Chapter 6 - Stability of Linear Feedback Systems Exercise-
1. To complete the discussion in Section 6.2, show that y(t) being bounded implies 0∫t|(hτ)|dτ is bounded (for bounded u(t)).
2. Show that a necessary and sufficient condition for a system to be BIBO stable is that all of the poles of the system transfer function have negative real parts.
3. Suppose the controller in the feedback loop in Figure 6.6 has the form
H (s) = s + p/s + z.
Use Routh-Hurwitz methods to find the regions of stability for the parameters p and z. Select values for p and z, and analyze the step disturbance response. Evaluate the stability as the motorcycle velocity varies 0 < V ≤ 5 m/sec.
4. What changes would you make to the robot-controlled motorcycle (that is, h, c, and L), to make it more robust to changes in forward speed? Interpret robust as an insensitivity of the system stability to changes in forward speed.
5. The task is to develop a robot-controlled motorcycle for operation on the moon. Develop a feedback controller to operate the motorcycle on the moon using a feedback controller structure of your choosing. After showing closed-loop stability to step disturbances on the moon, discuss the use of the same feedback controller on the earth. What realistic disturbances would the motorcycle encounter on the moon?
Format for Formal Lab Reports-
Besides answering specific questions, your formal lab write-up should include the following:
- Title and Date of the Experiment
- Purpose or Objective of the Experiment
- Brief Theory of the Experiment
- Experimental Apparatus Set-up and Description
- Procedure of the Experiment
- Experimental Results (tabulated, graphed, computed, analyzed, etc)
- Comparison of Experimental and Theoretical Results
- Numbered Figures with Captions
- Conclusions
- Appendices (if necessary)
Attachment:- Assignment.rar