基于S函数的simulink仿真

基于S函数的simulink仿真

S函数可以用计算机语言来描述动态系统。在控制系统设计中，S函数可以用来描述控制算法、自适应算法和模型动力学方程。

S函数中使用文本方式输入公式和方程，适合复杂动态系统的数学描述，并且在仿真过程中可以对仿真参数进行更精确的描述、

1.1 S函数简介

S函数是系统函数（system function）的简称。可以用MATLAB代码、C、C++等语言来编写S函数。

1.2 S函数的使用步骤

步骤如下：

1. 创建S函数源文件
2. 在动态系统的simulink模型框图中添加S-function模块，并且进行正确设置
3. 在simulink模型框图中按照定义好的功能连接输入输出端口

1.3 S函数的基本功能及重要参数设定

S函数的基本功能及重要参数设定如下：

1. S函数功能模块：各种功能模块完成不同的任务，这些功能模块（函数）称为仿真例程或回调函数（call - back functions），包括初始化（initialization）、导数（mdlDerivative）、输出（mdlOutput）等。
2. NumContStates表示S - 函数描述的模块中连续状态的个数。
3. NumDiscStates表示离散状态的个数。
4. NumOutputs和NumInputs分别表示模块输出和输入的个数。
5. 直接馈通（dirFeedthrough）为输入信号是否在输出端出现的标识，取值为0或1。例如，形如$y=k\times u$的系统需要输入（即直接反馈），其中，$u$是输入，$k$是增益，$y$是输出，形如等式$y=x,\dot{x}=u$的系统不需要输入（即不存在直接反馈），其中，$x$是状态，$u$是输入，$y$为输出。
6. NumSampleTimes为模块采样周期的个数，S函数支持多采样周期的系统。 除了sys外，还应设置系统的初始状态变量$x_0$、说明变量str和采样周期变量$t_s$。$t_s$变量为双列矩阵，其中每一行对应一个采样周期。对连续系统和单个采样周期的系统来说，该变量为$[t_1,t_2]$，$t_1$为采样周期，$t_1=-1$表示继承输入信号的采样周期，$t_2$为偏移量，一般取为0。对连续系统来说，$t_s$取为$[-1,0]$。

1.4 S函数描述实例

在控制系统设计中，S函数可以用于控制器、自适应律和模型描述。

以模型$J\ddot{\theta }=u+d(t)$为例，其中，$u$为控制输入，$d(t)$为加在控制输入端的扰动，模型输出为$\theta 和\dot{\theta }$，即转动角度和角速度，$J$为转动惯量，该模型可以描述如下：
$$\begin{array}{rl}{\dot{x}}_1& =x_2\\ {\dot{x}}_2& =\frac{1}{J}(u+d(t))\end{array}$$
其中：$x_1=\theta ,x_2=\dot{\theta }$

1 首先，初始化Initialization函数

采用S函数来描述动力学方程，可选取1输人2输出系统，如果角度和角速度的初始值取零，则模型初始化参数写为[0，0]，模型初始化S函数描述如下：（见模板)

2 微分方程描述的mdlDerivative函数

该函数可用于描述微分方程并实现数值求解。在控制系统中，可以采样该函数来描述被控对象和自适应律等，并通过Simulink环境下选择数值分析方法来实现对模型的数值求解

取$J=2，d(t)=sint$，则采用S函数可以实现模型角度和角速度的求解，描述如下：

function sys=mdlDerivatives(t,x,u)J=2;
dt=sin(t);
ut=u(1);
sys(1)=x(2);
sys(2)=1/J*(ut+dt);sys = [dx1;dx2];

3 用于输出的mdlOutput函数

S函数的mdlOutput函数通常用于描述控制器或模型的输出。采用S函数的mdlOutput模块来描述模型角度和角速度的输出：

function sys=mdlOutputs(t,x,u)sys(1) = x(1);
sys(2) = x(2);

最后，给出S函数模板

function [sys,x0,str,ts,simStateCompliance] = plant(t,x,u,flag,pa)
%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,pa);%%%%%%%%%%% 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 %%%%%%%%%%%%%%%%%%%%%otherwiseDAStudio.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  = 2;
sizes.NumDiscStates  = 0;
sizes.NumOutputs     = 2;
sizes.NumInputs      = 1;
sizes.DirFeedthrough = 0;
sizes.NumSampleTimes = 1;   % at least one sample time is neededsys = simsizes(sizes);%
% initialize the initial conditions
%
x0  = [0,0];%
% 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,pa)
k=pa.k;
m=pa.m;x1=x(1);
x2=x(2);dx1=x2;
dx2=-k/m*x1^3+u/m;sys = [dx1;dx2];% 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 = x;% 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