BRASS QUINTET MUS A 45
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This 8 page Class Notes was uploaded by Cecelia Emmerich on Thursday October 22, 2015. The Class Notes belongs to MUS A 45 at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/226995/mus-a-45-university-of-california-santa-barbara in Music at University of California Santa Barbara.
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Date Created: 10/22/15
INTRODUCTION 39nrin A h 5 lon Next GETTING STARTED IN Up No Title Previous No Title INTRODUCTION The objective of this tutorial is to acquaint the student with the basic tools needed to use the SIMULINK package on the Unix workstations of the Rensselaer Computing System RCS SlMULlNK is an extension to MATLAB which uses a iconidriven interface for the construction of a block diagram representation of a process A block diagram is simply a graphical representation of a process which is composed of an input the system and an output inputs gt System outputs Figure 1 A VERY simple block diagram of a 11mm Typically the MATLAB mifile ode45 is used to solve sets of linear and nonlinear ordinary differential equations The traditionalquot numerical methods approach is used eg supply the equations to be solved in a function file and use a general purpose equation solver linear or nonlinear algebraic linear or nonlinear differential equation etc which callsquot the supplied function le to obtain the solution One of the reasons why MATLAB is relatively easy to use is that the equation solversquot are supplied for us and we access these through a command line interface CLI aka the MATLAB prompt gt gt However SIMULINK uses a graphical user interface GUI for solving process simulations Instead of writing MATLAB code we simply connect the necessary iconsquot together to construct the block diagram The iconsquot represent possible inputs to the system parts of the systems or outputs of the system SlMULINK allows the user to easily simulate systems of linear and nonlinear or 39 differential equations A good background in matrix algebra and lumped parameter systems as well as an understanding of MAT LAB is required and we highly recommend that the student thoroughly reads and works through this tutorial Many of the features of SlMUIINK are userifriendly due to the iconidriven interface yet it is important to spend some time experimenting with SlMULlNK and its many features Dynamic simulation packages such as MATLAB SIMULINK etc are being used more and more frequently in the chemical process industries for process simulation and control system design After completing this tutorial the student should be able to buildquot and simulate block diagram representations of dynamic systems Next GETTING STARTED IN Up No Title Previous No Title 112009 1049 PM GETTING STARTED IN ltbgtSIMULINKltbgt httpwwwrpiedudeptchem7engWWWfacultybequett Next BLOCK DIAGRAM CONSTRUCTION Up No Title Previous INTRODUCTION GETTING STARTED IN SIMULINK SlMULINK is aniconidriven state of the art dynamic simulation package that allows the user to specify a block diagram representation of a dynamic process Assorted sections of the block diagram are represented by icons which are available Via various quotwindowsquot that the user opens through double clicking on the icon The block diagram is composed of icons representing different sections of the process inputs stateispace models transfer functions outputs etc and connections between the icons which are made by quotdrawingquot aline connecting the icons Once the block diagram is quotbuiltquot one has to specify the parameters in the various blocks for example the gain of a transfer function Once these parameters are speci ed then the user has to set the integration method of the dynamic equations stepsize start and end times of the integration etc in the simulation menu of the block diagram window In order to use SlMULLNK the student must startquot a MATLAB session click on the MATLAB button Once MATLAB has started up type simulink SMALL LETTERS at the MATLAB prompt gt gt followed by a carriage return press the return key A SlMULINK window should appear shortly with the following icons Sources Sinks Discrete Linear Nonlinear Connections Extras t 39 window is shown inFigure 2 Next go to the le menuin this window and choose New in order to begin building the block diagram representation of the system of interest EEEE lE Sources Sinks Discreet Linear Nonlimar Connections Extras SIMULINK Block Library Version 1 2d Figure 2 Simnlink block library windcrw Lou Russo Howard P Isermann Dept ofChemicalEngineering Iofl 1120091057PM BLO CK DIAGRAM C 0 NS TRUCTI ON 10f2 httpwwwrpiedu deptchem7engWWWfacultybequett Next GENERAL SlMULlNK TIPS Up No Title Previous GETTING STARTED lN BLOCK DIAGRAM CONSTRUCTION As mentioned previously the block diagram representation of the system is made up of various type of icons Basically one has to specify the model of the system state space discrete transfer functions nonlinear ODE39s etc the input source to the system and where the output sink of the simulation of the system will go Open up the Sources Sinks and Linear windows by clicking on the appropriate icons Note the different types of sources step function sinusoidal white noise etc sinks scope le workspace and linear systems transfer function state space model etc For example you may be interested in simulating a step input to a rstiorder transfer function in the Laplace domain and viewing the result graphically in MATLAB The resulting block diagram is shown in Figure 3 To do this you would quotdragquot a step function icon from the Sources window a transfer function icon from the Linear window two to workspace icons from the Sinks window and a clock icon from the Source window to the blank block diagram window Clock To Wolkspaccl E 5 F To Workspace up c Transfer Fcn Figure 3 Simulink block dingam for a rstorder transfer function The next step is to connect these icons together by drawing lines connecting the icons using the leftimost mouse button hold the button down and drag the mouse to draw a line Connect the step function icon to the input of the transfer function icon then connect the output of the transfer function icon to rst to workspace icon Then connect the clock icon to the second to workspace icon Openquot the icons by double clicking on them with the leftimost mouse button and set the values of the various parameters for example the step size and step time in the step function icon the transfer function coef cients in the transfer function icon and the variable names in the to workspace icons generally the clock variable is denote as time whereas the output variable is denoted y Select the parameter eld from the simulation menu in the block diagram window and set the proper lrn plotted as one would normally plot eg plottimey since the variables lime and y are now de nedin the MATLAB workspace The result is shown in Figure 4 for a rstiorder transfer rnction with a time 112009 1058 PM BLO CK DIAGRAM CONSTRUCTION http wwwrpiedu deptchem7engWWWfacultybequett constant 2 and a unit step input at time 1 I I Figure 1 samu nhimuumm of nut2mm innIa funcu39m Next GENERAL SlMULlNK TIPS Up No Title Previous GETTlNG STARTED 1N lou Russo Howard P Isermann Dept ofChemicalEngineering 20f2 1120091058PM GENERAL SIMULINK TIPS 10f3 httpwwwrpiedu deptchem7engWWWfacultybequett Next TABLE OF SIMULINK Up No Title Previous BLOCK DIAGRAM CONSTRUCTION GENERAL SIMULINK TIPS The following are general tips and should be used often N w 3 m m N In order to save your work select Save from the file menu and give the le that you want to save a name or choose an old name if you are writing overquot an old version and click the ok button using the leftimost mouse button Realize that you have a choice of the folderquot that the le is saved in K The PID Controller block parameters are entered in as P Kn I 39 71 D Kg 7 1 The following transfer function in the Laplace domain 2 s 1 B 9 10 a 5 s 1 is entered into the transfer function icon by double clicking on the transfer function icon and entering the numerator and denominator polynomial coefficients The numerator coefficients would be entered as 2 1 and the denominator coef cients are entered as 10 S 1 The following stateispace A matrix 10 31 28 02 A is enteredinto the state space icon as 10 728731 02 The results of a simulation can be sent to the MATLAB window by the use of the to workspace icon from the Sinks window Open the to workspace icon and select the variable name that you want the results stored in the MATLAB workspace If your simulation has n state or output variables and you want to save them as different names then you have to use a special connection called a Demux as in demultiplexer icon which is found in the Connections window Basically it takes a vector input and converts it into several scalar lines You can set the number of outputs scalar lines by double clicking on the icon and changing the number of outputs A MuX icon takes several scalar inputs and multiplexes those in a vector useful sometimes in transferring the results of a simulation to the MATLAB workspace for example You can generate white random noise by selecting the white noise icon from the Source window You can use a Gain icon from the Linear window if you need to multiple a signal by a constant number 112009 1058 PM GENERAL SIMUIINK TIPS http wwwrpiedu deptchem7engWWWfacultybequett 9 You can convert back to physical variables after a stateispace or transfer function simulation by using the Constant icon from the Sources window and a Sum icon from the Sources window To do this for a scalar output signal just enter the value of the steadyistate into the Constant icon and add this to the scalar output using the Sum icon For a vector output you must first quotbreakiupquot the vector into scalar outputs using the DemuX icon and then add the steadyistate value to each scalar output o The signs of the Sum icon may be changed to negative in order to subtract by double clicking on the Sum icon and changing the sign from a positive to a negative sign The number of inputs to the Sum icon may be changed by double clicking on the Sum icon and setting the number of inputs in the window 1 1 Make sure to set the integration parameters in the simulation menu In particular the default minim an ax1mum step sizes must be changed they should be around 1100 to 110 of the dominant slowest time constant of your system N Parameters can be quotpassedquot to SIMULINK from the MATLAB window by using the parameter in a SlMULINK block or parameter box and de ning the parameter in the MATLAB window For example say that one wants to run the simulation with many different process gains then in the transfer function icon the gain in the numerator can be given the symbol k or any symbol and then at the MATLAB prompt define k 10 Run the simulation then at the MATLAB prompt rede ne k 15 etc This is very useful if the student wants to study the in uence of a parameter on the dynamic behavior of aprocess important in determining stability w In order to print the block diagram rst save the block diagram Then at the MATLAB prompt print sname 0f simulink block where name of simulink block is the name that you saved the block diagram under For example if you saved the block diagram as homework1m then you would type print shomeworkl 3 Time delays deadn39mes can be simulated in SIMULINK easily by using a transport delay icon from the Nonlinear window Double click on the transport delay icon to set the value of the deadn39me 1 5 Nonlinear systems can be simulated in SlMUIINK using an s function icon from the Extras window The nonlinear ordinary differential equations must be speci ed in an mi le and the name of this mi le is speci ed in the s function by the user We will generally supply the student with the mi le containing the nonlinear ordinary differential equations Next TABLE OF SlMUIIN39K Up No Title Previous BLOCK DIAGRAM CONSTRUCTION 20f3 1120091058PM TABLE OF SIMULINK BLOCKS httpwwwrpiedudeptchemiengWWWfacultybequett Up No Title PreV1ous GENERAL SIMULINK TIPS TABLE OF SIMULINK BLOCKS SOURCES Clock Provide and display system time Constant Inject a constant value From File Read data from a le Dom Workspace Read data from a matrix Signal Generator Generate various waveforms Sine Wave Generate a sine wave Step Fcn Generate a step function White Noise Generate random noise SINKS Scope Display signals during a simulation To File Write data to a file To Workspace Write data to a matrix DISCRETE Discrete StateSpace Discrete statespace system Discrete Chansfer Fcn Discrete transfer function Discrete ZeroPole Discrete system as zeros poles and gain Filter Implement 11R and FIR filters Unit Delay Delay siglal for one sample period 10f3 1120091059PM
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