ECE-205 Lab 3 Time Domain Modeling of One Degree of Freedom Systems Overview In this lab you will be modeling two one degree of freedom (second order) systems using time-domain analysis. The goal is develop some intuition into how the parameters in a second order system affect the output by varying parameters in a model to match the step response of two second order systems. You will also use the log-decrement method to estimate these parameters. If your station has both a rectilinear (model 210) and torsional (model 205)system you should make one model of each type of system. Otherwise make two different systems (and corresponding models) using either the model 210 or model 205. Background A one degree of freedom rectilinear mass-spring-damper system can be modeled as By drawing a free body diagram and balancing forces, we get the equation of motion: cmkk1211F(t)x (t)1 11 11 1 2 1() () ( ) () ()mxt cxt k k xt Ft+++ =  A one degree of freedom rotational mass-spring-damper system can be modeled as By drawing a free body diagram and balancing torques, we get the equation of motion () () () ()Jt ct kt Ttθθθ++ =  1Despite the fact that the systems appear quite different, the transfer functions for both of the one degree of freedom systems can be put into the standard form we have been using to model our circuits: 22() 2 () () (=K ) nn nyt yt yt xtζω ω ω++  Here is the static gain, Knωis the natural frequency, and ζis the damping ratio. These are the parameters we need to determine for these models. You will need to set up a folder on the desktop for ECE-205, and then a folder for Lab 3. Then copy Lab3 files.rar (from the class website) into this folder and install the files. Start Matlab and change the default folder to the folder where these files are located. You will need to go through the following steps for two different configurations (different masses and/or springs) unless you are going to use one torsional and one rectilinear system. PART I : Setting up communications In this part we get the systems ready to run and start (hopefully) communications between Simulink, the miniPMAC card, and the ECP system. Sometimes this can take a few tries, so be patient and ask for help. 1) We need to inform the ECP system that we will be using Simulink and the real-time windows target. To do this, click Start -> Programs -> ECP First select on Utility-> Download Controller Personality File. Then select C: -> Program Files -> ECP Systems -> cn (it may default to this) Finally select m210_rtwt_3.pmc for the Model 210 (or m205_rtwt_3.pmc for the Model 205) and click on open. Wait for the ECP system to load the personality file, then close the window (do not just minimize it). 2) Now we need to reset the system. You need to do this each time before you run the system. From Matlab, open the Simulink file ECPDSPReset.,mdl. It should look like the following: 2We first need to be sure the Base I/O Address is correct for your work station. Double click on the blue ECPDSP Reset box, and you will get the following: The correct Base I/O Addresses are on the board at the front of the room. (Ask if you need help). Be sure to save your file if you change the Base I/O Address. Now we need to compile this file. Once you have clicked on the icon (shown in the figure below), wait until Matlab indicates the file was successfully generated (it will be at the end of a lot of messages in the command window). 3 Click here to compile the fileFinally, we need to run this file. First connect to the system, 4 Connect to the system This should say External Then click on the play button Click on the play button to If you will do all of this correctly, nothing (obvious) will happen. In the Matlab command window it will say you have connected and disconnected to the system. However, you have reset the counters and zeroed the system.PART II: Second order rectilinear system (ECP Model 210) 1) Set Up the Mechanical System. Only the first cart should move, all other carts should be fixed. You need to have at least one spring connected to the cart and at least one mass on the cart. 2) Open up the Simulink file Model210_Openloop.mdl, it should look like the following: The yellow block in the middle is what actually connects to the ECP system. Note that the output of this system is labeled x1. Do not change this! 3) Double click on the yellow block, and you will get the following: Double click on the blue ECPDSP Driver block to be sure your Base I/O Address is correct. Then save the files. 54) Now we want to change the input to the system. Double click on the Step block, and enter an input value. Note that some of the systems have a static gain of more than 40, and they don’t like moving more than about 2 cm, so start with something small, like a final value of 0.02. Click OK and then save the file. 5) Compile the file, just as you did in PART 1, then connect to the system, and then run it. The cart should move. There are three (usual) outcomes here: a) If the cart does not move, go back though PART I. You don’t need to change the Base I/O Address or recompile, but you do need to reload the controller personality file and reset the system. b) If the cart moved, but the XY Graph does not look smooth, the communications are still not correctly set up (this is not your fault). Go back though PART I. You don’t need to change the Base I/O Address or recompile, but you do need to reload the controller personality file and reset the system. c) If the cart moved and the XY Graph looks reasonable, be sure the system recorded data for three seconds. If it did not record for three seconds, first look at the output level. If the maximum value of the output is between 1 and 2 cm (or larger), try resetting (ECPDSPREset) and rerunning the system a few times. If the maximum value of the output is less than about 1.5 cm, then increase the value of the amplitude in the Step, reset the system (ECPDSPReset) and rerun the system. Before you go on, be sure your system has run for 2-3 seconds and recorded enough good data. 6) Modify the file second_order_driver.m to plot the data from the ECP system and the results from the simulation on the same graph. Be sure to use different line types and a legend. There are two different time arrays (one from the simulation and one from the ECP system), and two different outputs. You may