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Control System

(a) The first-order system has the transfer function

T(s)=\frac{A}{1+s T}

Find the system output response in time domain when a unit ramp signal, r(t)=t, is applied to its input.

(b) The transfer function of a second-order system is:

T(s)=\frac{4}{s^{2}+4 s+4}

Find the system output response in time domain when a unit ramp signal, r(t)=t, is applied to its input.

\text { (Note: The inverse Laplace transform of } F(s)=\frac{1}{(s+a)^{2}} \text { is } f(t)=t \cdot e^{-a t} \text {.) }

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Control System

2. For the system shown below, find the output c(t) if the input r(t) is a unitstep. For full credit, transfer function should be computed correctly, C(s)should be computed correctly, and c(t) should be computed correctly.Partial credit may be earned.

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Control System

1. Reduce the block diagram shown below to a single block,T(s) = C(s)/R(s). For full credit, all loops should be correctly reduced.Partial credit may be earned for correctly reducing some loops.

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Control System

a) Knowing the format of state space representation:

\dot{x}=A x+B u

y=C x+D u

If a second order system is modeled in a state space representation, what will be the dimensions of Aand B matrix?

b) Consider a system modeled via the third order differential equation:

\dddot{x}+3 \ddot{x}+4 \dot{x}+x=5 \dot{u}+u

Where, x(t) is displacement, u(t) is force. Develop a state space representation for the system. The desired output is all state variables.

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Control System

Q1) Given the following block diagram system.

a) Reduce the block diagram to a single transfer function.

b) Plot the root locus of the system. Explain the plot.

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Control System

O Which of the following statements is incorrect?

i. Root-locus is symmetric about x-axis.

ii. Root-locus starts at open-loop poles and ends at open-loop zeros.

iii. Root-locus graph tracks the closed-loop poles as the gain varies.

iv. None.

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Control System

) If the open-loop transfer function is given by

\frac{K(s+2)}{s^{4}+2 s+2}

how many open-loop zeros are at infinity?

i. 1ii. 3iii. 4iv. 0

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Control System

) If KG(s)H(s) represents the open-loop transfer function of a system, then thegain K and the closed-loop poles of the system satisfy which equation?

i. KG(s)H(s) =1

ii. KG(s)H(s) = -1

ii. KG(s)Н (s) — 0

iv. KG(s) = H(s)

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Control System

If the static error constant K.100, then the stead-state errors for step and ramp inputs are

\text { i. } e_{\text {rtep }}(\infty)=0, e_{\text {ramp }}(\infty)=0

\text { ii. } e_{\text {step }}(\infty)=0, e_{\text {ramp }}(\infty)=\infty

\text { iii. } e_{\text {step }}(\infty)=\infty, e_{\text {ramp }}(\infty)=0

\text { iv. } e_{\text {step }}(\infty)=\infty, e_{\text {ramp }}(\infty)=\infty

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Control System

) In the unity feedback system in Figure 1, at least how many poles of G(s) mustbe at the origin for the steady-state error due to the ramp input is zero?

i. 1ii. 2iii. 3iv. 4

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Control System

(5 pts.) Sketch the root locus (rough sketch) for the following problems, and for each problem find the range of K where the system is stable.

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**Use of solution provided by us for unfair practice like cheating will result in action from our end which may include permanent termination of the defaulter’s account.Disclaimer:The website contains certain images which are not owned by the company/ website. Such images are used for indicative purposes only and is a third-party content. All credits go to its rightful owner including its copyright owner. It is also clarified that the use of any photograph on the website including the use of any photograph of any educational institute/ university is not intended to suggest any association, relationship, or sponsorship whatsoever between the company and the said educational institute/ university. Any such use is for representative purposes only and all intellectual property rights belong to the respective owners.

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