homework4_f10_sol

Homework4_f10_sol - University of California Davis Department of Chemical Engineering and Materials Science ECH 157 Process Dynamics and Control

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
University of California, Davis Department of Chemical Engineering and Materials Science ECH 157 Process Dynamics and Control Ahmet Palazoglu HOMEWORK 4 Fall 2010 (60 points) 1. (10 pts) For the following state-space process model, show that the eigenvalues of the state matrix and the system poles are identical. 2 2 1 2 1 1 ) 25 / 2 ( ) 2 / 1 ( ) 10 / 1 ( ) 5 / 7 ( ) 5 / 1 ( x y u x x dt dx u x dt dx = + + = + = What can you say about the stability of this system? The state-space model is expressed in the following form: Cx y Bu Ax x = + = With [] 1 0 ; ) 25 / 2 ( ) 5 / 7 ( ; ) 2 / 1 ( ) 10 / 1 ( 0 ) 5 / 1 ( ; 2 1 = = = = C B A x x x The A matrix is triangular, so the eigenvalues simply are the diagonal elements: ) 2 / 1 ( ); 5 / 1 ( 2 1 = = λ Both are negative, thus the system is stable. The transfer function model can be obtained as: [] B A sI C s g 1 ) ( = Or you can use the ss2tf command in MATLAB: >> [n,d]=ss2tf([-(1/5) 0;-(1/10) -(1/2)],[7/25;2/25],[0 1],[0]) n = 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
0 0.0800 -0.0120 d = 1.0000 0.7000 0.1000 >> g=tf(n,d) Transfer function: 0.08 s - 0.012 ----------------- s^2 + 0.7 s + 0.1 >> pole(g) ans = -0.5000 -0.2000 Thus, the poles and the eigenvalues are the same.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/01/2011 for the course ECH 157 taught by Professor Palagozu during the Spring '08 term at UC Davis.

Page1 / 8

Homework4_f10_sol - University of California Davis Department of Chemical Engineering and Materials Science ECH 157 Process Dynamics and Control

This preview shows document pages 1 - 3. Sign up to view the full document.

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