ES205 Analysis and Design of Engineering Systems: Lab 1: An Introductory Tutorial: Getting Started with SIMULINK

Transcription

1 ES05 Analyi and Deign of Engineering Sytem: Lab : An Introductory Tutorial: Getting Started with SIMULINK What i SIMULINK? SIMULINK i a oftware package for modeling, imulating, and analyzing dynamic ytem. It upport linear and non-linear ytem modeling in continuou time, ampled time, or a combination of the two. It provide a graphical interface for building model a block diagram uing the moue by click-and-drag operation. It alo provide a variety of imulated output device that can be attached to the ytem to monitor the output or tate variable of the ytem. By defining the ytem graphically, the mathematical calculation required to imulate the differential equation that repreent the model are hidden from your view. You only need to be able to upply the model tructure and parameter, the imulation parameter, and the output variable and form. You don't have to get bogged down in the math to determine the behavior of the ytem of interet. Thi tutorial will conit of 4 part: A) Launching and becoming familiar with the SIMULINK environment B) Creating a imple t order model C) Creating a nd order model of a ma, pring, damper ytem D) Creating a model on your own of an electrical ytem. 3) When SIMULINK open you will ee the box called the SIMULINK Library Brower. The Library conit of a number of different SIMULINK block with which a ytem model may be built. To build a model, you firt need to create a pace to make the model. Click the new model icon in the upper left corner to open a new SIMULINK file workpace. Next, elect the SIMULINK icon to expand the lit of the available element that are ued to create a ytem model. Part A: Launching Simulink: ) SIMULINK i run from the MATLAB prompt, >>, o the firt tep i to get MATLAB running. -- Connect to the Network -- Launch MATLAB. ( if you have not already intalled MATLAB you will need to do o at thi time.) ) At the prompt, >>, in the MATLAB Command Window, type imulink and pre Enter. 4) After making the election in Step 3, the SIMULINK Library Brower will how folder that contain the mot commonly ued element you will be uing for model creation. Click on each of the following folder and quickly note the element that are contained in each. -- Continuou -- Dicontinuou -- Dicrete -- Look-up Table -- Math Operation -- Sink -- Source When needed, thee element may imply be clicked, dragged, and dropped into the model workpace. ES05 Getting tarted with Simulink Page of 6 ES05 Getting tarted with Simulink Page of 6

2 During Step 3 you alo opened a window called Untitled, which i the model workpace where the model will be created. Part B) Example : A Simple Model ) The firt model you are going to build will olve a imple t order differential equation given by = 3 in( t ) with an initial condition x(0) = -. ) To create a model of thi equation, we firt ketch a imulation diagram of the mathematical model. The imulation diagram will conit of: an input --> the forcing function, 3 in(t) an output --> the olution, / a parameter --> the initial condition, x(0) = - an operator --> integration block I.C.: x(0) = - 5) You have not yet created a model, but if you had, you would want to be able to ave the model. input: 3in(t) x output: x(t) To ave a model, pull down the File menu and elect Save_A or Click on the File Save Button While we won't ave a file right now, we will have you create a new folder to ave any model you will create. 3) To contruct thi model in Simulink, will require three element: -- a Sine Wave Block --an Integrator Block -- a Scope Block Locate the Sine Wave under the Source folder and Click, Drag, and Drop it in the model workpace window to create the Input Block Create a new folder called, imulink_file by clicking on on the new folder button. and upply the correct name. ES05 Getting tarted with Simulink Page 3 of 6 ES05 Getting tarted with Simulink Page 4 of 6

3 4) Locate the Integrator under the Continuou folder and Click, Drag, and Drop it in the model workpace window to create the Operator Block. 6) Connecting the block. Block can be connected by dragging a line from the output of one block to the input of another block. Make the following connection: Output of the Sine Wave --> Input of the Integrator Output of the Integrator --> Input of the Scope 5) Locate the Scope under the Sink folder and Click, Drag, and Drop it in the model workpace window to create the Output Block The arrow indicate the direction of the ignal flow. 7) Selecting Simulation Parameter. Mot block have different parameter that are aociated with them. To acce the parameter, imply double-click on the block of interet. Thi will bring up a dialog box which allow the parameter to be changed. Double click on the Sine Wave and et the following parameter: Amplitude = 3 Frequency = ES05 Getting tarted with Simulink Page 5 of 6 ES05 Getting tarted with Simulink Page 6 of 6

4 Double click on the Integrator Block and et the parameter for the initial condition. x(0) = - 9) Simulation Reult Your reult hould look like the figure. Meaure the magnitude of peak and valley and the period of the ignal. Peak = Valley = Period = Double Click on the Scope Block. Thi doe not have any parameter which need etting, but intead diplay the cope diplay creen. 0) Simulation Verification: To verify that thi plot repreent the olution to the problem, let' look at the analytical olution. = 3in(t) with x(0) = - Thi equation can eaily be olved by integration. The reult i ( t ) x ( t ) = 3 co Thi i the function that wa plotted in the SIMULINK Scope window. Save thi SIMULINK model in the imulink_file folder a a Example.mdl 8) Now that the model ha been defined and created, the model imulation i ready to run. To Start a imulation, pull down the Simulation menu, and elect Start. View the output of the imulation on the Scope window. ES05 Getting tarted with Simulink Page 7 of 6 ES05 Getting tarted with Simulink Page 8 of 6

5 Part C: Example, a ma, pring, damper ytem ) The econd model will ue SIMULINK to create a model of a ma-pringdamper ytem which may be modeled with a nd order differential equation. Other parameter of the ytem include: -- initial condition: x(0) = 0 and /(0) = 0 -- the input f(t) i a tep function with magnitude 3 at t=0 -- ma, m = damping coefficient, c = pring contant, k = The model equation: d x m + c + kx = f ( t) 3) Let' walk through the tep. For comparion, tart by olving the model equation for the highet order derivative term. d x m = f ( t) c k x The firt block you create hould be a Sum block, where the output of the Sum block i the left-hand term of the equation above. Aume all unit are conitent for the model. You will work through the following tep: a) Draw the imulation diagram b) Create and ave the SIMULINK Model c) Run the Simulation. ) In the pace below attempt to draw the imulation diagram for thi model: um block Now uing SIMULINK, Create a new workpace... File... New...Model Locate the Sum Block in the library and Click, Drag and Drop it into your new workpace. ES05 Getting tarted with Simulink Page 9 of 6 ES05 Getting tarted with Simulink Page 0 of 6

6 The Sum block i to have 3 input. Double click on the Block and et the parameter to rectangular and ) Gain Block. Add a title to the Gain Block. 5) Add two integrator to your Simulation diagram. Add a gain (multiplier) block to normalize the coefficient, m, to modify the ignal o it i equal to the highet order derivative term alone. m d x um block m gain d x Integrator x Integrator um block gain Click, Drop, and Drag two Integrator Block into your SIMULINK workpace from the library. Click, Drag, and Drop a Gain Block from the library into the SIMULINK workpace. Alo: Set the initial condition parameter to zero for both integrator. Add a cope block to the output of the econd integrator Connect the output port to the input port a hown Label each of the ignal by double clicking on the leader line. Double-click on the Gain block to change the block parameter. Ue a Gain of ES05 Getting tarted with Simulink Page of 6 ES05 Getting tarted with Simulink Page of 6

7 6) Return Branch Gain Block In the Simulation Diagram, connect the integrated ignal with gain block to create the term on the right-hand ide of the model equation. 7) Connect all Input Signal. In the Simulation Diagram, connect all the input ignal to the appropriate input of the Sum Block. um block m c d x c x Input: f(t) m c d x c x Output: x(t) k x k k x k In SIMULINK, Drag in two additional Gain block from the Math library to the workpace. --Flip thee block by electing each block and uing... Format...Flip Block --Double click on each of the block and et the appropriate parameter c = 0.5 k =.0 --Connect the ignal line: Either Click the gain block input and drag to each of the branch point. or Ctrl-Click to elect the branch point firt and drag to the gain input. --Add appropriate title to the gain block In the SIMULINK workpace: -- Add a Step Block from the Source library and et it parameter. Step time = 0 Initial value = 0 Final value = 3 -- Connect the ignal line to the um Block, paying attention to the ign of the input. c = 0.5 k =.0 ES05 Getting tarted with Simulink Page 3 of 6 ES05 Getting tarted with Simulink Page 4 of 6

8 8) Your completed SIMULINK model hould look like the following. Complete any miing title or label. Thi conclude the SIMULINK Tutorial Module. You are now to complete Part D: Lab Workheet. To complete the workheet you are expected to undertand and ue the term below. Term ued on the workheet: Steady State Value i the final value of the ytem ettle at after tranient behavior ha diipated. Overhoot i characterized a the maximum repone wing pat the teady tate value. Rie time i time required for the ytem to rie from ten to ninety percent of the teady tate value. Settling time i the amount of time the ytem take to value ettle cloe to the teady tate condition (to within approximately % of the tep ize). Settling Time Overhoot Steady State Value Save your model a Example.mdl +/- % of tep 9) Running your imulation Double click on the Scope to make it output viible. Run your imulation. What i it maximum value of x reached? What i it final value of x reached? Rie Time I thi behavior underdamped, overdamped, or critically damped? ES05 Getting tarted with Simulink Page 5 of 6 ES05 Getting tarted with Simulink Page 6 of 6