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State space representation

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Consider the following system whose state space representation is as follows:

a) Assume that the initial conditions are zero. If the reference input is a unit step input , compute x1(t), x2(t), and y(t)

b) Find the transfer function of the system.

c) Using the transfer function found in (b), Compute y(t).

d) Plot x1(t), x2(t), and y(t) using MATLAB

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Consider the following system whose state space representation is as follows:

x'1(t) 0 1 x1(t) 0
= + u(t)
x'2(t) -8 -4 x2(t) 1

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Solution Summary

This calculation solves 4 problems, addressing reference inputs, transfer functions and plotting in MATLAB.

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Find the transfer function from state space representation

Consider the following system (see attachment) whose state space representation is as follows:

a) Find the transfer function of the system.
b) Compute eAt using the eigenvalues and eigenvectors method.
c) Compute eAt using the partial fraction method.
d) If u (t)=0 for t ≥ 0,compute x (t), y(t), and x(1) =[ -1 2]T
e) Assume that the initial conditions are zero. Using MATLAB ,Plot x(t), y(t), given that u(t)= -5 for 0 ≤ t ≤ 3 and u(t)=5 for 3 ≤ t ≤ 6

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