practice-midterm1

practice-midterm1 - P RACTICE M ID - TERM E XAM L INEAR S...

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

View Full Document Right Arrow Icon
P RACTICE M ID - TERM E XAM L INEAR S YSTEMS Jo˜ao P. Hespanha Please explain all your answers. 1. Consider the one-link robot in the following figure: θ τ m x y where denotes the angle of the link with the horizontal, the torque applied at the base, ( x , y ) the position of the tip, the length of the link, I its moment of inertia, m the mass at the tip, g gravity’s acceleration, and b a friction coefficient. This system evolves according to the following equation: I ¨ = - b ˙ - gm cos + . (a) Compute the state-space model for the system when u = is regarded as the input and the vertical position of the tip y is regarded as the output. Please denote the state vector by z to avoid confusion with the horizontal position of the tip x . Hint: Do not forget the output equation! (b) Show that ( t ) = π / 2, ( t ) = 0, 2 t 0 is a solution to the system and compute its linearization around this solution. From your answer, can you predict if there will be problems when one wants to control the tip position
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/29/2011 for the course ME 243a taught by Professor Abamieh during the Fall '09 term at UCSB.

Page1 / 2

practice-midterm1 - P RACTICE M ID - TERM E XAM L INEAR S...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online