Solved: Problem 3. (15 points) Design the lag compensator such that you achiev

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problem 3 15 points design the lag compensator such that you achieve t

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Control System

Problem 3. (15 points) Design the lag compensator such that you achieve the both requirements.

D_{c}(s)=\frac{T_{i} s+1}{\alpha T_{i} s+1}

where a > 1. Use K you designed in Prob. 1. Provide the Bode plot of the open-loop with the stability margins. You will need iterations to find the correct T; and a.

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Question 45498

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.

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.

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.

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.

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.

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

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)

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

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

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.