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System Identification for the Torsional Plant

Module by: Robert Bishop. E-mail the author

Summary: The objective of this lab is to review of the behavior of second-order systems. Students will gain a better understanding of the importance system identification. Students will also develop a hands-on understanding of the concept of hardware gain and why it will play a crucial role in controller design. System Identification will be implemented in LabVIEW using the System Identification Toolkit.

System Identification for the Torsional Plant

Objectives

  • Understand the dynamic equivalence between rotational and translational systems.
  • Perform system identification using two different methods and compare the results.

Pre-Lab

  1. Assume that the least squares estimate has already been found for the unloaded and loaded sine sweep tests, so x ˆ d1 x ˆ d1 , x ˆ d2 x ˆ d2 , x ˆ d3 x ˆ d3 , x ˉ ˆ d1 x ˉ ˆ d1 , x ˉ ˆ d2 x ˉ ˆ d2 , x ˉ ˆ d3 x ˉ ˆ d3 are known values. Formulate the linear least squares equation to estimate the 9 individual plant parameters. In other words, find the y y vector and H H matrix that would go into the equation y = H x + ε y= H x +ε where the vector of parameters to be estimated, x x, is defined as x = J d1 J d2 J d3 c 1 c 2 c 3 k 1 k 2 k h w x= J d1 J d2 J d3 c 1 c 2 c 3 k 1 k 2 k h w
  2. Outline the experimental steps you will take to identify the torsional plant using the second-order model method similar to Lab #2. Your procedure should allow you to find J d1 , J d3 , c 1 , c 3 , k 1 , k 2 , J d1 , J d3 , c 1 , c 3 , k 1 , k 2 , and k h w k h w . You may exclude the procedure for identifying the inertia and damping for disk 2. When formulating your procedures, remember that disks 2 and 3 can be clamped, disk 1 cannot.

Lab Procedure

System Identification Using Least Squares

  1. Configure the plant with all three disks rotating freely and no brass weights attached.
  2. Perform a 1638 count (0.5V) linear sine sweep from 0 0 to 8 H z 8 H z with a sweep time of 20 20 seconds. When the execution is complete, enter a file name such as 3DiskSweepUnloaded 3DiskSweepUnloaded and save the raw data from the front panel.
  3. Now load two 0.5 k g 0.5 k g brass weights onto each of the three disks so their centers are 9.0 c m 9.0 c m from the axis of rotation.
  4. Perform the sine sweep again. Enter a file name such as 3DiskSweepLoaded 3DiskSweepLoaded and save the raw data.
  5. You are now ready to identify the system parameters using least squares estimation.

System Identification Using Second-Order Model

  1. Follow the steps you outlined in the pre-lab to identify the system parameters using the second-order model method.

Post-Lab

  1. Complete the table below; remember to include units.
    Figure 1: Post Lab Table
    Figure 1 (postlabtable.jpg)
  2. How close are your least-squares values compared to your second-order model values. Can you explain any discrepancies between them. Which method do you think is more accurate?

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