Multiple Choice Explanation Chlorine Ross Bredeweg Ryan Wong

Question 1 The CN, or condition number a) Is the ratio of the smaller number (s 2 ) to the larger number (s 1 ) b) Determines the feasibility of decoupling a system c) Is the unit eigenvectors of the m x m matrix G T G d) Is always less than 50

Question 1 The CN, or condition number a) Is the ratio of the smaller number (s 2 ) to the larger number (s 1 ) The CN is defined as: – CN = s2/s1 if s2>s1, or CN = s1/s2 if s1>s2 – Or more simply the ratio of the larger number to the smaller number

Question 1 The CN, or condition number b) Determines the feasibility of decoupling a system The feasibility can be determined through a couple of ways: – Conditional number (CN) – Singular value decomposition (SVD)

Question 1 The CN, or condition number c) Is the unit eigenvectors of the m x m matrix G T G – The unit eigenvectors of the m x m matrix GG T is defined as the column vectors of the matrix U in the SVD calculation

Question 1 The CN, or condition number d) Is always less than 50 – The CN can be any number that is greater than 1 though when it is CN<50 the system can be decoupled

Question 2 For MIMO systems a) Control loops are isolated b) Each controlled variable is only manipulated by one variable c) Decoupling the system makes it more complicated d) Manipulated variables may affect several controlled variables

Question 2 For MIMO systems a) Control loops are isolated In a MIMO system it is best to have all isolated loops but sometimes this cannot be achieved if interacting systems cannot be decoupled

Question 2 For MIMO systems b) Each controlled variable is only manipulated by one variable The definition of a MIMO system is multiple input and multiple output meaning that there are more than one variable controlling something

Question 2 For MIMO systems c) Decoupling the system makes it more complicated The process of decoupling may be complicated to perform but the effect it has on the system is to make it easier to control

Question 2 For MIMO systems d) Manipulated variables may affect several controlled variables The MIMO by definition is that there are multiple outputs meaning that the change in any variable can affect the output for multiple responses