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Ensure the masses are firmly secured by screws, Be sure to stay clear of the mechanism when turning on the controller Selecting. Implement Algorithm immediately implements the specified controller If there is an. instability or large control signal immediately abort the control If the system. appears stable after implementing the controller first displace the disk with a light. non sharp object e g a plastic ruler to verify stability prior to touching plant. Hardware Software Equipment Check, Before starting the lab make sure the equipment is working by following the steps. Step 1 Enter the ECP program by double clicking on its icon You should see the. Background Screen Gently rotate the drive or load disk by hand You. should observe some following errors and changes in encoder counts The. Control Loop Status should indicate OPEN and the Controller Status should. indicate OK, Step 2 Make sure that you can rotate the disks freely Now press the black ON. button to turn on the power to the Control Box You should notice the green. power indicator LED lit but the motor should remain in a disabled state Do. not touch the disks whenever power is applied to the Control Box since there is. a potential for uncontrolled motion of the disks unless the controller has been. safety checked,Experiment 1 System Identification, In practice the system parameters of a piece of equipment such as the inertia spring. constant and damping ratios are often unknown In this section of the lab these unknown. parameters will be determined using a process called system identification These same. parameters will be used later to implement various controllers. Figure 1 Configuration For Plant Identification, 1 Secure four 500g masses on the upper and lower disks as shown in the.

figure Verify that the masses are secured and that each is at a center. distance of 9 0 cm from the shaft center line, 2 Clamp the center disk to put the mechanism in the configuration shown. in Figure 1 1a using the 1 4 bolt square nut and clamp spacer Please. use the washer in between the spacer and the disk to avoid bending. and possibly breaking the apparatus, 3 With the controller powered up enter the Control Algorithm box via the. Set up menu and set Ts 0 00442 and Continuous Time Enter the. Command menu go to Trajectory and select Step Select Open Loop Step. and input a step size of 0 zero a duration of 3000 ms and 1 repetition. Exit to the Background Screen by consecutively selecting OK This. puts the controller board in a mode for acquiring 6 sec of data on. command but without driving the actuator This procedure may be. repeated and the duration adjusted to vary the data acquisition period. 4 Go to Set up Data Acquisition in the Data menu and select Encoder 3 as. data to acquire and specify data sampling every 2 two servo cycles. i e every 2 Ts s Select OK to exit Select Zero Position from the Utility. menu to zero the encoder positions, 5 Manually displace the upper disk approximately 20 deg Select Execute. from the Command menu With the upper disk displaced approximately. 20 deg 1000 encoder counts as read on the Background Screen. display in either direction release the disk and click run immediately. after The disk will oscillate and slowly attenuate while encoder data is. collected to record this response Select OK after data is uploaded Plot. the data on screen to see the response, 6 Export the data to save in a file using export raw data in the data. menu Use the matlab program plotdata m on the class website to plot. Encoder 3 position vs time plot key iplot 1 Clearly label the plots. 7 Find the natural frequency of the system using the following steps Use. matlab data curser tool to choose several consecutive cycles say 5 to. 10 in the amplitude range between 100 and 1000 counts Divide the. number of cycles by the time taken to complete them Convert the. resulting frequency in Hz to radians sec This damped frequency d. approximates the natural frequency n according to,dd 31 Equation 1 2.

where the d31 subscript denotes disk 3 trial 1, 8 The next experiment is done with the four masses removed from the. third upper disk Repeat Steps 5 through 7 to obtain nd32 for the. unloaded disk Plot and label the results as you did in trial 1 and then. calculate nd32, 9 Find the damping ratio of the system in Test trial 2 Measure the. reduction from the initial cycle amplitude Xo to the last cycle amplitude. Xn for n cycles measured in Step 8 Use the following logarithmic. decrement for small d 32 to calculate the damping ratio. d 32 ln Equation 1 2,1 d232 2 n X n, 10 Perform the same experiments for the loaded and unloaded lower disk. part of the system similar to what you did for the upper part Go to Set. up Data Acquisition in the Data menu and select Encoder 1 as data to. acquire Determine nd11 nd12 and d12 How does this damping ratio. compare with that for the upper disk Why might it be different. 11 Use parallel axis theorem to calculate the total inertia of the four. weights about the center of the disk Jm The mass and size of the. weight are,Brass Mass incl bolt nut 0 5kg,Diameter of Brass Mass 0 05 m. 12 Determine the disk inertia without the weights Jd3 and upper torsional. shaft spring stiffness kd3 using the following eqs. kd3 Jm Jd3 nd31 2 Equation 1 3,kd3 Jd3 nd32 2 Equation 1 4.

13 Find the damping coefficient cd3 by equating the first order terms in the. following equation where c is cd3 and J is Jd3 for the given problem. s 2 2 n s n2 s 2 c Js k J Equation 1 5, 14 Repeat the above calculations for the lower part of the system to. determine Jd1 kd1 and cd1 which include the effects associated with. motor belt and pulleys, System basic property parameters have now been determined Values for J1 and J2 for. any configuration of masses may be found by adding the calculated inertia contribution. of the masses to that of the unloaded disk,The final report is expected to include. Four 4 MATLAB plots with two 2 data cursor points on each plot along with. titles labels and legends if necessary to show which plot corresponds to which. Disk 3 Trial 1,Disk 3 Trial 2,Disk 1 Trial 1,Disk 1 Trial 2. Calculations showing how you found the following values along with units for. every quantity,4 Natural frequencies nd31 nd32 nd11 nd12.

2 Damping ratios d32 d12,Inertia of the 4 masses Jm. Inertia of Disk 1 Jd1 including motor etc,Inertia of Disk 3 Jd3. Spring constant for upper shaft kd3,Spring constant for lower shaft kd1. Damping constant of upper part cd3,Damping constant of lower part cd1. For all the questions highlighted the questions should be copied and pasted into your lab. report and answered immediately thereafter,Experiment 2 a Rigid Body P PD and PID Control.

In this part of the lab a proportional controller will be implemented so that the. system will act like a specific frequency spring Effects of various control configurations. and control parameters on the system performance will be studied. Note You will need this value khw 17 4 N m rad,Proportional Control Action. 1 Using the results from Experiment 1 to construct a model of the plant. with two mass pieces at 9 0 cm radial center distance on the bottom. disk both other disks removed, 2 Set up the plant in the system configuration described in Step 1. 3 Use Eq 2 1 to determine the value of kp so that the system behaves like. a n 2 rad s or 1 0 Hz spring inertia oscillator,k p k hw Equation 2 1. 4 Set up a closed loop step of 0 zero counts dwell time 3000 ms and. 1 one rep Trajectory in the Command menu Set up to collect Encoder 1. and Command Position via the Data Acquisition box in the Data menu. 5 Now set up the controller Enter the Control Algorithm box set. Ts 0 00442 s and select Continuous Time Control Select PI Velocity. Feedback which is the return path derivative form control Enter kp. value determined above for 1 Hz or n 2 rad s oscillation kd ki. 0 and select OK Do not input value greater than kp 0 20. Select Implement Algorithm then OK, 6 Run the experiment Manually rotate the lower disk roughly 60 deg and. hold not for too long Select Execute under Command Release disk. and click Run immediately after, 7 Export the data to MATLAB Plot the encoder 1 position and command.

position vs time, Calculate to confirm the frequency using the Data Cursor Tool in the. MATLAB Figure Be sure to show the calculations and units. If the calculated kp does not give you the right n talk to TA or. experimentally determine a kp which does, The final report of this part is expected to include. One MATLAB Plot with titles labels and two data curses used to determine. natural frequency,Plot of the free response, Calculations showing how you found the following values along with units for. every quantity, Inertia of the System J for this experimental setup. Calculation for kp in Step 3,Frequency of the response.

Experiment 2 b PD Control Design Step Response, This part is a continuation of Experiment 2 a with the same experimental. setup Control values of kp and kd are determined to results in a. underdamped critically damped and overdamped system as studied in. me370 and me450, 9 Use Eqs 2 1 to determine a value of kp to result in a system natural. frequency of n 4 rad s Then use Eq 2 2 below to determine three. values of kd to result in a system with 1 0 1 underdamped 2. 1 0 critically damped and 3 2 0 overdamped,k dk hw k dk hw Equation 2 2. 2J n 2 Jk p k hw, 10 Implement the underdamped controller via PI Velocity Feedback and. set up a trajectory for a 2500 count closed loop Step with 4000 ms. dwell time and 1 rep, 11 Execute this trajectory Plot on screen both the command and response.

on the same vertical axis so that there is no graphical bias Make sure. your results indeed show an underdamped step response before you. proceed to export data to matlab, 12 Repeat Step 11 for the critically damped and over damped cases Make. sure they are indeed largely damped with no oscillations in the. 13 Export the data to your matlab folder Then plot all three damping cases. in one figure using program plotdata3 m comparing and commenting. on the damping characteristics, 14 Now for the underdamped design reduce the value of kp to 50 and. 10 of the current value and run the two experiments Observe the. response on monitor Increase the runtime if it does not reach a steady. state before the command is dropped off Export the data to matlab and. plot the responses for all three kp values in one figure Use matlab data. curser to determine the following from the response curves. 1 Percentage steady state error ess as a function of kp which is the. difference between the command level and the response divided by the. command It measures accuracy of the response, 2 Settling time tss which is the time taken for the response to reach. within 2 to steady state It measures how fast to reach target. 3 Percentage overshoot Mp which is the difference between the. peak value of the response and its steady state level divided by the. steady state value It measures response stability characteristics. 4 Peak time tp which is the time taken to reach the peak response It. measures response speed, Fill the results in Table 1 below in increasing order of kp. Table 1 Response characteristics as functions of control gain. kp ess tss Mp tp, Briefly discuss the effect of the control gain on the system steady state.

and transient performance in terms of these results Which of the three. control gains produces the best results, The final report of this part is expected to include. Two matlab plots along with titles and labels,Plot for all three damping cases. Plot for all three kp cases including the calculation data cursers. Calculations showing how you found the following values along with units. kp in Step 9,Under damped kd,Critically damped kd,Over damped kd. ess and Mp in Table 1,Experiment 2 c Adding Integral Action. In this part of the lab a full PID controller will be implemented By adding. integral action to the controller the settling time and overshoot of the. response will be impacted, 15 Determine ki such that kikhw 3 N m rad sec Implement a controller.

with this value of ki and the critically damped kp kd parameters from. Step 9 Do not input ki 0 4, 16 Execute a 2500 count closed loop step of 4000 ms duration 1 rep. 17 Plot the encoder 1 response and command position in MATLAB. 18 Experimentally determine a value of ki that visibly gives you a better. response judged by the overshoot and steady state error in comparison. to the previous run This ki may be smaller than the one used in Step 15. 19 Plot responses and command position for three cases of ki 0 from. Experiment 2 b the calculated ki and the better ki Briefly describe. the effects of adding integral action to the controller. The final report is expected to include,One MATLAB Plot along with title label and legend. Calculated ki with calculation equation,Experimentally determined better ki. Experiment 2 d Frequency Response, In this portion of the lab the input will now be a series of increasing. frequency sine waves used to determine the frequency performance of the. Part 1 Single DOF system, 20 Implement the underdamped system configuration from Step 9.

For all the questions highlighted the questions should be copied and pasted into your lab report and answered immediately thereafter Experiment 2 a Rigid Body P PD and PID Control In this part of the lab a proportional controller will be implemented so that the system will act like a specific frequency spring Effects of various control

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