Question

Represent the following differential equation using a state space model. y''(t) - 6y'(t) + 4y(t) = 2 x(t) , x=4 step , y'(0) = 0 , y(0) = 0 Then find: a) Convert the state space model to transfer function. b) Response time equation y(t). c) Observability test.

          Represent the following differential equation using a state space model.
y''(t) - 6y'(t) + 4y(t) = 2 x(t) , x=4 step , y'(0) = 0 , y(0) = 0
Then find:
a) Convert the state space model to transfer function.
b) Response time equation y(t).
c) Observability test.

Represent the following differential equation using a state space model.
y”(t) - 6y'(t) + 4y(t) = 2 x(t) , x=4 step , y'(0) = 0 , y(0) = 0
Then find:
a) Convert the state space model to transfer function.
b) Response time equation y(t).
c) Observability test.

Added by Ethan R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/23/2023

Step 1

Convert the given differential equation to a state-space model. The given differential equation is: $$y''(t) - 6y'(t) + 4y(t) = 2x(t)$$ Let's define two state variables: $$x_1(t) = y(t)$$ $$x_2(t) = y'(t)$$ Then, we have: $$x_1'(t) = x_2(t)$$ $$x_2'(t) = y''(t) Show more…

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Represent the following differential equation using a state space model. y''(t) - 6y'(t) + 4y(t) = 2x(t) , x=4 step , y'(0) = 0 , y(0) = 0 Then find: a) Convert the state space model to transfer function. b) Response time equation y(t). c) Observability test.