initialization, return system sizes in SYS,
%                             initial state in X0, state ordering strings
%                             in STR, and sample times in TS.
%         DX                 Return continuous state derivatives in SYS.
%         DS                 Update discrete states SYS = X(n+)
%         Y                  Return outputs in SYS.
%         TNEXT              Return next time hit for variable step sample
%                             time in SYS.
%                            Reserved for future (root finding).
%         []                 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 = , the following information
%   should be returned:
%
%      SYS() = Number of continuous states.
%      SYS() = Number of discrete states.
%      SYS() = Number of outputs.
%      SYS() = Number of inputs.
%               Any of the first four elements in SYS can be specified
%               as - indicating that they are dynamically sized. The
%               actual length for all other flags will be equal to the
%               length of the input, U.
%      SYS() = Reserved for root finding. Must be zero.
%      SYS() = Direct feedthrough flag (=yes, =no). The s-function
%               has direct feedthrough if U is used during the FLAG=
%               call. Setting this to  is akin to making a promise that
%               U will not be used during FLAG=. If you break the promise
%               then unpredictable results will occur.
%      SYS() = 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- matrix containing the sample time
%               (period, offset) information. Where m = number of sample
%               times. The ordering of the sample times must be:
%
%               TS = [      ,      : Continuous sample time.
%                           ,      : Continuous, but fixed in minor step
%                                      sample time.
%                     PERIOD OFFSET, : Discrete sample time where
%                                      PERIOD >  & OFFSET < PERIOD.
%                     -     ];     : Variable step discrete sample time
%                                      where FLAG= 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-. 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() =  and TS = [- ]. For functions which
%               are held during minor steps, this is done by specifying
%               SYS() =  and TS = [- ].
%
%      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 - The MathWorks, Inc.
 
%
% The following outlines the general structure of an S-function.
%
switch flag,
 
  %%%%%%%%%%%%%%%%%%
  % Initialization %
  %%%%%%%%%%%%%%%%%%
  case ,
    [sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes;
 
  %%%%%%%%%%%%%%%
  % Derivatives %
  %%%%%%%%%%%%%%%
  case ,
    sys=mdlDerivatives(t,x,u);
 
  %%%%%%%%%%
  % Update %
  %%%%%%%%%%
  case ,
    sys=mdlUpdate(t,x,u);
 
  %%%%%%%%%%%
  % Outputs %
  %%%%%%%%%%%
  case ,
    sys=mdlOutputs(t,x,u);
 
  %%%%%%%%%%%%%%%%%%%%%%%
  % GetTimeOfNextVarHit %
  %%%%%%%%%%%%%%%%%%%%%%%
  case ,
    sys=mdlGetTimeOfNextVarHit(t,x,u);
 
  %%%%%%%%%%%%%
  % Terminate %
  %%%%%%%%%%%%%
  case ,
    sys=mdlTerminate(t,x,u);
 
  %%%%%%%%%%%%%%%%%%%%
  % Unexpected flags %
  %%%%%%%%%%%%%%%%%%%%
  otherwise
    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  = ;
sizes.NumDiscStates  = ;
sizes.NumOutputs     = ;
sizes.NumInputs      = ;
sizes.DirFeedthrough = ;
sizes.NumSampleTimes = ;   % 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  = [ ];
 
% 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)
 
sys = [];
 
% 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 [- ] in the sample time array in
% mdlInitializeSizes.
%=============================================================================
%
function sys=mdlGetTimeOfNextVarHit(t,x,u)
 
sampleTime = ;    %  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

S-函数的几个概念:

1）  直接馈通

在编写S-函数时，初始化函数中需要对sizes.DirFeedthrough 进行设置，如果输出函数mdlOutputs或者对于变采样时间的mdlGetTimeOfNextVarHit是输入u的函数，则模块具有直接馈通的特性sizes.DirFeedthrough=1;否则为0。

2）  采样时间

仿真步长就是整个模型的基础采样时间，各个子系统或模块的采样时间，必须以这个步长为整数倍。

连续信号和离散信号对计算机而言其实都是采样而来的，只是采样时间不同，连续信号采样时间可认为趋于0且基于微分方程，离散信号采样时间比较长基于差分方程。离散信号当前状态由前一个时刻的状态决定，连续信号可以通过微分方程计算得到。如果要将连续信号离散化还要考虑下信号能否恢复的问题，即香农定理。

采样时间点的确定：下一个采样时间=（n*采样间隔）+ 偏移量，n表示当前的仿真步，从0开始。

对于连续采样时间，ts可以设置为[0 0]，其中偏移量为0；

对于离散采样时间，ts假设为[0.25 0.1]，表示在S-函数仿真开始后0.1s开始每隔0.25s运行一次，当然每个采样时刻都会调用mdlOutPuts和mdlUpdate函数；

对于变采样时间，即离散采样时间的两次采样时间间隔是可变的，每次仿真步开始时都需要用mdlGetTimeNextVarHit计算下一个采样时间的时刻值。ts可以设置为[-2 0]。

对于多个任务，每个任务都可以以不同的采样速率执行S-函数，假设任务A在仿真开始每隔0.25s执行一次，任务B在仿真后0.1s每隔1s执行一次，那么ts设置为[0.25 0.1;1.0 0.1]，具体到S-函数的执行时间为[0 0.1 0.25 0.5 0.75 1.0 1.1…]。

如果用户想继承被连接模块的采样时间，ts只要设置为[-1 0]。

子函数的作用

(1).mdlInitializeSizes函数-初始化函数
function[sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes
sizes = simsizes;
sizes.NumContStates  = ;  %连续状态个数
sizes.NumDiscStates  = ;  %离散状态个数
sizes.NumOutputs     = ;  %输出个数
sizes.NumInputs      = ;  %输入个数
sizes.DirFeedthrough = ;  %是否直接馈通
sizes.NumSampleTimes = ;  %采样时间个数，至少一个
sys = simsizes(sizes);     %将size结构传到sys中
x0  = [];                     %初始状态向量，由传入的参数决定，没有为空
str = [];
ts  = [ ];                  %设置采样时间，这里是连续采样，偏移量为0
% Specify the blocksimStateCompliance. The allowed values are:
%    'UnknownSimState', < The defaultsetting; warn and assume DefaultSimState
%    'DefaultSimState', < Same sim state as abuilt-in block
%    'HasNoSimState',   < No sim state
%    'DisallowSimState' < Error out whensaving or restoring the model sim state
simStateCompliance = 'UnknownSimState';  

(2).mdlGetTimeOfNextVarHit(t,x,u)函数-计算下一个采样时间
functionsys=mdlGetTimeOfNextVarHit(t,x,u)
sampleTime = ;    %  Example, set the next hit to be one secondlater.
sys = t + sampleTime;  

(3).mdlOutputs函数-计算S函数输出
functionsys=mdlOutputs(t,x,u)
sys = [];  

(4).mdlUpdate函数-更新
function sys=mdlUpdate(t,x,u)
sys = [];  

(5).mdlDerivatives函数-微分函数（计算连续状态导数）
functionsys=mdlDerivatives(t,x,u)
sys = [];  

(6).mdlTerminate函数-终止仿真
functionsys=mdlTerminate(t,x,u)
sys = [];  

function [sys,x0,str,ts,simStateCompliance] = sfuntmpl_c(t,x,u,flag)
 
%%%%Simulink中s函数模板的翻译版
%[sys,x0,str,ts,simStateCompliance] = sfuntmpl(t,x,u,flag，p1,…pn)
 
% flag result 描述
% —– —— ——————————————–
%  [sizes,x0,str,Ts] 初始化，返回SYS的大小，初始状态x0,str,采样时间Ts
%  DX 返回连续状态微分SYS.
%  DS 更新离散状态 SYS = X(n+)
%  Y 返回输出SYS.
%  TNEXT Return next time hit for variable step sample time in SYS.
%  Reserved for future (root finding).
%  [] 结束 perform any cleanup SYS=[].
 
% 当flag=0时，以下信息必须赋值回传
% SYS() = 连续状态个数
% SYS() = 离散状态个数
% SYS() = 输出量个数
% SYS() = 输入量个数 注：上述4个变量可以赋值为-，表示其值可变
% SYS() = 保留值。为0.
% SYS() = 直接馈通标志(=yes, =no).如果u在flag=3时被使用，说明S函数是直接馈通，赋值为1. 否则为0.
% SYS() = 采样时间个数，Ts的行数
%
% X0 = 初始状态。没有则赋值为[].除flag=0外，被忽略。
% STR = 系统保留，设为[].
% TS = m* 矩阵。（采样周期，偏移量）
% TS = [ , : 连续采样
%  , : 在1个Ts后连续采样
% PERIOD OFFSET, : Discrete sample time where
% PERIOD >  & OFFSET < PERIOD.
% - ]; : 变步长离散采样，
% flag=4用于决定下一个采样时刻
% 注：
% 若希望每个时间步都运行，则设Ts=[,]
% 若希望继承采样时间运行，则设Ts=[-,]
% 若希望继承采样时间运行，且希望在微步内不变化，应该设Ts=[-,]
% 若希望仿真开始0.1s后每隔0.25秒运行，则设Ts=[0.25,0.1]
% 若希望按照不同速率执行不同任务，则Ts应按照升序排列。
% 即：每隔0.25秒执行一个任务，同时在开始0.1秒后，每隔1秒执行另一个任务
% Ts=[0.25,; 1.0,0.1],则simulink将在下列时刻执行s函数[,0.1,0.25,0.5,0.75,,1.1,…]
 
% 以下是S函数的主函数
switch flag,
case , % 初始化
[sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes;
 
case , % 连续时间导数
sys=mdlDerivatives(t,x,u);
 
case , % 更新离散状态量
sys=mdlUpdate(t,x,u);
 
case , % 计算输出
sys=mdlOutputs(t,x,u);
 
case , % 计算下一步采样时刻
sys=mdlGetTimeOfNextVarHit(t,x,u);
 
case , % 结束仿真
sys=mdlTerminate(t,x,u);
 
otherwise % 未知flag值
DAStudio.error('Simulink:blocks:unhandledFlag', num2str(flag));
end % S函数主程序结束
 
%=============================================================================
% mdlInitializeSizes
% 返回s函数的sizes、初始条件、采样时刻
%=============================================================================
function [sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes
% 调用simsizes函数为sizes结构赋值
% simsizes函数是S函数模块特有的。它的结构和代码是固定的。
 
sizes = simsizes;
sizes.NumContStates = ; %连续状态个数
sizes.NumDiscStates = ; %离散状态个数
sizes.NumOutputs = ; %输出量个数
sizes.NumInputs = ; %输入量个数
sizes.DirFeedthrough = ; %直接馈通标志
sizes.NumSampleTimes = ; % 至少有一个采样时刻
sys = simsizes(sizes);
 
x0 = ; % 状态初始化
str = []; % str 始终为空
ts = [ ];% 初始化采样时间
 
% 指定simStateCompliance的值.
% ‘UnknownSimState’, < 默认值; 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';
% 子函数mdlInitializeSizes 结束
 
%=============================================================================
% mdlDerivatives
% 返回连续状态量的导数
%=============================================================================
function sys=mdlDerivatives(t,x,u)
 
sys = [];
 
% 子函数mdlDerivatives结束
 
%=============================================================================
% mdlUpdate
%更新离散时间状态，采样时刻和主时间步的要求。
%=============================================================================
function sys=mdlUpdate(t,x,u)
 
sys = [];
% 子函数 mdlUpdate 结束
 
%=============================================================================
% mdlOutputs
% 计算并返回模块输出量
%=============================================================================
function sys=mdlOutputs(t,x,u)
 
sys = [];
 
% 子函数 mdlOutputs 结束
 
%=============================================================================
% mdlGetTimeOfNextVarHit
% 返回下一个采样时刻。注意返回结果是一个绝对时间，只在Ts=[-,]时使用。
%=============================================================================
function sys=mdlGetTimeOfNextVarHit(t,x,u)
 
sampleTime = ; % 例子。设置下一个采样时刻为1s后。
sys = t + sampleTime;
 
% 子函数 mdlGetTimeOfNextVarHit 结束
 
%=============================================================================
% mdlTerminate
% 仿真结束
%=============================================================================
%
function sys=mdlTerminate(t,x,u)
 
sys = [];
 
% 子函数 mdlTerminate结束

function [sys,x0,str,ts,simStateCompliance]=limintm(t,x,u,flag,lb,ub,xi）
%传入的三个参数放在后面lb,ub,xi的位置
%LIMINTM Limited integrator implementation.
%   Example MATLAB file S-function implementing a continuous limited integrator
%   where the output is bounded by lower bound (LB) and upper bound (UB)
%   with initial conditions (XI).
%
%   See sfuntmpl.m for a general S-function template.
%
%   See also SFUNTMPL.  
 
%   Copyright - The MathWorks, Inc.
%   $Revision: 1.1.6.2 $  
 
switch flag  
 
  %%%%%%%%%%%%%%%%%%
  % Initialization %
  %%%%%%%%%%%%%%%%%%
  case
    [sys,x0,str,ts,simStateCompliance] = mdlInitializeSizes(lb,ub,xi);  
 
  %%%%%%%%%%%%%%%
  % Derivatives %
  %%%%%%%%%%%%%%%
  case
    sys = mdlDerivatives(t,x,u,lb,ub);  
 
  %%%%%%%%%%%%%%%%%%%%%%%%
  % Update and Terminate %  
 
  %%%%%%%%%%%%%%%%%%%%%%%%
  case {,}
    sys = []; % do nothing  
 
  %%%%%%%%%%
  % Output %
  %%%%%%%%%%
  case
    sys = mdlOutputs(t,x,u);   
 
  otherwise
    DAStudio.error('Simulink:blocks:unhandledFlag', num2str(flag));
end  
 
% end limintm  
 
%
%=============================================================================
% mdlInitializeSizes
% Return the sizes, initial conditions, and sample times for the S-function.
%=============================================================================
%
function [sys,x0,str,ts,simStateCompliance] = mdlInitializeSizes(lb,ub,xi)  
 
sizes = simsizes;
sizes.NumContStates  = ;%1个连续状态，即积分状态
sizes.NumDiscStates  = ;
sizes.NumOutputs     = ;
sizes.NumInputs      = ;
sizes.DirFeedthrough = ;
sizes.NumSampleTimes = ;  
 
sys = simsizes(sizes);
str = [];
x0  = xi; %积分状态初始条件‘
ts  = [ ];   % sample time: [period, offset]  
 
% speicfy that the simState for this s-function is same as the default
simStateCompliance = 'DefaultSimState';  
 
% end mdlInitializeSizes  
 
%
%=============================================================================
% mdlDerivatives
% Compute derivatives for continuous states.
%=============================================================================
%
function sys = mdlDerivatives(t,x,u,lb,ub)  
 
if (x <= lb & u < )  | (x>= ub & u> )
  sys = ;
else
  sys = u;
end  
 
% end mdlDerivatives  
 
%
%=============================================================================
% mdlOutputs
% Return the output vector for the S-function
%=============================================================================
%
function sys = mdlOutputs(t,x,u)  
 
sys = x;  
 
% end mdlOutputs