Problem 5a: Consider the first-order system given below.

T₁ = 8/s+8

i) Find the 2% settling time.

ii) Find the rise time.

iii) Given the quantities above, sketch and label the time response of the system.

Problem 5b: In class, you have derived the response of a first-order

system to a unit-step input. Given a first-order system of the form G(s) = K/(1+Ts),

where T is the time-constant, and K is the constant, find:

i) The time-response to a unit-ramp input r(t) = t.

ii) The steady-state error for error measured as e(t) = r(t)- c(t). (Hint: the steady-state error

is measured as t tends to infinity).