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3 years ago

15

A controller for a satellite attitude control with transfer function G = 1 s 2 has been designed with a unity feedback structure

and has the transfer function D(s) = 8(s+2) s+4 . Find the system type and the corresponding error constant for this system.

1 answer:

S_A_V [24]3 years ago

5 0

Answer:

type 2, k = 4

Explanation:

(a) The transfer function of the controller for a satellite attitude control is

$G = \frac{1}{s^2}$

The transfer function of unity feedback structure is

$D(s) = \frac{10(s+2)}{s+5}$

To determine system type for reference tracking, identify the number of poles at origin in the open-loop transfer function.

For unity feedback system, the open-bop transfer function

$G(s)D_c(s)=\frac{1}{s^2}\frac{10(s+2)}{s+5}$

$=\frac{10(s+2)}{s^2(s+5)}$

Determine the poles in G(s)4(s).

s = 0,0,-5

Type of he system is decided by the number of poles at origin in the open loop transfer function.

Since, there are two poles at origin, the type of the system will be 2.

Therefore, the system type is

Type 2

check the attached file for the concluding part of the solution

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A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 350 MPa. Using the distortion-energy a

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Using the distortion energy theory to determine the factors of safety FOS can be expressed by the relation:

$\dfrac{Syt}{FOS}= \sqrt{ \sigma x^2+\sigma y^2-\sigma x \sigma y+3 \tau_{xy^2}}$

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USing the maximum-shear stress theory;

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$\dfrac{350}{2 FOS} =\sqrt{ (\dfrac{110-100}{2})^2+ (0)^2$

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Using distortion- energy theory formula:

$\dfrac{350}{FOS}= \sqrt{ 90^2+20^2-90*20+3(-20)^2}$

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USing the maximum-shear stress theory;

$\dfrac{350}{2 FOS} =\sqrt{ (\dfrac{90-20}{2})^2+ (-20)^2$

$\dfrac{350}{2 FOS} =\sqrt{ (35)^2+ (-20)^2$

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