Consider the equation 5y 7y 4y ft Express this equation i

Consider the equation: 5y + 7y + 4y = f(t) Express this equation in state space form along with the output. Define your variables clearly.

Solution

Consider the second-order equation
5 ¨y + 7 y + 4y = f (t)
Solve it for the highest derivative:
¨y = 1
5
f (t) 4
5
y 7
5
y
Now define two new variables, x1 and x2, as follows: x1 = y and x2 = y. This implies
that x1 = x2 and
x2 = 1
5
f (t) 4
5
x1 7
5
x2