Rectilinear Dynamic Control System by cmlang


									             Rectilinear Dynamic Control System
                                By: Dr. Hong Zhang

1. To Learn simple system identification methods through experiments.
2. To understand the effect of damping ration of system response
3. To understand the system response of sinusoidal input.

                                System Overview
The rectilinear dynamic and control system is consisted of three parts: the physical
rectilinear plant (hardware), the control electronics (hardware), and the user interface
                           DSP BasedController /
                           Data Acquisition Board

                                                                Dynamic System -
    User Interface                                              - Rectilinear
                             Drive Electronics
                              Control System
The rectilinear plant is essentially a mass-spring-damper system driven by electric motor
(see following figure). It is designed to emulate a broad range of real-world systems.
Together with the other control hardware and software, it can be used to illustrate many
theoretical concepts in the courses including Vibration, System Dynamics and Control,
and Linear Control.

Because of the modulated design, the system can be placed in a variety of
spring/mass/damper configurations with 1, 2, and 3 degree of freedom (DOF).
Mechanically, the springs may be mounted interchangeably to obtain different stiffness,
the mass can be added/subtracted as the multiplication of 500g (the number of brass
weights), and the damping constant can be altered by adjusting the airflow valve of the
dashpot. Moreover, the spring and damping constant can both be modified conveniently
through controlling the electromechanical system.

For both motor and the load shafts, the system uses incremental rotary shaft encoders to
measure the incremental displacements. The encoder resolution is 16,000 counts per
revolution or 2266 counts per cm.

Read the separate safety notice carefully. Here we just highlight some important issues:
1. Always exercise caution during the whole operation. The speed of the mass can be
   fast and the motion can be violent.
2. When start up the system, first turn on the PC then turn on the control box.
3. When shut down the system, first turn of the control box, then turn off the PC.
4. Stay clear of and do not touch any part of the mechanism while it is moving.
5. When physically contacting the system is necessary, always safety-check the
   controller. See the separate safety notice for the method.
6. Prior to operation, the user should verify that: a) the brass mass pieces are properly
   secured, b) the mass carriages travel freely, and c) the limit stop blocks are properly
   set and secured to limit motion of the mass carriages.

                                 System Analysis
The system configured in this experiment is
                          f(t)      m

The mathematical model of the system is:
       m  cx  kx  f (t )
        x 
The damping ratio  and the natural frequency n are:
             c                 k
                and  n 
          2 km                m
The damped frequency d is:
        d  1  2  n
d can also be identified from the plot.
For example, if the time measured
between the peak X 0 and the next one
 X 1 is 1second, the frequency will be
1Hz or 2 rad/s.
Further, if the plot of the data is like the
figure on right, we define the
logarithmic decrement between the amplitude X 0 and X n for n cycles as:
           X               
        ln 0  2  n
           Xn            1 2
Preparation: Construct a method to determine  and n, and then c, m, and k from

1) Get started:
   From the desktop, find the icon named Dynamics. Double click to launch the
   software. It should look like this:

2) Identify the damping ratio  and the natural frequency n:
   1. Check the hardware; make sure the system is clear from any obstacle. The first
      mass carriage (the left most one) should be empty, connected to motor with a rod,
      and attached with a spring on left. The second and third should be clamped and
      separated from the first one.
   2. Turn the power of the controller on (the black button). Observe the system. There
      should be no abnormal motion. The first mass carriage (the left most one) should
      be able to move freely. You should use a plastic ruler or pen before using your
      finger to touch it.
   3. Click Setup --> Setup Driving Function. In the new window, select Force
      (Torque), then Setup Driving Function, Click OK (from within the Force
      (Torque) dialog box), then Enable Driving Function, and finally OK again to
      return to the Background Screen. Now, the Driving Function Control should be
      ENABLED, and the System Status is OK.
   4. Click Command -->Input Shape... Select Step, then Setup. In the new dialog
      box, input Step Size 0 (zero), Dwell Time 3000, and Number of reps 1. Exit to
      the background screen by consecutively selecting OK. This puts the controller
      board in a mode for acquiring 6sec of data on command but without actually
      introducing drive force. This procedure may be repeated and the duration adjusted
      to vary the data acquisition period.
   5. Click Data --> Setup Data Aquisition.... A window named Setup Data
      Acquisition should pop up. Make sure the Sample Period is 2, Selected Items are
      Drive input and Encoder 1 Position. Click OK.
   6. Click Utility --> Zero Position tozero the encoder positions.

   7. Click Command --> Execute. A new window named Execute Trajectory will be
      shown. Prepare to manually displace the first mass carriage approximately 2.5cm.
      Exercise caution in displacing the carriage so the travel limit switch will not be
      triggered. With the first mass displaced approximately 2.5cm to left, click Run.
      After approximately 1 second, release the mass. The mass will oscillate and
      attenuate while encoder data is collected to record this response. Select OK after
      data is uploaded. Note: If at any time during this procedure a limit switch is
      triggered, you must return to the Driving Function box and Enable Driving
      Function before proceeding.
   8. Click Plotting --> Setup Plot. In Plot Title, type "System Identification (Team
      #)". In Left Axis, you should have Encoder 1 Position, and then select Plot Data
      at the lower right corner.

   9. Click Data --> Export Raw Data, Save the data to your home directory or a
       removable storage. Then you can use Notepad to open the file and read the raw
   10. Install and secure two weights into the first carriage. Repeat step 6 to 9.

Homework: Calculate  and n for two cases and identify m, c, and k.

3) Step response for different damping ratios.
   1. Click Command --> Input Shape. Select Step, Setup. In the Configure Step
      dialog box, enter Step Size: 5, Dwell Time 2000, Number of reps: 1. Click OK
      twice to go back to background screen.
   2. Click Setup --> Setup Driving Function. Select Force+Spring+Damper, then
      Setup Driving Function. In new window, enter Spring Constant k: 0.0, the
      Damping constant c: 0. Click OK, then Enable Driving Function, then OK.
   3. Click Command --> Execute --> Run.
   4. Click Plotting --> Plot Data to plot the result.
   5. Repeat step 2 to 4 by varying c between 0 and 100. Warning: Never exceed c to
      more than 100.
   6. Save the data of c= 10, 50, 100 for homework.

Homework: Plot the response vs. time for c=10, 50, 100. Explain why the shapes are
different for the three cases.

4) Sinusoidal response for different damping ratios:
   1. Click Command --> Input Shape. Select Sinusoidal, Setup. In the Configure
      Sinusoidal dialog box, enter Amplitude (N): 5, Frequency (Hz): 5, Number of
      reps: 30. Click OK, OK.
   2. Click Setup --> Setup Driving Function. Select Force+Spring+Damper, then
      Setup Driving Function. In new window, enter Spring Constant k: 0.0, the
      Damping constant c: 0. Click OK, then Enable Driving Function, then OK.
   3. Click Command --> Execute --> Run.
   4. Click Plotting --> Plot Data to plot the result.
   5. Repeat step 2 to 4 by varying c between 0 and 100 and Frequency between 0.5
      and 10. Warning: Never exceed c to more than 100, or Frequency to more
      than 10.
   6. Save data for homework: c=10, 50, 100 and Frequency f =1, 2, 10 Hz. Note you
      should have 9 sets of data with these combinations.

 1. Draw the response vs. time.
 2. Observe the effect of damping ratio and input frequency on the system
    response, i.e., the magnitude and phase shift.
 3. Use sinusoidal transfer function to prove your observation.

5) Clean up:
   1. Turn the power off (red button).
   2. Close the software interface and log out. If you saved file to a removable storage,
      remember to take the media with you.
   3. Return the stools to their original places. If you are the last group of the day,
      shutdown the computer.


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