利用matlab编写S函数求解微分方程

1、无自动化专业综合设计报告自动化专业综合设计报告设计题目：设计题目：利用利用 matlab 编写编写 S 函数求解微函数求解微分方程分方程所在实验室：所在实验室：自动化系统仿真实验室自动化系统仿真实验室指导教师：指导教师：郭卫平郭卫平学生姓名学生姓名律迪迪律迪迪班级班级文自文自 0921学号学号200990519114成绩评定：成绩评定：无一、一、设计目的设计目的了解使用 simulink 的扩展工具S-函数，s 函数可以利用 matlab 的丰富资源，而不仅仅局限于 simulink 提供的模块，而用 c 或 c+等语言写的 s 函数还可以实现对硬件端口的操作，还可以操作 windowsAPI

2、 等的， 它的魅力在于完美结合了 simulink 框图简洁明快的特点和编程灵活方便的优点，提供了增强和扩展 sinulink 能力的强大机制，同时也是使用 RTW 实现实时仿真的关键。二、二、设计要求设计要求求解解微分方程y=y-2x/yy(0)=1要求利用 matlab 编写 S 函数求解三、三、设计内容（可加附页）设计内容（可加附页）【步骤【步骤 1】获取状态空间表达式。】获取状态空间表达式。在 matlab 中输入dsolve(Dy=y-2*x/y,y(0)=1，x)得到y=(2*x+1).(1/2);【步骤【步骤 2】建立】建立 s 函数的函数的 m 文件。文件。利用 21用 S 函

3、数模板文件。以下是修改之后的模板文件 sfuntmpl.m 的内容。function sys,x0,str,ts = sfuntmpl(t,x,u,flag)%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 S

4、imulink 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.%FLAGRESULTDESCRIPTION%-%0SIZES,X

5、0,STR,TSInitialization, return system sizes in SYS,%initial state in X0, state ordering strings无%in STR, and sample times in TS.%1DXReturn continuous state derivatives in SYS.%2DSUpdate discrete states SYS = X(n+1)%3YReturn outputs in SYS.%4TNEXTReturn next time hit for variable step sample%time in

6、SYS.%5Reserved for future (root finding).%9Termination, 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 =

7、 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 lengt

8、h 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 no

9、t 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 s

10、ample time%(period, offset) information. Where m = number of sample%times. The ordering of the sample times must be:%无%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

11、 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 h

12、its 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 models sampling times%and simulation time.%You can also specify that the sample time of the S-function%is inherited from the driving blo

13、ck. 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

14、structure of an S-function.%switch flag,% Initialization %case 0,sys,x0,str,ts=mdlInitializeSizes;% Derivatives %无case 1,sys=mdlDerivatives(t,x,u);% Update %case 2,3,9,sys=;% Outputs % GetTimeOfNextVarHit % Terminate % Unexpected flags %otherwiseerror(Unhandled flag = ,num2str(flag);end% end sfuntmp

15、l%=% mdlInitializeSizes% Return the sizes, initial conditions, and sample times for the S-function.%=%function sys,x0,str,ts=mdlInitializeSizes%无% 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% re

16、commended 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= 0;sizes.NumInputs= 0;sizes.DirFeedthrough = 1;sizes.NumSampleTimes = 1;% at least one sample time is neededsys

17、= simsizes(sizes);% initialize the initial conditions%x0= 0 1.0000;% str is always an empty matrix%str = ;% initialize the array of sample times%ts= 0 0;% end mdlInitializeSizes%=% mdlDerivatives% Return the derivatives for the continuous states.%=%function sys=mdlDerivatives(t,x,u)无sys(1)=（u-2*x/u）

18、*t+u;【步骤【步骤 3】利用】利用 matlab 调用函数得到结果。调用函数得到结果。利用 sys=sfuntmpl(,x,1)调用 S 函数，替换 x 得到不同的结果四、四、设计实验结果及分析设计实验结果及分析替换不同德 x 得到不同结果。为检验结果是否正确在命令窗口运行x1(1)=0;y1(1)=1; h=0.1;for k=1:10 x1(k+1)=x1(k)+h;endx=0:0.1:1;y=(2*x+1).(1/2);x1=x1(1:11),y=y(1:11),无与 S 函数所对应，所以上述实验结果正确。五、五、结论结论上述为本次解微分方程得到的结果。六、六、设计感受设计感受通过本次试验充分理解了 S 函数的框图简洁明快的特点和编程灵活方便的优点。同时复习总结了 matlab 程序的使用。实验过程遇到得问题通过咨询老师，同学讨论，查阅资料的都得到了解决，充分锻炼了自己认识问题解