Q1)(15 pts) Consider a system represented by the differential equation d’y(1) , 4dyO) + 3y(t)=2u(t) dr dt dy(0) where the initial conditions are y(0)=1, dt = 0 and u(t)=1, t20 a. Find the Laplace transform of the system b. Find y(t) (output) by using inverse Laplace transform. Find steady state error of the system.

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Q1)(15 pts) Consider a system represented by the differential equation
d²y(1) , dy0) + 3y(t)=2u(1)
+4
di
dt
dy(0)
where the initial conditions are y(0)=1,·
= 0 and u(t)=1, t20
dt
a. Find the Laplace transform of the system
b. Find y(t) (output) by using inverse Laplace transform.
c. Find steady state error of the system.
Transcribed Image Text:Q1)(15 pts) Consider a system represented by the differential equation d²y(1) , dy0) + 3y(t)=2u(1) +4 di dt dy(0) where the initial conditions are y(0)=1,· = 0 and u(t)=1, t20 dt a. Find the Laplace transform of the system b. Find y(t) (output) by using inverse Laplace transform. c. Find steady state error of the system.
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