# Homework_3 - CBE 162 Chemical Process Control Homework 3...

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CBE 162: Chemical Process Control Homework 3 Due on 26th Feb, 2013 You may turn it in the same day by 5pm (no penalty), or with 25% deduction/day at 384 Tan Hall. Clearly state all assumptions. Please make sure that pages are numbered, and the questions are in order. Question 1. Consider the CSTR dynamics studied in Homework 2. For certain values of steady state and input parameters, the matrix A is given by 0 13 8 4 4 9 8 4 8 6 12 8 0 5 0 - 4 (a) What is the characteristic equation for this matrix? (5 pts) (b) Solve the characteristic equation to obtain the roots (eigenvalues) of the matrix. Verify your results using the ’eig’ function in MATLAB. (5 pts) (c) Based on the eigenvalues, discuss the stability of the system. (5 pts) (d) For a different set of steady state and input parameters, one eigenvalue of the A is determined to be zero. What type of an output response would you expect, and why? (5 pts) Question 2.

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