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Engineering Β· Electrical Engineering
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Find the equation for the steady-state output (𝑦𝑠𝑠) for the following system with a step input (𝑋(𝑠)=1/𝑠). Find the steady-state values when 𝐾𝑝=48.Plot the system (use ltiview in MATLAB). Include the MATLAB commands used and a copy of the plot.

G(s) = s2+2s+2

X(s) Y(s)

Simulate the 𝐾𝑝 = 48 system in Simulink with MATLAB with a unit step input with a picture of the model and results from the Scope (make sure to scale the results of the Scope).
Add an integrator to the system so the controller has the form 𝐾𝑝(1 +1/𝑠) and use a unit step
input. Provide a picture of the Simulink model and the results from the Scope.

Finally add a derivative to your model so the controller has the form 𝐾𝑝(1 +1/𝑠+ 𝑠). Provide a picture of the
Simulink model and the results from the Scope.

How does the response of each system compare to each other qualitatively in terms of rise time, overshoot, damping, steady-state value, etc.?

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