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
%   -----  ------             --------------------------------------------
%   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);

  %%%%%%%%%%%%%%%%%%%%%%%
  % GetTimeOfNextVarHit %
  %%%%%%%%%%%%%%%%%%%%%%%
  case 4,
    sys=mdlGetTimeOfNextVarHit(t,x,u);

  %%%%%%%%%%%%%
  % Terminate %
  %%%%%%%%%%%%%
  case 9,
    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  = 0;
sizes.NumDiscStates  = 0;
sizes.NumOutputs     = 0;
sizes.NumInputs      = 0;
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  = [0 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)

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 [-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

(1).mdlInitializeSizes函数-初始化函数
function[sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes  
sizes = simsizes;  
sizes.NumContStates  = 0;  %连续状态个数  
sizes.NumDiscStates  = 0;  %离散状态个数  
sizes.NumOutputs     = 0;  %输出个数  
sizes.NumInputs      = 0;  %输入个数  
sizes.DirFeedthrough = 1;  %是否直接馈通  
sizes.NumSampleTimes = 1;  %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  = [0 0];                  %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 = 1;    %  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 
% —– —— ——————————————– 
% 0 [sizes,x0,str,Ts] 初始化，返回SYS的大小，初始状态x0,str,采样时间Ts 
% 1 DX 返回连续状态微分SYS. 
% 2 DS 更新离散状态 SYS = X(n+1) 
% 3 Y 返回输出SYS. 
% 4 TNEXT Return next time hit for variable step sample time in SYS. 
% 5 Reserved for future (root finding). 
% 9 [] 结束 perform any cleanup SYS=[].

% 当flag=0时，以下信息必须赋值回传 
% SYS(1) = 连续状态个数 
% SYS(2) = 离散状态个数 
% SYS(3) = 输出量个数 
% SYS(4) = 输入量个数 注：上述4个变量可以赋值为-1，表示其值可变 
% SYS(5) = 保留值。为0. 
% SYS(6) = 直接馈通标志(1=yes, 0=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(7) = 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*2 矩阵。（采样周期，偏移量） 
% TS = [0 0, : 连续采样 
% 0 1, : 在1个Ts后连续采样 
% PERIOD OFFSET, : Discrete sample time where 
% PERIOD > 0 & OFFSET < PERIOD. 
% -2 0]; : 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=[0,0] 
% 若希望继承采样时间运行，则设Ts=[-1,0] 
% 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=[-1,1] 
% 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=[0.25,0; 1.0,0.1],则simulink将在下列时刻执行s函数[0,0.1,0.25,0.5,0.75,1,1.1,…]

% 以下是S函数的主函数 
switch flag, 
case 0, % 初始化 
[sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes;

case 1, % 连续时间导数 
sys=mdlDerivatives(t,x,u);

case 2, % 更新离散状态量 
sys=mdlUpdate(t,x,u);

case 3, % 计算输出 
sys=mdlOutputs(t,x,u);

case 4, % 计算下一步采样时刻 
sys=mdlGetTimeOfNextVarHit(t,x,u);

case 9, % 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 = 0; %连续状态个数 
sizes.NumDiscStates = 0; %离散状态个数 
sizes.NumOutputs = 0; %输出量个数 
sizes.NumInputs = 0; %输入量个数 
sizes.DirFeedthrough = 1; %直接馈通标志 
sizes.NumSampleTimes = 1; % 至少有一个采样时刻 
sys = simsizes(sizes);

x0 = 0; % 状态初始化 
str = []; % str 始终为空 
ts = [0 0];% 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=[-2,0]时使用。 
%============================================================================= 
function sys=mdlGetTimeOfNextVarHit(t,x,u)

sampleTime = 1; % 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 1990-2009 The MathWorks, Inc.  
%   $Revision: 1.1.6.2 $  
   
switch flag  
   
  %%%%%%%%%%%%%%%%%%  
  % Initialization %  
  %%%%%%%%%%%%%%%%%%  
  case 0           
    [sys,x0,str,ts,simStateCompliance] = mdlInitializeSizes(lb,ub,xi);  
   
  %%%%%%%%%%%%%%%  
  % Derivatives %  
  %%%%%%%%%%%%%%%  
  case 1  
    sys = mdlDerivatives(t,x,u,lb,ub);  
   
  %%%%%%%%%%%%%%%%%%%%%%%%  
  % Update and Terminate %  
    
  %%%%%%%%%%%%%%%%%%%%%%%%  
  case {2,9}  
    sys = []; % do nothing  
   
  %%%%%%%%%%  
  % Output %  
  %%%%%%%%%%  
  case 3  
    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;%1个连续状态，即积分状态  
sizes.NumDiscStates  = 0;  
sizes.NumOutputs     = 1;  
sizes.NumInputs      = 1;  
sizes.DirFeedthrough = 0;  
sizes.NumSampleTimes = 1;  
   
sys = simsizes(sizes);  
str = [];  
x0  = xi; %积分状态初始条件‘  
ts  = [0 0];   % 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 < 0)  | (x>= ub & u>0 )  
  sys = 0;  
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