1 ECE-320 Lab 1 System Identification and Model Matching Control of Two One Degree of Freedom Rectilinear Systems In this lab you will be modeling and controlling two one degree of freedom rectilinear systems. For each system you will first fit the parameters of a transfer function model of your system 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. A one degree of freedom rectilinear mass-spring-damper system can be modeled as 22()121nnKGsss Here Kis the static gain, nis the natural frequency, and is the damping ratio. These are the parameters we need to determine to match the model to your system. You will need to set up a folder for this lab and copy and unzip all of the files from Lab1 files.rar from the class website. You may need to review the file shortguide.pdf. You may also need to set the base address for your system. Your memo should include a detailed descriptions of your systems (so you can set them up again), the name of your model files, two tables comparing the estimated values of K, n and using the time domain and frequency domain estimates (one for each system), and a brief comparison of the time and frequency domain estimates. The damping ratios are often quite different, so that's OK. The other values should be close. The values for the two systems should not be compared, since we expect them to be different. You should include as attachments 8 graphs ( log-decrement and frequency response graphs, and two model matching results for each system), each with a Figure number and caption. However, do not include the data for constructing the Bode plot.2 Part A: Time Domain Modelling of Your First One degree of Freedom System 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. You need to fill out the data sheet indicating each configuration on the last page of the lab and turn it in! You also need to include this information in your memo. Step 2: Preparing to Use the ECP System with Simulink. Be sure the connector box (black and gray box on the top of the shelf) is off before connecting the system. Do not force the connectors. If they don't seem to fit, ask for help! - Read the file shortguide.pdf and change the Base Address of both ESCPDSPReset.mdl and Model210_Openloop.mdl if necessary. - Be sure to save the files after changing the Base Address. - Be sure to load the correct controller personality file for the ECP system !!! Step 3: Log Decrement Estimate of and n The log decrement method is a way of estimating the natural frequency nand damping ratio of a second order system. 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. - Run the m-file log_dec.m. (be sure the file log_dec.fig is in the same folder). The program log_dec comes up with the following GUI:3 You need to - Select Cart 1 - Select Load IC (initial condition) Response (the variables time and x1 will be loaded from the workspace). At this point some initial estimates will be made. - Set/modify the Final Time - Select Plot IC Response to plot the initial condition response - Choose to identify the positive peaks (Locate + Peaks) or negative peaks (Locate - Peaks) . If the peaks are not numbered consecutively, you need to decrease the Samples Between Peaks and try again until all peaks have been identified. - Choose the initial peak (Peak x(n)) and final peak (Peak x(n+N)) to use in the log-decrement analysis. These should be fairly close to the beginning of the initial condition response. Don't try and use more than a few peaks. - Select Estimate Parameters to get the initial estimates of and n - Select Make Log-Decrement Figure to get a plot and summary of the results. You need to include this figure in your memo. Step 4: 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.4 - 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,ssx 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. Part B: Frequency Domain Modelling of a One degree of Freedom System Step 1: 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