Question

0 0 1 [13 Marks]: The differential equation appearing below represents the mathematical dynamic model of an unknown system. Answer the following questions: $0 \frac{d^2y(t)}{dt^2} + 56 \frac{dy(t)}{dt} + 132y(t) = -16 \frac{dx(t)}{dt} + 12x(t)$ (a) Derive the transfer function of this system (3 marks). (b) Find the poles and zeros, and state whether the system is stable or not (2 marks). (c) Obtain the time-response of this system to the input $x(t) = 3te^{-4t}$, $t \ge 0$ (5 marks). (d) Calculate the minimum undershoot amount assuming that the response settles down within a 3% deviation band in 1.12 seconds (2 marks). (e) What happens to the system's response if the poles are moved further to the left? (1 mark). OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

          0 0 1 [13 Marks]: The differential equation appearing below represents the mathematical dynamic model
of an unknown system. Answer the following questions:
$0 \frac{d^2y(t)}{dt^2} + 56 \frac{dy(t)}{dt} + 132y(t) = -16 \frac{dx(t)}{dt} + 12x(t)$
(a) Derive the transfer function of this system (3 marks).
(b) Find the poles and zeros, and state whether the system is stable or not (2 marks).
(c) Obtain the time-response of this system to the input $x(t) = 3te^{-4t}$, $t \ge 0$ (5 marks).
(d) Calculate the minimum undershoot amount assuming that the response settles down within a 3%
deviation band in 1.12 seconds (2 marks).
(e) What happens to the system's response if the poles are moved further to the left? (1 mark).
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

0 0 1 [13 Marks]: The differential equation appearing below represents the mathematical dynamic model
of an unknown system. Answer the following questions:
0 (d^2y(t))/(dt^2) + 56 (dy(t))/(dt) + 132y(t) = -16 (dx(t))/(dt) + 12x(t)
(a) Derive the transfer function of this system (3 marks).
(b) Find the poles and zeros, and state whether the system is stable or not (2 marks).
(c) Obtain the time-response of this system to the input x(t) = 3te^-4t, t ≥ 0 (5 marks).
(d) Calculate the minimum undershoot amount assuming that the response settles down within a 3%
deviation band in 1.12 seconds (2 marks).
(e) What happens to the system's response if the poles are moved further to the left? (1 mark).
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

Added by Jennifer F.

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