{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

e483h7_07

# e483h7_07 - Simon Fraser University School of Engineering...

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

Simon Fraser University School of Engineering Science ENSC 483 - Modern Control Systems Spring 2007–Assignment 7 1. Consider the inverted pendulum mounted on a motor driven cart as shown in the Figure 1. This is a model of the attitude control of a space booster on takeoff, where the objective of the attitude control problem is to keep the space booster in a vertical position. Applying Newton’s second law and making some simplifying assumptions (e.g. that the rod is massless, pendulum mass is concentrated at the end, sin θ θ, cos θ 1, and θ ˙ θ 2 0) we get the following state space representation of the system: ˙ x = 0 1 0 0 M + m Ml g 0 0 0 0 0 0 1 - m M g 0 0 0 x + 0 - 1 Ml 0 1 M u, x = θ ˙ θ x ˙ x y = ˆ 1 0 0 0 0 0 1 0 ! x Figure 1: Inverted pendulum on a cart (a) Assuming that M = 2 kg, m = 0 . 1 kg and l = 0 . 5 m , investigate if this system is com- pletely controllable and observable.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ 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