計算機仿真-北京交通大學(xué)電氣工程學(xué)院

1、在抗擊“非典”期間，學(xué)校課程安排受到很大的影響，因此對授課的方式和內(nèi)容作了相應(yīng)的修改：,1、取消第四章，將仿真實例的學(xué)習(xí)排入前三章，要求同學(xué)通過自己的上機實踐學(xué)習(xí)Matlab和Simulink的基本操作。2、原上機實踐部分的內(nèi)容安排為幾個范例的學(xué)習(xí)。同學(xué)們應(yīng)充分利用范例對所涉及的關(guān)鍵內(nèi)容進行實踐。,計 算 機 仿 真 技 術(shù),童 亦 斌2003.4,系統(tǒng)的分析方法,系統(tǒng)：客觀世界中相互作用的實體所構(gòu)成的具有特定功能的整體。為了定量

2、分析系統(tǒng)，可將其本身的特點和內(nèi)部的相互關(guān)系抽象出來，構(gòu)造出系統(tǒng)的模型。對系統(tǒng)的分析變成對系統(tǒng)模型的分析。系統(tǒng)模型：分物理模型和數(shù)學(xué)模型，由于計算機技術(shù)的發(fā)展，數(shù)學(xué)模型的應(yīng)用越來越廣泛。系統(tǒng)的數(shù)學(xué)模型：描述系統(tǒng)動態(tài)特性的數(shù)學(xué)表達式。根據(jù)系統(tǒng)的性質(zhì)和數(shù)學(xué)分析工具可分為：連續(xù)系統(tǒng)、離散時間系統(tǒng)、離散事件系統(tǒng)、混合系統(tǒng)等。,系統(tǒng)的仿真分析方法,仿真技術(shù)：用模擬的方法模擬實際系統(tǒng)的表現(xiàn)。仿真技術(shù)的基本方法：數(shù)學(xué)模型仿真、物理模型仿真、硬件

3、仿真、操作仿真、虛擬現(xiàn)實。系統(tǒng)仿真：根據(jù)系統(tǒng)數(shù)學(xué)模型研究系統(tǒng)性能。計算機仿真：利用計算機完成對系統(tǒng)的仿真。本課程特指利用計算機、根據(jù)系統(tǒng)的數(shù)學(xué)模型對電路系統(tǒng)進行仿真。,計算機仿真技術(shù)講授內(nèi)容,計算機仿真技術(shù)概述Matlab和Simulink簡介計算機仿真的建模計算機仿真實例計算機仿真上機實踐,本課程的學(xué)習(xí)方法、作業(yè)和考試,學(xué)習(xí)方法：特別強調(diào)直接在計算機進行實踐，強調(diào)學(xué)習(xí)利用Matlab各種資源解決問題；作業(yè)：分別關(guān)于Mat

4、lab的基本使用、Simulink的建模、S函數(shù)和Simulink結(jié)果的調(diào)用；考試：建立一個交流異步電機變頻啟動的計算機仿真模型，對交流異步電機的變頻啟動過程進行觀察；,交流電機變頻系統(tǒng)框圖,考試的基本要求和條件,基本要求－利用搭建的模型研究變頻啟動過程中電機電流的變化情況；條件：電源電壓直流600V、電機為Simulink默認(rèn)的交流異步電機、電機空載、采用理想IGBT逆變器橋、開關(guān)頻率固定為2500Hz、輸出頻率從5Hz變化到50

5、Hz、啟動時間可調(diào)；,第一章 計算機仿真技術(shù)概述,為什么要進行計算機仿真？計算機仿真能完成什么任務(wù)？計算機仿真技術(shù)的關(guān)鍵仿真軟件的發(fā)展?fàn)顩r電子設(shè)計自動化的主要應(yīng)用領(lǐng)域計算機仿真的基本步驟計算機仿真設(shè)計的原則,§1.1 為什么要進行計算機仿真？,實際系統(tǒng)的理論分析往往非常復(fù)雜，傳統(tǒng)的分析方法幾乎不可能完成；很多時候幾乎不可能或很難進行真實實驗的分析和驗證；實驗的成本高、效率低、周期長；,通過計算機仿真我們能夠

6、：,提高設(shè)計效率、縮短設(shè)計周期；準(zhǔn)確、全面地模擬和分析系統(tǒng)；提高產(chǎn)品和技術(shù)的設(shè)計質(zhì)量；降低設(shè)計成本；充分發(fā)揮設(shè)計人員的創(chuàng)造性；降低干擾因素的影響，集中注意于關(guān)鍵問題；優(yōu)化系統(tǒng)和參數(shù)的設(shè)計,§1.2 計算機仿真能完成什么任務(wù)？,動態(tài)系統(tǒng)的仿真分析；參數(shù)的優(yōu)化；極限參數(shù)的設(shè)計；環(huán)境參數(shù)對系統(tǒng)性能的影響；突發(fā)或偶發(fā)事件的模擬；電子設(shè)計自動化（Electronic Design Automation）,

7、7;1.3 計算機仿真技術(shù)的關(guān)鍵,數(shù)值計算算法；電路數(shù)學(xué)模型建立的模塊化；不同應(yīng)用軟件間的數(shù)據(jù)共享；仿真計算的效率和準(zhǔn)確性；混合系統(tǒng)的建模和仿真；仿真結(jié)果的可視化；,§1.4 仿真軟件的發(fā)展?fàn)顩r,現(xiàn)代仿真軟件的特點：功能強大的數(shù)學(xué)軟件包作為計算引擎、交互式的編程方式、友好的圖形界面、豐富的模型資源和良好的程序接口等；,早期仿真語言和程序,早期數(shù)學(xué)軟件包,現(xiàn)代的仿真軟件,§1.5 電子設(shè)計自動化的主要應(yīng)

8、用領(lǐng)域,EDA的主要應(yīng)用領(lǐng)域包括：－集成電路設(shè)計－模擬電路仿真－動態(tài)系統(tǒng)的仿真EDA主要軟件及特點：Protel、Pspice、Saber、Matlab,§1.6 計算機仿真的基本步驟,計算機仿真過程包括分析、建模、計算和驗證；模型的調(diào)試和計算主要依靠仿真軟件的設(shè)計和使用；驗證過程非常重要；人為的干預(yù)和控制對仿真的效果有很大的影響；,系統(tǒng)和任務(wù)分析,建立系統(tǒng)的仿真模型,模型的調(diào)試與計算,仿真結(jié)果的驗證

9、,§1.7 計算機仿真設(shè)計的原則,“分級仿真”原則：對系統(tǒng)的分析應(yīng)根據(jù)任務(wù)的不同采用不同的仿真模型或算法，合理簡化系統(tǒng)，突出問題的關(guān)鍵；“準(zhǔn)確度與速度合理兼顧”原則：在仿真的不同階段合理調(diào)整對準(zhǔn)確度和速度的要求，提高仿真效率；“可信驗證”原則：所有仿真結(jié)果應(yīng)有可信的驗證方法或依據(jù)；,第二章 Matlab和Simulink簡介,Matlab和Simulink簡介MATLAB InstallationMATLAB De

10、sktopArrayScripts and FunctionsSimulink交互式仿真環(huán)境SolverS-Function,§2.0 Matlab和Simulink簡介,Matlab是集數(shù)值計算、符號運算和圖形處理功能于一身的超級科學(xué)計算語言；與其它計算語言相比，Matlab在功能、開放性和易學(xué)性等方面獨占鰲頭；Matlab的核心是數(shù)值計算，Simulink是建立系統(tǒng)框圖和仿真的環(huán)境；,* Battery(s

11、)V0 43 0 DC 15V; V1 39 0 DC 15V; *DISCHARGEV_0 41 0 PULSE(-15 15 196ms 10us 10us 20ms 200ms); *OFFSETV_1 5 0 PULSE(5 -5.7 150ms 10us 10us 50ms 200ms); *PIBIASV_2 1 0 PULSE(10 -10 190ms 2us 2us 10ms 200ms); *

12、Misc.TRAN 10us 210ms 0s 10ms UIC,語句方式,框圖方式,§2.1 MATLAB Installation,The main Products of Matlab for modeling and simulating dynamical systems：－Matlab－Symbolic Math－Simulink－Control System,§2.2 MATL

13、AB Desktop,Command Window（指令窗）Command History（歷史指令窗）Launch Pad（交互界面分類目錄窗）Help Browser（幫助瀏覽器）Current Directory Browser（當(dāng)前目錄瀏覽器）Workspace Browser（工作空間瀏覽器）Array Editor（內(nèi)存數(shù)組瀏覽器）Editor/Debugger（M文件編輯/調(diào)試器）,Launch Pad,,C

14、urrent Directory Browser,Command Window,Matlab常用標(biāo)點的功能,§2.3 Array,Array（數(shù)組）的基本概念數(shù)組在Matlab仿真計算中的應(yīng)用Numeric Array（數(shù)值數(shù)組）數(shù)值元素的標(biāo)識Character Array（字符串?dāng)?shù)組）Cell Array（元胞數(shù)組）Structure Array（架構(gòu)數(shù)組）,§2.3.1 Array（數(shù)組）的基本概

15、念,MATLAB works with only a single object－the array（數(shù)組）。數(shù)組：一組數(shù)組成的長方陣列。Its typeIts dimensionsIts contentThe data associated with this arrayIf numeric,whether the variable is real or complexIf a structure,the n

16、umber of fields and field names,數(shù)組與矩陣的區(qū)別,矩陣：作為一種變換或映射算子的體現(xiàn)，矩陣有著明確而嚴(yán)格的數(shù)學(xué)規(guī)則；數(shù)組：Matlab設(shè)置數(shù)組的目的主要是為了簡化數(shù)據(jù)的管理和操作、使指令的形式更加自然、程序的運行更加有效；Matlab中對數(shù)組的計算實際上是對數(shù)組中每個元素平等地施加同樣地操作；,§2.3.2 數(shù)組在Matlab仿真計算中的應(yīng)用,Matlab中數(shù)據(jù)的存放和處理均采用數(shù)組；M

17、atlab中的數(shù)組主要分為：Numeric Array，Character Array，Cell Array， Structure ArrayCharacter Array可用于仿真結(jié)果和過程的可視化；Structure Array可用于與Simulink交換信息，包括仿真參數(shù)的設(shè)定、結(jié)果的獲取和處理等；,§2.3.3 Numeric Array（數(shù)值數(shù)組）,數(shù)值數(shù)組是Matlab中最基本地數(shù)組形式；數(shù)值數(shù)組分實數(shù)

18、數(shù)組和復(fù)數(shù)數(shù)組；,>> A=[1 2 3 4,5 6 7 8]A = 1 2 3 4 5 6 7 8>> A=[1 2 3 4;5 6 7 8]A = 1 2 3 4 5 6 7 8>> A*4ans = 4 8 12 16

19、 20 24 28 32,§2.3.4 數(shù)組元素的標(biāo)識,“全下標(biāo)”標(biāo)識“單下標(biāo)”標(biāo)識,>> A(4)ans = 6>> A(1,4)ans = 4>> A(2,3)=0;>> AA = 1 2 3 4 5 6 0 8,A = 1 2 3 4

20、 5 6 7 8,單下標(biāo),全下標(biāo),冒號的使用,j:kis the same as [j,j+1,...,k]j:i:kis the same as [j,j+i,j+2i, ...,k]A(:,j)is the j-th column of AA(i,:)is the i-th row of A,§2.3.5 Character Array（字符串?dāng)?shù)組）,字符串?dāng)?shù)組－基本元素是字

21、符串。字符串?dāng)?shù)組可用于計算過程和結(jié)果的可視化。字符串?dāng)?shù)組的直接創(chuàng)建。利用串操作函數(shù)創(chuàng)建串?dāng)?shù)組。,A = ‘The exmaple of the Character Arrays',>> A=['1234 ';'12345']A =1234 12345,>> A=char('1234','12345')A =1234 1234

22、5,轉(zhuǎn)換函數(shù)產(chǎn)生數(shù)碼字符串,Int2str（整數(shù)數(shù)組轉(zhuǎn)換為串?dāng)?shù)組）；Num2str（非整數(shù)數(shù)組轉(zhuǎn)換為串?dāng)?shù)組）；,A=rand(2,4)A =0.9501 0.6068 0.8913 0.4565 0.2311 0.4860 0.7621 0.0185B=num2str(A,2),C=int2str(A)B =0.95 0.61 0.89 0.46

23、 0.23 0.49 0.76 0.019C =1 1 1 0 0 0 1 0class(B),class(C)ans =charans =char,clear%清除內(nèi)存中地所有變a=2,w=3;%t=0:0.01:10;%取自變量采樣數(shù)組y=exp(-a*t).*sin(w*t);%計算函數(shù)值，產(chǎn)生函數(shù)數(shù)組[y_max,i_max]=

24、max(y);%找最大值的位置t_text=[‘t=’,num2str(t(i_max))];%生成最大值點的橫坐標(biāo)字符串y_text=[‘y=’,num2str(y_max)];%生成最大值點的眾坐標(biāo)字符串max_text=char('maximum',t_text,y_text);%生成最大值點的字符串tit=['y=exp(-',num2str(a),'t)*

25、sin(',num2str(w),'t)'];%plot(t,zeros(size(t)),‘k’);%畫縱坐標(biāo)為0的基準(zhǔn)線hold on%plot(t,y,‘b’);%繪制函數(shù)曲線plot(t(i_max),y_max,‘r.’,‘MarkerSize’,20);%標(biāo)注最大值點text(t(i_max)+0.3,y_max+0.05,max_text);%標(biāo)注最

26、大值點的字符串title(tit),xlabel(‘t’),ylabel(‘y’),hold off%標(biāo)注圖名、橫坐標(biāo)名、縱坐標(biāo)名,字符串?dāng)?shù)組用于計算結(jié)果的可視化實例,字符串?dāng)?shù)組用于計算結(jié)果的可視化實例,§2.3.6 Cell Array（元胞數(shù)組）,The elements of a cell array are cells, containers that can hold other MATLAB arrays.

27、,§2.3.6.1 Creating Cell Arrays,Cell indexing（元胞外標(biāo)識）:A(1,1) = {[1 4 3; 0 5 8; 7 2 9]};A(1,2) = {'Anne Smith'};A(2,1) = {3+7i};A(2,2) = {-pi:pi/10:pi};,A(1,1) = {[1 4 3; 0 5 8; 7 2 9]};A(1,2) = {'Ann

28、e Smith'};A(2,1) = {3+7i};A(2,2) = {-pi:pi/10:pi};A = [3x3 double] 'Anne Smith' [3.0000+ 7.0000i] [1x21 double],Content indexin（元胞內(nèi)標(biāo)識）:A{1,1} = [1 4 3; 0 5 8; 7 2 9];A{1,2} = 'Anne Smith'

29、;A{2,1} = 3+7i;A{2,2} = -pi:pi/10:pi;,§2.3.6.2 Obtaining Data from Cell Arrays,調(diào)取元胞數(shù)據(jù)分：元胞的調(diào)取和元胞內(nèi)容的調(diào)?。辉貥?biāo)識分：元胞外標(biāo)識和元胞內(nèi)標(biāo)識；,A{1,1}ans =1 4 3 0 5 8 7 2 9A{1,1}(1,2)ans = 4,A

30、(1,1)={[1 2 3;4 5 6]};A(1,1)=[2x3 double]A{1,1}=1 2 3 4 5 6,§2.3.7 Structure Array（構(gòu)架數(shù)組）,The elements of a Structure Array are Structures.Structures are MATLAB arrays with "dat

31、a containers" called fields. The fields of a structure can contain any kind of data. Structure Array的基本組分是架構(gòu)( Structure) ，在Structure以下劃分了域（Field），域可用于存放任何形式的數(shù)據(jù)。,§2.3.7.1 Structure Array的基本結(jié)構(gòu),patient.name = &

32、#39;John Doe';patient.billing = 127.00;patient.test = [79 75 73; 180 178 177.5; 220 210 205];,A Structure Array,A Structure,§2.3.7.2 Building Structure Arrays,方法一：直接聲明patient(2).name = 'Ann Lane';pa

33、tient(2).billing = 28.50;patient(2).test = [68 70 68; 118 118 119; 172 170 169];,方法二：利用struct指令patient(2)=struct('name','Ann Lane','billing',28.50,'test',[68 70 68; 118 118 119; 172 170

34、169])patient = 1x2 struct array with fields:namebillingtest,§2.3.7.3 Accessing Data in Structure Arrays,架構(gòu)數(shù)組的存取：架構(gòu)－>域－>內(nèi)容,mypatients = patient(1:2)1x2 struct array with fields: name billing

35、test,mypatients(1)ans = name: 'John Doe' billing: 127 test: [3x3 double],str = patient(2).namestr =Ann Lane,patient(2).testans = 68 70 68 118 118 119 172 170 169,

36、§2.4 Scripts and Functions,Scripts（腳本文件）, which do not accept input arguments or return output arguments. They operate on data in the workspace.Functions（函數(shù)文件）, which can accept input arguments and return output a

37、rguments. Internal variables are local to the function.,§2.4.1 Scripts,When you invoke a script, Matlab simply executes the commands found in the file. Scripts can operate on existing data in the workspace, or the

38、y can create new data on which to operate. Although scripts do not return output arguments, any variables that they create remain in the workspace, to be used in subsequent computations.Scripts在使用Simulink時的主要作用：作為調(diào)用Simu

39、link模型的外部環(huán)境。,§2.4.2 Flow Control,Scripts中可以使用各種流程控制，用于控制Simulink的調(diào)用或參數(shù)的設(shè)置。主要的流程控制包括：－if statements－switch statements－for loops－while loops,§2.4.2.1 if statements,判斷結(jié)構(gòu),if rem(n,2) ~= 0 M = odd_magi

40、c(n)elseif rem(n,4) ~= 0 M = single_even_magic(n)else M = double_even_magic(n)end,§2.4.2.2 switch statements,選擇結(jié)構(gòu),switch (rem(n,4)==0) + (rem(n,2)==0) case 0 M = odd_magic(n) case 1 M

41、 = single_even_magic(n) case 2 M = double_even_magic(n) otherwise error('This is impossible') end,§2.4.2.3 for loops,For循環(huán),for n = 3:32 r(n) = rank(magic(n));end,§2.4.2.4 wh

42、ile loops,While（條件）循環(huán),while b-a > eps*b x = (a+b)/2; fx = x^3-2*x-5; if sign(fx) == sign(fa) a = x; fa = fx; else b = x; fb = fx; endend,§2.4.3 Functions（函數(shù)）,Create a Function,Call a

43、Function,function area=circle(r,s)%CIRCUIT this is keyword of the function% next is comment linesclf; %clear current figure windowsita=0:pi/100:2*pi;y=r*exp(i*sita);plot(y,s);area=pi*r^2;,c

44、ircle(2,'r')ans = 12.5664 x=circle(2,'b')x= 12.5664,Function最典型的應(yīng)用S-Function,§2.5 Simulink交互式仿真環(huán)境,Simulink,the most widely used software package in academia and industry for modeling and si

45、mulating dynamical systems.Interactive,you can change parameters and see what happens immediately.Simulink provides a graphical user interface (GUI).Simulink is practical,it is being used by thousands of engineers aro

46、und the world.,Simulink的基本操作Modeling Dynamic SystemsSimulating Dynamic SystemsModeling and Simulating Discrete Systems,§2.5.1 Modeling Dynamic Systems,Blocks（模塊）States（狀態(tài)）System Functions（仿真運行功能）Continuous an

47、d Discrete Blocks（連續(xù)和離散系統(tǒng)）Sample Time（采樣時間）,§2.5.1.1 Blocks（模塊）,Blocks－Each block represents an elementary dynamic system that produces an output.Simulink本身具有比較豐富的Block資源，應(yīng)首先予以考慮。,為方便設(shè)計，最好遵照下述命名規(guī)則：u：輸入x：（內(nèi)部）狀態(tài)

48、y：輸出,§2.5.1.2 States（內(nèi)部狀態(tài)）,A block that has a state must store previous values of the state to compute its current state.Examples of the blocks that have STATES：Integrator，Unit DelayThe Simulink Gain block is

49、an example of a stateless block.,§2.5.1.3 System Functions（仿真運行功能）,所謂System Functions是指仿真計算的三個循環(huán)步驟：1、An output function（輸出）：Relates the system's outputs to its inputs, states, and time,y=f(t,x,u)2、An update f

50、unction（離散狀態(tài)刷新）: Relates the future values of the system‘s discrete states to the current time,inputs, and states,xdk+1= f(t,x,u)3、A derivative function（連續(xù)狀態(tài)刷新）：Relates the derivatives of the continuous states to time a

51、nd the present values of the states and inputs,xc’= f(t,x,u),§2.5.1.4 Continuous and Discrete Blocks,Continuous blocks respond continuously to continuously changing input.Discrete blocks respond to changes in inpu

52、t only at the block's sample time. Discrete blocks hold their output constant between successive sample time hits.Some blocks can be either continuous or discrete,depending on whether they are driven by continuous o

53、r discrete blocks.,§2.5.2 Simulating Dynamic Systems,Model Initialization PhaseModel Execution PhaseProcessing at Each Time Step,§2.5.2.1 Model Initialization Phase,During the initialization phase, Simulink

54、:1、Evaluates the model's block parameter expressions to determine their values.2、Flattens the model hierarchy by replacing virtual subsystems with the blocks that they contain.3、Sorts the blocks into the order in

55、which they need to be executed during the execution phase.4、Determines signal attributes.5、Determines the sample times.6、Allocates and initializes memory used to store the current values of each block's states and

56、 outputs.,§2.5.2.2 Model Execution Phase,Simulink successively computes the states and outputs of the system at intervals from the simulation start time to the finish time, using information provided by the model.

57、The successive time points at which the states and outputs are computed are called time steps. The length of time between steps is called the step size.Simulink決定計算步長依據(jù)：用戶的設(shè)定、離散模塊或系統(tǒng)的采樣時間、數(shù)值計算的誤差。,§2.5.2.3 Proces

58、sing at Each Time Step,At each time step, Simulink1、Updates the outputs of the models' blocks in sorted order.2、Updates the states of the model's blocks in sorted order.3、Optionally checks for discontinuiti

59、es in the continuous states of blocks.4、Computes the time for the next time step.,§2.5.3 Modeling and Simulating Discrete Systems,Discrete BlocksSample TimePurely Discrete SystemsMultirate SystemsDetermining

60、 Step Size for Discrete SystemsSample Time PropagationInvariant ConstantsMixed Continuous and Discrete Systems,§2.5.3.1 Discrete Blocks,Each of the discrete blocks hasA built-in sampler at its inputA zero-or

61、der hold at its output,§2.5.3.2 Sample Time,The Sample time parameter sets the sample time at which a discrete block's states are updated.Specify an offset time (or skew) by specifying a two-element vector in

62、this field.Cannot change the sample time of a block while a simulation is running.,§2.5.3.3 Purely Discrete Systems & Multirate Systems,Purely Discrete Systems:系統(tǒng)中所有模塊都按單一的采樣率進行工作.Multirate Systems:系統(tǒng)中的模塊采用不同

63、的采樣率進行工作.,§2.5.3.4 Determining Step Size for Discrete Systems,The fundamental sample time of a discrete system is the greatest integral divisor of the system's actual sample times.You can direct Simulink to us

64、e either a fixed-step or a variable-step discrete solver to solve a discrete system.,§2.5.3.5 Mixed Continuous and Discrete Systems,Mixed continuous and discrete systems are composed of both sampled and continuous

65、blocks.For most mixed continuous and discrete systems, the Runge-Kutta variable step methods, ode23 and ode45, are superior to the other methods in terms of efficiency and accuracy. Due to discontinuities associated wit

66、h the sample and hold of the discrete blocks, the ode15s and ode113 methods are not recommended for mixed continuous and discrete systems.,§2.6 Solver（解算控制）,The Solver pane allows you to:－Set the simulation start

67、 and stop times－Choose the solver and specify its parameters－Select output options,§2.7 Data Exchange Within Simulink and Workspace,Workspace I/O Pane-You can direct simulation output to workspace variables and

68、 get input and initial states from the workspace.,From Workspace Block & To Workspace Block,§2.8 S-Function,What Is an S-Function?-An S-function is a computer language description of a Simulink block.When to

69、 Use an S-Function?-Adding new general purpose blocks to Simulink-Adding blocks that represent hardware device drivers-Incorporating existing C code into a simulation-Describing a system as a mathematical set of

70、equations-Using graphical animations (see the inverted pendulum demo, penddemo),Mathematics of Simulink Blocks,S-Function:實際上是利用Matlab的編程語言直接設(shè)計模塊的數(shù)學(xué)模型S-Function的運行主要由三個環(huán)節(jié)組成:output,derivative,update,The stages of a sim

71、ulation.,S-Function的運行實際上是一個循環(huán)調(diào)用的過程,Implementing S-Functions,An M-file S-function: [sys,x0,str,ts]=f(t,x,u,flag,p1,p2,...)f-S-function's namet-the current timex-the state vector of the S-function blocku-the b