Control design specifications

Question 1

If we consider a closed loop system where C(S) = K Zc/Pc and G(S) = Zg /Pg what can we observe about the poles and zeros?

Answer 1

the TF = ZcZg / (1/K PcPg + ZcZg)

The poles in Pg can be moved but the zeros in Zg cannot move

This is a problem if G(s) has values in RHP
-system can become unstable for large values of K]
-this may stop us having a fast rise time

Question 2

Give 2 real life examples of limitations of feedback control

Answer 2

Actuators have min/max value (saturation) and make some rise times unachievable

Static friction may prevent a low ess.

Question 3

How can peak time be appproximated?

Answer 3

The oscillating system peaks at about a half cycle (approx pi)

Tp = π/ wd

Question 4

How can overshoot be determined algebraically

Answer 4

At peak time , y(t) = 1 - e^ (-zwoTp)

sub in Tp and wd expressions to find overshoot in terms of just zeta

Question 5

How can settling time be determined?

Answer 5

Ts = 3/zetaxWo