Section 5

Question 1

What are the steps required to create a NMSS model?

Answer 1

1. Find the models Difference Equation
2. Define the Integral of Error
3. Convert the IoE to difference equation form and substiute Yk
4. Fill in the State Space Model matrixies

Question 2

What is the purpose of the NMSS equation?

Answer 2

To find a control algorithm with enough parameters to make the model controllable (assign poles)

Question 3

How many states will a model with ‘m’ numerator states and ‘n’ denominator states have?

Answer 3

n+m states

Question 4

What are the steps to develop the state space vector?

Answer 4

1. Check the number of states required (n+m)
2. Fill in Yk and Zk (top and bottom)
3. Fill in additional output states (Yk-1,2,3…ect)
4. Fill in additional input states (Uk-1,2,3…ect)

Question 5

Write the general form of the NMSS control algorithm with a Yk, Uk-1 and Zk gain.

Answer 5

Uk=-[f0 g1 ki]|Yk |
|Uk-1|
|Zk |

Format in this answer is shit. Yk, Uk-1 and Zk are a column vector.

Question 6

Write the general form of the Integral of Error

Answer 6

Zk=1/(1-z^-1) {Yd-Yk}

Format is shit. Check notes if unsure.