State Space

Question 1

What is rule 1?

Answer 1

If numerator (top)is constant value then only A and B matrix is used

Question 2

What is rule 2?

Answer 2

If numerator (top) power is smaller than denominator (bottom) power then A, B and C matrix is used

Question 3

What is rule 3?

Answer 3

If numerator power is equal to denominator power then A,B,C and D matrix is used

Question 4

How to do you find rule 1 matrix?

Answer 4

1. Denominator power determines size of A matrix (eg. 3x3 or 4x4) and B matrix (eg. 3x1 or 4x1)
2. The A matrix is built by 0 1 0 … 0 in first row and 0 0 1 0 …. 0 in second row and the 1 moves to the right for each row
3. The A matrix bottom row consists of denominator constants written from right to left in the matrix and all are minus values
4. The B matrix is all 0’s and bottom row contains numerator
5. The final answer is matrix A + matrix B

Question 5

How to do you find rule 2 matrix?

Answer 5

1. Matrix A is same a rule 1
2. Matrix B last row is always 1
3. Matrix C is 1 x (denominator power) and values are numerator values written from right to left from the function to the matrix written from left to right
4. Final answer is matrix A + matrix B + matrix C

Question 6

How to do you find rule 3 matrix?

Answer 6

1. Matrix A is same as rule 1
2. Matrix B is same as rule 2 (last row is always 1)
3. Matrix C is built by taking far right numerator - far left numerator x far left denominator and keep working inside until all values are calculated (only work inside from Left to right keep using first constant on left)
4. Matrix D is always the first number on numerator

Question 7

How do you find poles in state space?

Answer 7

1. Use formula |(SI - A)|
2. Find determinate
3. Use Second degree equation
4. Both values of X1 and X2 are final answer

Question 8

How do you find the determinate of a matrix?

Answer 8

If it’s 2 by 2 just cross multiply and minus both answers to get final answer

If it 3 by 3 cover row and column of A, B and C and cross multiply remaining numbers. Then the formula is:
|A| - |B| + |C|

Question 9

What does a typical state space block diagram look like?

Answer 9

|— D ————|
     |                        |
— B — state space — C 
           |                 |
           | — A ——|

Question 10

How do you convert function to transfer function?

Answer 10

Y always on bottom

U always on top

Y with power = S with corresponding power, Same with U

Y with 2 dots on top is S with power 2 and same for U

Y and U with no dots and just a constant is just the constant

Y and U with no dots or constant is just S