Assignment1 control
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This document describes two state controllable systems and poses four questions about analyzing and comparing the systems: 1) Find the control sequence to transfer each system from the initial state [0 0 0] to the final state [1 1 1] 2) Find the pulse transfer functions of the two systems 3) Determine the static gain of each system 4) Explain the difference in amplitude of the control sequences based on the zeros and poles of each system The response should be submitted as a PDF by the deadline of 4 PM on Sunday March 22nd and include the MATLAB functions used.
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![Given the two completely state controllable systems described by
𝑥( 𝑘 + 1) = [
−0.6 0 −0.2
0.2 0.6 1.2
−0.2 0 −0.6
] 𝑥( 𝑘) + [
0.6067
1.2319
−1.2179
] u(k), y(k) = [2 1 1] 𝑥(𝑘)
𝑥̃( 𝑘 + 1) = [
−0.6 0 −0.2
0.2 0.6 1.2
−0.2 0 −0.6
] 𝑥̃( 𝑘) + [
0.5280
1.132
−1.068
] 𝑢̃ (k), 𝑦̃(k) = [2 1 1] 𝑥̃(𝑘)
a) Find the control sequence that transfer each system from the zero-initial state to the final
state 𝑥 𝑓 = [
1
1
1
]
b) Find the pulse transfer functions of the two systems
c) Determine the static gain of each of the two systems Gain = lim
z→1
G(z) =
Y(z)
U(z)
d) Can you explain the difference of the amplitude of the two control sequences from the
zeros poles of each system?
- Use MATLAB for your computation and submit a word document that contains your
results accompanied with the MATLAB functions you have used to get your results.
You have a week to submit your report with deadline ending Sunday March 22 before
4 PM. Send report as pdf file to erasmy@gmial.com
Best wishes and hope all of you are in good health
Dr. Emad Rasmy](https://image.slidesharecdn.com/assignment1-200826105811/85/Assignment1-control-1-320.jpg)
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Assignment1 control
- 1. Given the two completely state controllable systems described by 𝑥( 𝑘 + 1) = [ −0.6 0 −0.2 0.2 0.6 1.2 −0.2 0 −0.6 ] 𝑥( 𝑘) + [ 0.6067 1.2319 −1.2179 ] u(k), y(k) = [2 1 1] 𝑥(𝑘) 𝑥̃( 𝑘 + 1) = [ −0.6 0 −0.2 0.2 0.6 1.2 −0.2 0 −0.6 ] 𝑥̃( 𝑘) + [ 0.5280 1.132 −1.068 ] 𝑢̃ (k), 𝑦̃(k) = [2 1 1] 𝑥̃(𝑘) a) Find the control sequence that transfer each system from the zero-initial state to the final state 𝑥 𝑓 = [ 1 1 1 ] b) Find the pulse transfer functions of the two systems c) Determine the static gain of each of the two systems Gain = lim z→1 G(z) = Y(z) U(z) d) Can you explain the difference of the amplitude of the two control sequences from the zeros poles of each system? - Use MATLAB for your computation and submit a word document that contains your results accompanied with the MATLAB functions you have used to get your results. You have a week to submit your report with deadline ending Sunday March 22 before 4 PM. Send report as pdf file to erasmy@gmial.com Best wishes and hope all of you are in good health Dr. Emad Rasmy