EEE 480 Lab 2

 

Part 1

Transfer Function H(s) = 1/(s+1)

  1. Create a Bode plot using a bode command for w = 10-2 to 104 radians/second. Hint: Use the MATLAB help to learn how to use logspace command. Note: When using the logspace command, using many points (example 200) will help to create smoother plots.
  2. Create a Bode plot using freqs command for w = 10-2 to 104 radians/second. Use the graph from part a to check your graphs.

    3. Use the semilogx command to make your graphs. This creates an x-axis with a logarithmic distribution of points and

    an y-axis with the usual linear distribution of points.

    You can create separate plots for the magnitude and phase plots or try to use the subplot command to create two

    graphs in one figure window or on one page.

    Get the graphs (magnitude and phase) initialed by the TA and turn in as part of your lab report.
  3. In the lab report describe the frequency ranges where an input signal is attenuated and the frequency where an input signal amplified.

Part 2

 

  1. Consider the following system

    2. P = 10000/(s3 + 101s2 + 10100s + 10000)

    K = k

    Find the transfer functions for the error signal, e/r, control signal, u/r, and output signal, y/r.

    Include your derivations of the error, control, and output transfer functions in your report.

     

  2. Create Bode plots (magnitude and phase) for the error, control, and output transfer functions for (K = 10, 50, 75). Create separate Bode plots for error, control, and output. Plot the magnitude and phase (for each K) on the same graph. The result is three magnitude and three phase graphs (error, control, and output). Both the magnitude and phase graphs will have three plots (k = 10, 50, 75).

    3. Get the TA to initial these graphs and turn the graphs in as part of the report.

     

     

     

  3. Output Step Response

    4. Create one graph of the plots of the output, y(t), step responses for each K.

    Get the TA to initial these graphs and turn the graphs in as part of the report.

  4. Tracking Error Step Response

    5. Create one graph of the plots of the tracking error, e(t), step responses for each K.

    Get the TA to initial these graphs and turn the graphs in as part of the report.

     

  5. Control Signal Step Response

    6. Create one graph of the plots of the control signal, u(t), step responses for each K.

    Get the TA to initial these graphs and turn the graphs in as part of the report.

  6. Using only the controller, k = 50, create this system in Simulink. Use a sine wave signal generator for the reference command and include a "To Workspace" sink for each the reference, error, control, and output signals.

    7. Include your Simulink block diagram in your report.
  7. Simulate the system using for three different input signals. The input signals will be sine waves at different frequencies (8 rad/sec, 80rad/sec, 800rad/sec).
  8. Plot the three error signals on one graph and label each with the frequency of the corresponding reference command. Create similar graphs for the control and output signals. Use either text or gtext MATLAB commands to label the graphs.

    9. Get the TA to initial these graphs and turn the graphs in as part of the report.

     

  9. Compare the magnitude of each response to the Bode plot for each signal. Describe any relationship between the bode plots and plots created using Simulink.

Include your description of the error, control, and output plots in your report.