Please breifly answer each z domain question with some explination! 1. If the tr
ID: 3558345 • Letter: P
Question
Please breifly answer each z domain question with some explination!
1. If the transfer function in the z domain has its zeroes outside the unit circle but its poles inside the unit circle, is that a stable or unstable system?
2. The poles of a z domain transfer function are located at z=0.8±j 0.8. Is this a stable or unstable system? Briefly justify your answer.
3. Suppose you are given the step response of a z domain system and this is the only information available to you. How will you deduce stability of the system from this information?
4. What is the significance of the damping ratio associated with a pole of the z domain transfer function? What happens to the behavior of a system when the damping ratio associated with a pole is exactly zero? What will the denominator of a second-order z domain system be if its poles are located exactly on the imaginary axis of the z plane?
Explanation / Answer
1)
Firstly, stability does not depend on zeroes, only on poles. Zeroes can exist outside the unit circle no problem. so system is stable poles are inside
2)
as the poles are inside the unit cirlce the system is stable (0.8,0.8),(0.8,-0.8) inside cirlce
3)by finding the poles of the step responce if they are inside the unit circle system is stable else unstable
4) the damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance. 0 damping ratio means there is no damping in the system undamped. imaginary poles exist in pairs so it will like z^2+x^2 form