# Matlab and Designing Controller System

Consider the following system whose state space representation is as follows: (see attached file for better representation)

x'1 0 1 0 x1 0

x'2 = 0 0 1 x2 + 0 u

x'3 24 14 -1 x3 1

y = [2 -1 1]x

a) Design a controller for the system, place the poles at s=-10 and s = -15Â± 5j.

b) Design (if possible) a full-order observer for the system. Place the observer poles at s= -20,-20,-20.

c) Using MATLAB, repeat part (a) and (b). Also check that the matrices A-BK and A-LC have the desired eigenvalues.

d) Using MATLAB, plot x1,x2,x3, x1,x2 ,x3 in the same graph. Note that the initial state of the system is (-3,-3,-3); the initial state of the observer is 0.

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

x'1 0 1 0 x1 0

x'2 = 0 0 1 x2 + 0 u

x'3 24 14 -1 x3 1

y = [2 -1 1]x

a) Design a controller for the system, place the poles at s=-10 and s = -15Â± 5j.

b) Design (if possible) a full-order observer for the system. Place the observer poles at s= -20,-20,-20.

c) Using MATLAB, repeat part (a) and (b). Also check that the matrices A-BK and A-LC have the desired eigenvalues.

d) Using MATLAB, plot x1,x2,x3, x1,x2 ,x3 in the same graph. Note that the initial state of the system is (-3,-3,-3); the ...

#### Solution Summary

This solution has full explanations and step-by-step calculations to design a controller and full-order observer for the system using Matlab.