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Sheet 6

This document contains 6 problems related to analyzing sampled data systems and calculating their characteristics such as damping ratio, natural frequency, percentage overshoot, peak time, and pole locations. Problem 1 asks to find damping ratio and natural frequency for 4 different characteristic equations. Problem 2 involves calculating the transfer function, step response, damping factor, and natural frequency of a closed loop system. Problems 3 and 4 involve calculating time domain characteristics from a step response such as percentage overshoot and peak time. Problems 5 and 6 involve calculating pole locations in the z-plane from given s-plane poles.

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84 views2 pages

Sheet 6

This document contains 6 problems related to analyzing sampled data systems and calculating their characteristics such as damping ratio, natural frequency, percentage overshoot, peak time, and pole locations. Problem 1 asks to find damping ratio and natural frequency for 4 different characteristic equations. Problem 2 involves calculating the transfer function, step response, damping factor, and natural frequency of a closed loop system. Problems 3 and 4 involve calculating time domain characteristics from a step response such as percentage overshoot and peak time. Problems 5 and 6 involve calculating pole locations in the z-plane from given s-plane poles.

Uploaded by

Apdo Mustafa
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Sheet 6

1. Find the damping ratio and the undamped natural frequency of the sampled
data systems whose characteristic equations are given below

(a) z2 − z + 2 = 0
(b) z2 + 1 = 0
(c) z2 − z + 1 = 0
(d) z2 + 0.81 = 0

2. Consider the closed-loop system of Figure below. Assume that T = 1


s.
(a) Calculate the transfer function of the system.
(b) Calculate and plot the unit step response at the sampling instants.
(c) Calculate the damping factor and the undamped natural frequency
of the system.
3. A unit step input is applied to the system in previous Figure
Calculate:
(a) The percentage overshoot.
(b) The peak time.
(c) The rise time.
(d) Settling time to 5 %.

4. The closed-loop transfer functions of four sampled data systems are


given below. Calculate the percentage overshoots and peak times.

5. The s-plane poles of a continuous-time system are at s = −1 and s = −


2. Assuming T = 1s, calculate the pole locations in the z-plane.

6. The s-plane poles of a continuous-time system are at s1,2 = −0.5 ±


j0.9. Assuming T = 1s, calculate the pole locations in the z-plane.
Calculate the damping ratio and the undamped-natural frequency of
the system.

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