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Transfer Function PDF

The document discusses transfer functions and stability analysis of discrete-time systems. It provides 7 different difference equations and asks to find the transfer function, poles, and unit pulse response for each system. It also provides a difference equation and asks to determine the output for a unit step input. Finally, it gives a transfer function and asks to find and plot the unit step response.

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Yahya Abdul Razek Yahya Abdul Razek
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83 views1 page

Transfer Function PDF

The document discusses transfer functions and stability analysis of discrete-time systems. It provides 7 different difference equations and asks to find the transfer function, poles, and unit pulse response for each system. It also provides a difference equation and asks to determine the output for a unit step input. Finally, it gives a transfer function and asks to find and plot the unit step response.

Uploaded by

Yahya Abdul Razek Yahya Abdul Razek
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Faculty of Engineering Digital Control

Electrical Power Dept. Transfer function and


Level four stability

▪ Transfer function and stability

1) Consider the following difference equations


a) y[k] = y[k-1]+u[k]
b) y[k] = 0.6y[k-1]+u[k]
c) y[k] = 0.3y[k-1]+u[k]
d) y[k] = u[k-1]
e) y[k] = 0.707y[k-1]-0.25y[k-2]+u[k-1]
f) y[k] = -0.25y[k-2]+u[k-1]
g) y[k] = -0 .707y[k-1]-0.25y[k-2]-u[k-1]
i. Find the transfer function for each system
ii. Find the poles of each system, identify which system is stable
iii. Assuming zero initial conditions, find the unit pulse response for each
system analytically.
iv. Assuming zero initial conditions, find the unit pulse response for each
system by successive substitution.

2) Use the z-transform to determine the output of the difference equation


𝑦(𝑘 + 2) − 1.5𝑦(𝑘 + 1) + 0.5𝑦(𝑘) = 𝑢(𝑘 + 1)
where u is a unit step applied at 𝑘 = 0 and 𝑦(0) = 0.5, 𝑦(−1) = 1

3) The transfer function of a discrete-time system is

0.1 𝑧 + 0.2 𝑧 2 − 0.4𝑧 3 + 0.3 𝑧 4 + 𝑧 5


𝐺(𝑧) =
𝑧6

Find and plot the unit step response of the above system.

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