Performace In Time Domain

Question 1

How do you find a transfer function?

Answer 1

1. Formula = SinACosB + CosASinB
2. Find lap-lace of Sin = W/(S+A)^2+W^2
3. Find lap-lace of Cos = S+A/(S+A)^2+W^2
4. Plus both lap-lace and simplify

Question 2

How do you find system input?

Answer 2

Formula = min x u(t) + (max - min) u(t-1)

Question 3

How do you find system output?

Answer 3

Formula = min x y(t) + (max - min) y(t - rise point) + 1/1+js

Js = when line curves or system to reach 63% - when the line rises

Final answer is made up of:
(Y) initial + (y) steady space

(Y) initial = min x y(t)

(Y) steady space = (max - min) y(t - rise point) + 1/1+js

Question 4

How do you find steady state gain?

Answer 4

Formula = max - min (step response graph) divided by max - min ( step input graph)

Question 5

How do you find percent overshoot?

Answer 5

Find Z and Wn using this formula:

Wn/S^n+2ZWn+Wn^2 compare to CL transfer function

Wn = Sqr Number in Wn^2 place

Z = rearrange 2 x Z x Wn to get Z by itself and solve for Z

Then substitute Z into this formula:

100e x -Z(pi) divided by sqr root 1-Z^2

Question 6

How do you find peak time?

Answer 6

Find Z and Wn using this formula:

Wn^2/S^n+2ZWn+Wn^2 compare to CL transfer function

Wn = Sqr Number in Wn^2 place

Z = rearrange 2 x Z x Wn to get Z by itself and solve for Z

Substitute Wn and Z into this formula:

Pi/Wn x sqr root 1-Z^2

Question 7

How do you find settling time?

Answer 7

Find Z and Wn using this formula:

Wn/S^n+2ZWn+Wn^2 compare to CL transfer function

Wn = Sqr Number in Wn^2 place

Z = rearrange 2 x Z x Wn to get Z by itself and solve for Z

Substitute Wn and Z into this formula:

4/Z x Wn

Question 8

How do you find initial value and final value?

Answer 8

Initial value = Sub infinity to S in CL transfer function answer is always zero

Final value = Sub 0 into S in CL transfer function and simplify

Question 9

How do you find natural frequency (Wn) from complex poles?

Answer 9

1. Insert N^2 + N^2 into a sqr root function to get the answer in rads (N = numbers in complex poles)

Basically Pythagoras