Question

Question 3 (15 points): The figure below represents a 2nd-order feedback system containinga 2-phase AC induction motor. Determine the following a. System undamped natural frequency, on b. Damping ratio, c. Maximum percent overshoot (assuming a unit step input) and time to peak Note: Submit graph with proper labeling 6 Y(s) G(S) = s(0.3s+ 1) U(s) 1

Answer 1

The characteristic equation of unity feedback system is given as:

1G(SH(s) =0

1+ s(0.3s1) x 1 0

s(0.3s1 6 0

0.3s2s6 0

Dividing 0.3 throughout we get:

10 2 s S20 0 3

Comparing it with the general form of the equation we get:

= 0 s22wnsw n

(Undamped natural frequency)

w20w v20 4.47rad/s =

And

2wn= (10/3)

2(4.47(10/3)

(Damping ratio)

0.37

Then Maximum percent overshoot is given by:

$M.O =100\times e^{-\frac{\pi \zeta}{\sqrt{1 - \zeta^2}}}$

$M.O =100\times e^{-\frac{\pi (0.37)}{\sqrt{1 - (0.37)^2}}}$

M.O 92.08%