利用matlab编写S函数求解微分方程Word格式.docx

利用matlab编写S函数求解微分方程Word格式.docx

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y'

=y-2x/y

y（0）=1

要求利用matlab编写S函数求解

三、设计内容（可加附页）

【步骤1】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2】建立s函数的m文件。

利用21·

用S函数模板文件。

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）

%SFUNTMPLS-function

M-fileGeneral

template

defineyoucanWith%M-fileS-functions,

youownordinarydifferential

systemequations（ODEs）,discrete%

equations,and/orjustabout

anytypeofalgorithmtobeusedwithina%

Simulinkblockdiagram.

%

%ThegeneralformofanM-FileS-function

syntaxis:

%[SYS,X0,STR,TS]=

SFUNC（T,X,U,FLAG,P1,...,Pn）

givenis%WhatreturnedbySFUNCata

pointintime,T,dependsonthe

valueoftheFLAG,thecurrentstatevector,%

X,andthecurrent

inputvector,U.%

%FLAGRESULT

DESCRIPTION

-----

------%

--------------------------------------------

[SIZES,X0,STR,TS]%0

Initialization,returnsystemsizesinSYS,

stateinitial%

inX0,stateorderingstrings

inSTR,and%

sampletimesinTS.

Return

%1DX

continuousstatederivativesinSYS.

%2DSUpdate

discretestatesSYS=X（n+1）

%3YReturn

outputsinSYS.

%4TNEXTReturn

nexttimehitforvariablestepsample

%timein

SYS.

%5Reserved

forfuture（rootfinding）.

%9[]Termination,

performanycleanupSYS=[].

%Thestatevectors,XandX0consistsof

continuousstatesfollowed

%bydiscretestates.

%Optionalparameters,P1,...,Pncanbe

providedtotheS-functionand

%usedduringanyFLAGoperation.

%WhenSFUNCiscalledwithFLAG=0,

thefollowinginformation

%shouldbereturned:

%SYS

（1）=Numberofcontinuousstates.

%SYS

（2）=Numberofdiscretestates.

%SYS（3）=Numberofoutputs.

%SYS（4）=Numberofinputs.

%Anyofthefirstfour

elementsinSYScanbespecified

%as-1indicatingthattheyare

dynamicallysized.The

%actuallengthforallother

flagswillbeequaltothe

%lengthoftheinput,U.

%SYS（5）=Reservedforrootfinding.

Mustbezero.

%SYS（6）=Directfeedthroughflag

（1=yes,0=no）.Thes-function

%hasdirectfeedthroughifU

isusedduringtheFLAG=3

%call.Settingthisto0isakin

tomakingapromisethat

%Uwillnotbeusedduring

FLAG=3.Ifyoubreakthepromise

%thenunpredictableresults

willoccur.

%SYS（7）=Numberofsampletimes.

ThisisthenumberofrowsinTS.

%X0=Initialstateconditionsor[]

ifnostates.

%STR=Stateorderingstrings

whichisgenerallyspecifiedas[].

%TS=Anm-by-2matrix

containingthesampletime

%（period,offset）information.

Wherem=numberofsample

%times.Theorderingofthe

sampletimesmustbe:

%TS=[00,:

Continuoussampletime.

%01,:

Continuous,butfixedinminorstep

sampletime.

%PERIODOFFSET,:

Discretesampletimewhere

PERIOD>

0&

OFFSET<

PERIOD.

%-20];

:

Variablestepdiscretesampletime

whereFLAG=4isusedtogettimeof

nexthit.

%Therecanbemorethanone

sampletimeproviding

%theyareorderedsuchthat

theyaremonotonically

%increasing.Onlytheneeded

sampletimesshouldbe

%specifiedinTS.When

specifyingthanone

%sampletime,youmust

checkforsamplehitsexplicitlyby

%seeingif

abs（round（（T-OFFSET）/PERIOD）-

（T-OFFSET）/PERIOD）

specifiedaiswithin%

tolerance,generally1e-8.This

toleranceisdependentupon%

yourmodel'

ssamplingtimes

andsimulationtime.%

Youcanalsospecifythatthe%

sampletimeoftheS-function

isinheritedfromthedriving%

block.Forfunctionswhich

steps,minorchange%during

thisisdoneby

%specifyingSYS（7）=1and

TS=[-10].Forfunctionswhich

%areheldduringminorsteps,

thisisdonebyspecifying

%SYS（7）=1andTS=[-11].

%Copyright1990-2002TheMathWorks,

Inc.

%$Revision:

1.18$

%Thefollowingoutlinesthegeneralstructure

ofanS-function.

switchflag,

%%%%%%%%%%%%%%%%%%

%Initialization%

case0,

[sys,x0,str,ts]=mdlInitializeSizes;

%%%%%%%%%%%%%%%

%Derivatives%

case1,

sys=mdlDerivatives（t