PSet3Solutions

# PSet3Solutions - Problem Set#3 16.30 Estimation and Control...

• Notes
• 2

This preview shows pages 1–2. Sign up to view the full content.

Problem Set #3 16.30: Estimation and Control of Aerospace Systems Posted: Mar 1, Due: Mar 7 Note: this problem set is very short, because you will be required to do a pre-lab assignment as well, coming up shortly 1 Problem 4.5 in DFT. (Upper and lower gain margins are the factors by which you can multiply or divide the gain while maintaining closed-loop stability.) Probably the easiest approach to solve this problem is based on the Nyquist plot. There are two main cases to be analyzed, summarized in the following figure. 1 Re( s ) Im( s ) 0 2 1 ω Re( s ) 3 Re( s ) Im( s ) 2 1 ω Figure 1: The Nyquist plots in the two main cases cases: α > 0 (left), α < 0 (right). The numbers on the real axis represent the number of unstable closed-loop poles should the - 1 point fall within those ranges. From the analysis of the Nyquist plots, one can conclude that the only case in which the closed- loop is positive is when α is positive, and the gain is positive and “small.” Since the gain is specified

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Spring '07
• Frazzolli
• Complex number, real axis, lower gain margins

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern