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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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