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
计算机中round函数怎么用
%  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 0is 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 = [00,      : Continuous sample time.
%                    01,      : Continuous, but fixed in minor step
%                                      sample time.
%                    PERIOD OFFSET, : Discrete sample time where
%                                      PERIOD > 0 & OFFSET < PERIOD.
%                    -20];    : Variable step discrete sample time
%                                      where FLAG=4is 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 = [-10]. For functions which
%              are held during minor steps, this is done by specifying
%              SYS(7) = 1 and TS = [-11].
%
%      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 %
%%%%%%%%%%%%%%%%%%
case0,
[sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes;
%%%%%%%%%%%%%%%
% Derivatives %
%%%%%%%%%%%%%%%
case1,
sys=mdlDerivatives(t,x,u);
%%%%%%%%%%
% Update %
%%%%%%%%%%
case2,
sys=mdlUpdate(t,x,u);
%%%%%%%%%%%
% Outputs %
%%%%%%%%%%%
case3,
sys=mdlOutputs(t,x,u);
%%%%%%%%%%%%%%%%%%%%%%%
% GetTimeOfNextVarHit %
%%%%%%%%%%%%%%%%%%%%%%%
case4,
sys=mdlGetTimeOfNextVarHit(t,x,u);
%%%%%%%%%%%%%
% Terminate %
%%%%%%%%%%%%%
case9,
sys=mdlTerminate(t,x,u);
%%%%%%%%%%%%%%%%%%%%
% Unexpected flags %
%%%%%%%%%%%%%%%%%%%%
otherwise
<('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  = [00];
% 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 [-20] 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
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  = 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  = [00];                  %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 = [00, : 连续采样
% 01, : 在1个Ts后连续采样
% PERIOD OFFSET, : Discrete sample time where
% PERIOD > 0 & OFFSET < PERIOD.
% -20]; : 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,
case0, % 初始化
[sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes;
case1, % 连续时间导数
sys=mdlDerivatives(t,x,u);
case2, % 更新离散状态量
sys=mdlUpdate(t,x,u);
case3, % 计算输出
sys=mdlOutputs(t,x,u);
case4, % 计算下⼀步采样时刻
sys=mdlGetTimeOfNextVarHit(t,x,u);
case9, % 结束仿真
sys=mdlTerminate(t,x,u);
otherwise % 未知flag值