note6 - MEEN 364 Notes from Session on October 13, 2004 304...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
MEEN 364 Notes from Session on October 13, 2004 304 Fermier Hall, 6:00~7:00 pm 1) Problem 2.31 of the textbook “Feedback control of dynamic systems”, 4 th Edition, by Franklin et al. (a) At equilibrium: 0 ) ( 0 = + = = + = v u g i dt dv v i dt di ( 1 ) v i = also 0 ) ( = i v u g 0 ) 4 ) )(( 1 ) )(( ( = v v u v u v u Since, 1 = u 0 ) 2 2 ( ) 3 )( )( 1 ( 2 = + = v v v v v v v 3 1 , 0 ± = v From (1): 3 1 , 0 0 0 ± = = v i (b) Writing the deviation equation about the equilibrium: () v v i v i v i i v i i v i v i v i + + + + + = = = = = = = 0 0 0 0 0 0 & 0 0 0 0 1 1 00 11 i i v v u u ii vv uu v i gu v i v u u ig uv i v iv = = = = = = == ∆ =−+ + −+ ∂∂ +− + − & ( 2 ) we get: v i v i i + = + = 0 & u v i v i u v + = + + + = 3 3 ) 3 ( ) 1 ( ) 3 ( 0 & u v i v i dt d + = 3 0 3 1 1 1 ( 3 ) (c) In general the linearized form will be: 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
MEEN 364 Notes from Session on October 13, 2004 304 Fermier Hall, 6:00~7:00 pm u u g v i v g v i dt d u u v v i i u u v v i i + = = = = = = = 0 0 0 0 0 0 0 1 1 1 Since 1 0 = u ) 2 2 ( ) , 1 ( ) , ( 2 + = = v v v v g v u g 3 2 5 ) 2 2 ( ) 2 2 ( 2 m = + + + = v v v v v g when 3 1 ± = v Also, note 3 2 5 ± = = v g u g u v i v i dt d ± + = 3 2 5 0 3 2 5 1 1 1 m (4) Equation (4) represents the linearized differential equations of motion. 2
Background image of page 2
MEEN 364 Notes from Session on October 13, 2004 304 Fermier Hall, 6:00~7:00 pm 2) The robot shown the following figure has the differential equations of motion given. Symbols m 1 , m 2 , I 1 , I 2 , l 1 and g are constant parameters, representing the characteristics of the rigid body links. Quantities θ 1 and d 2 are the coordinate variables and are functions of time. The inputs are τ 1 and 2 . Linearize the two equations about the operating point 0 1 = , , and Give your results in the state space form.
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 8

note6 - MEEN 364 Notes from Session on October 13, 2004 304...

This preview shows document pages 1 - 4. Sign up to view the full document.

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