S函数设计初学者实例.doc

利用matlab中s函数模板设计一个连续系统的s-function。给定控制系统的传递函数为。试利用仿真集成环境simulink中的s函数，绘制此控制系统的阶跃响应曲线。
【步骤1】获取状态空间表达式。
根据传递函数，写出该控制系统的运动方程，如下：

选取状态变量x=y，则系统的状态空间方程表示为：

【步骤2】建立s函数的m文件。
复制matlab安装文件夹下的toolbox\simulink\blocks子目录下的sfuntmpl.m文件，并将其改名为sfuction_example.m再根据状态方程修改程序中的代码。（1）重新命名函数；
function [sys,x0str,ts] = sfunction_example(t,x,u,flag,x_initial)
%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.
%
% The general form of an M-File S-function syntax is:
% [SYS,X0,STR,TS] = 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 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 1990-2002 The MathWorks, Inc.
% $Revision: 1.18 $

%
% The following outlines the general structure of an S-function.
%
switch flag,

%%%%%%%%%%%%%%%%%%
% Initialization %
%%%%%%%%%%%%%%%%%%
case 0,
[sys,x0,str,ts]=mdlInitializeSizes(x_initial);

%%%%%%%%%%%%%%%
% 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
（2）修改“初始化”子函数部分的代码；
function [sys,x0,str,ts]=mdlInitializeSizes(x_initial)

%
% 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 = 1;
sizes.NumDiscStates = 0;
sizes.NumOutputs = 1;
sizes.NumInputs = 1;
sizes.DirFeedthrough = 0;
sizes.NumSampleTimes = 1; % at least one sample time is needed

sys = simsizes(sizes);

%
% initialize the initial conditions
%
x0 = x_initial;

%
% str is always an empty matrix
%
str = [];

%
% initialize the array of sample times
%
ts = [0 0];
（3）修改“计算模块导数”子函数部分的代码；
function sys=mdlDerivatives(t,x,u)

dx=-x+u

sys =dx;
（4）修改“更新模块离散状态”子函数部分代码；
function sys=mdlUpdate(t,x,u)

sys = [];
（5）修改“计算模块输出”子函数部分代码；
function sys=mdlOutputs(t,x,u)

sys =x;
（6）修改“计算下一个采样时间点”子函数部分的代码；
function sys=mdlGetTimeOfNextVarHit(t,x,u)

sampleTime = 1; % Example, set the next hit to be one second later.
sys t + sampleTime;
（7）修改“仿真结束”子函数部分的代码。
function sys=mdlTerminate(t,x,u)

sys = [];

% end mdlTerminate

【步骤3】将sfunction_example创建成s-function模块。
打开simulink，在simulink中新建一个空白的模型窗口，拖动“User-Defined Function”库中的S-Function模块到其中，并相应放置输入的阶跃信号发生器和监测输出波形的示波器，如下图：

【步骤4】给状态变量赋值初始值。
在进行真正的仿真之前，还需要在matlab工作空间为状态变量x的初始值x_initial进行赋值。在matlab工作空间中输入如下命令：
clear;
x_initial=0;
参数设定之后，启动simulink仿真。得到的结果如下：

为了验证上述结果，可以在simulink中搭建下图所示的控制系统：

其结果跟上述的s-function仿真结果一致。