ECE-320 Lab 3 Time and Frequency Domain Modeling of One Degree of Freedom Systems Overview In this lab you will be modeling two one degree of freedom systems using time-domain analysis and frequency domain analysis. The steps we will go through in this lab are very commonly used in system identification (determining the transfer function) of unknown systems. We will utilize these models in later labs so do a good job in this lab, your results in later labs will be affected by how well you perform in this lab. If your lab station has only a rectilinear (model 210) or only a torsional (model 205) system you will make two different models using those systems. If your lab station has both a torsional and a rectilinear system then you need to make one model of each type of system A one degree of freedom rectilinear mass-spring-damper system or a rotational mass-spring-damper system cmkk1211F(t)x (t)1 can be modeled as 122()121nnKGsssζωω=++ Here Kis the static gain, nωis 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 for Lab3 and copy all files from the folder basic_files into this folder. In addition, you will need to download the files get_b.m, process_data_1dof.m, and model_1dof.m from the class website. Part A: One degree of Freedom Rectilinear Systems You will need to go through the following steps for each configuration (different masses and/or springs). You need to fill out the data sheet indicating each configuration on the last page of the lab and turn it in! It needs to be signed before you start the second system! Be sure to load the correct controller personality file for the ECP system (and reset the controller) !!! Step 1: Set Up the System. Only the first cart should move, all other carts should be fixed. You need to have at least one spring connecting the first cart to the second cart (you may also have an additional spring between the motor and the first cart) and at least two masses on the cart. Do not use the damper. If you use two springs, the stiffer of the two springs should be between the first cart and the motor! Be sure you write down all of the information you need to duplicate this configuration. Step 2: Log Decrement Estimate of ζand nω As you recall, the log decrement method is a way of estimating the natural frequency nωand damping ratio ζof a second order system. However, this method does not determine the static gain. You will go through the following steps: • Reset the system using ECPDSPresetmdl.mdl. • Modify Model210_Openloop.mdl so the input has zero amplitude. • Compile Model210_Openloop.mdl if necessary. • Connect Model210_Openloop.mdl to the ECP system. (The mode should be External.) • Displace the first mass, and hold it. • Start (play) Model210_Openloop.mdl and let the mass go. 2• Run the m-file log_dec.m. (be sure the file log_dec.fig is in the same folder). Include the final log-dec figure in your memo. Step 3: Estimating the Static Gain K You will go through the following steps: • Reset the system using ECPDSPresetmdl.mdl. • Modify Model210_Openloop.mdl so the input is a step. You may have to set the mode to Normal. • Set the amplitude to something small, like 0.01 or 0.02 cm. • Compile Model210_Openloop.mdl, if necessary. • Connect Model210_Openloop.mdl to the ECP system. (The mode should be External.) • Run Model210_Openloop.mdl. If the cart does not seem to move much, increase the amplitude of the step. If the cart moves too much, decrease the amplitude of the step. You may have to recompile after the change. • You only need to run the system until it comes to steady state, then stop it. Estimate the static gain as 1,ssxKA= where 1,ssxis the steady state value of the cart position, and Ais the input amplitude. You should determine the value 1,ssxof in Matlab, don't use the X-Y Graph. The variables x1 and time should be in your workspace. You should use three different input amplitudes and produce three different estimates for the static gain. Try and make your systems move so the steady state values are between 0.5 and 1.0 cm. Average your three estimates to produce a final estimate of the static gain. Your static gain should generally be between 10 and 30. If yours is not, it is likely you did not use the same units for A and1,ssx. Step 4: Fitting the Estimated Frequency Response to the Measured Frequency Response We will be constructing the magnitude portion of the Bode plot and fitting this measured frequency response to the frequency response of the expected transfer function to determineK, ζ, and nω. For each frequency 2fωπ= we have as input ()ut Acos( )tω= where, for our systems, Ais measured in centimeters. After a transition period, the steady state output will be1)xt() cos(B tωθ=+ , whereBis also measured in cm. Since we will be looking only at the magnitude portion of the Bode plot, we will ignore the phase angleθ. 3You will go through the following steps For frequencies Hz 0.5,1,1.5...7.5f = • Modify Model210_Openloop.mdl so the input is a sinusoid. You may have to set the mode to Normal. • Set the frequency and amplitude of the sinusoid. Try a small amplitude to start, like 0.01 cm. Generally this amplitude should be as large as you can make it without the system hitting a limit. This amplitude will probably vary with each frequency. The frequency needs to be entered in radians/sec! • Compile Model210_Openloop.mdl, if necessary. (Assume it is not necessary. The system will let you know if it is necessary!) • Connect Model210_Openloop.mdl to the ECP system. (The mode should be External.) • Run Model210_Openloop.mdl. If the cart does not seem to move much, increase the amplitude of the input sinusoid.. If the cart moves too much, decrease the amplitude of the input sinusoid. Record the input frequency (f), the amplitude of the input (A), and the amplitude of the output (B) when the system is in steady state. Not that the output may not be a sine wave symmetric about zero. Hence you need the average of the positive and negative values. The Matlab file get_B.m will help with this. Enter the values off, A, and B into the program process_data_1dof.m (you need to edit the file) At the Matlab prompt, type data = process_data_1dof; Run the program model_1dof.m. There are four input arguments to this program: •