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Andreas93 [3]
3 years ago
5

The output y and input x of a device are related by y = x + 1.4x3 . (a) Find the values of the output for steady-state operation

at the two operating points xo = 1 and xo = 2. (b) Obtain a linearized model for both operating points and compare them.
Mathematics
1 answer:
erma4kov [3.2K]3 years ago
5 0

Answer:

a) y(1) = 2.4 , y(2) = 13.2, b) y(x) = 2.4 + 5.2\cdot (x-1), y(1) = 2.4, y(2) = 7.6

Step-by-step explanation:

a) The values of the output for steady-state operation are:

y(1) = 1 + 1.4\cdot (1)^{3}

y(1) = 2.4

y(2) = 2 + 1.4\cdot (2)^{3}

y(2) = 13.2

b) The formula for linearization is:

y(x) = y(1) +\frac{dy}{dx}|_{x = 1} \cdot (x-1)

The first derivative of the formula evaluated at x = 1 is:

\frac{dy}{dx}|_{x=1} = 1 + 4.2\cdot (1)^{2}

\frac{dy}{dx}|_{x=1} = 5.2

The linearized model is:

y(x) = 2.4 + 5.2\cdot (x-1)

The output at x = 2 is presented below:

y(2) = 2.4 + 5.2\cdot (2-1)

y(2) = 7.6

Linearized model offers reasonable approximations for small intervals.

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