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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


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


  • Assume that the least squares estimate has already been found for the unloaded and loaded sine sweep tests, so x ˆ d1 , x ˆ d2 , x ˆ d3 , x ˉ ˆ d1 , x ˉ ˆ d2 , 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 vector and H matrix that would go into the equation y = H x + ε where the vector of parameters to be estimated, x , is defined as x = J d1 J d2 J d3 c 1 c 2 c 3 k 1 k 2 k h w
  • 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 , and 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

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

System identification using second-order model

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


  • Complete the table below; remember to include units.
    Post Lab Table
  • How close are your least-squares values compared to your second-order model values. Can you explain any discrepanciesbetween them. Which method do you think is more accurate?

Questions & Answers

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The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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Source:  OpenStax, Control systems laboratory. OpenStax CNX. Oct 20, 2005 Download for free at http://cnx.org/content/col10302/1.5
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