Question

Consider the system shown in the figure (a), design a lead compensator $G_c(s)$, as shown in figure (b) so that the dominant closed-loop poles have the damping ratio $\zeta = 0.5$ and the undamped natural frequency $\omega_n = 3$ rad/s. 

          Consider the system shown in the figure (a), design a lead compensator $G_c(s)$, as shown in figure (b) so that the dominant closed-loop poles have the damping ratio $\zeta = 0.5$ and the undamped natural frequency $\omega_n = 3$ rad/s.
Show more…
Consider the system shown in the figure (a), design a lead compensator Gc(s), as shown in figure (b) so that the dominant closed-loop poles have the damping ratio ζ = 0.5 and the undamped natural frequency = 3 rad/s.

Added by Paul S.

Close

University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
I need help with this as soon as possible, please. Solving it on a piece of paper would be great. Thanks in advance! Consider the system shown in figure (a) and design a lead compensator Gc(s) as shown in figure (b) so that the dominant closed-loop poles have a damping ratio (ζ) of 0.5 and an undamped natural frequency (ωn) of 3 rad/s. R(s) 10s(s + 1) C(s) R(s) 10s(s + 1) C(s) G(s) G(s) (a) (b)
Close icon
Play audio
Feedback
Powered by NumerAI
Ivan Kochetkov David Collins
Danielle Fairburn verified

Sri K and 71 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question
*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs
*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.
*

Recommended Videos

-
hi-can-you-solve-this-question-please-b-the-transfer-function-of-a-second-order-system-is-given-belowfind-s4-gs-s3s9-b1-b2-b3-b4-b5-find-the-dc-gain-find-damping-ratio-and-undamped-natural-f-88152

The transfer function of a second-order system is given below: G(s) = (s+4) / (s^2 + 3s + 9) (b.1) Find the DC gain. (b.2) Find the damping ratio and undamped natural frequency. (b.3) Find the zeros and poles. (b.4) Identify the zeros and poles in a polar diagram. (b.5) State if the system is stable or not and explain why.

Sri K.
consider-the-model-for-a-space-vehicle-control-system-shown-in-the-figure-a-design-a-lead-compensator-gcs-suach-that-the-damping-ratio-and-the-un-damped-natural-frequency-wn-of-the-dominant-12148

Consider the model for a space-vehicle control system shown in the figure. a) Design a lead compensator Gc(s) such that the damping ratio and the undamped natural frequency wn of the dominant closed-loop poles are 0.3 and 3 rad/sec respectively. b) Modify the shape of the root loci, using two lead networks, each contributing half the necessary lead angle. Choose s = -5.4 as the location of the zeros. c) Plot the root loci of both systems. d) Plot the unit-step response of both systems.

Adi S.
o4-consider-the-system-shown-in-fig-3-athe-damping-ratio-of-this-system-is-0158-and-the-undamped-natural-frequency-is-316-radsecto-improve-the-relative-stabilitywe-employ-tachometer-feedback-94693

Consider the system shown in Fig (3-a). The damping ratio of this system is 0.158 and the undamped natural frequency is 3.16 rad/sec. To improve the relative stability, we employ tachometer feedback. Fig (3-b) shows such a tachometer-feedback system. Determine the value of Kh so that the damping ratio of the system is 0.5 in Fig (3-b). Find Tr, Tp, Ts (2% criterian), Mp and ess for Fig (3-a) and Fig (3-b) and Compare between results where I/P is a unit step.

Adi S.
*

Recommended Textbooks

-
University Physics with Modern Physics

University Physics with Modern Physics

Hugh D. Young 14th Edition
achievement 1,514 solutions
Physics: Principles with Applications

Physics: Principles with Applications

Douglas C. Giancoli 7th Edition
achievement 1,192 solutions
Fundamentals of Physics

Fundamentals of Physics

David Halliday, Robert Resnick , Jearl Walker 10th Edition
achievement 1,543 solutions
*

Transcript

-
00:01 To solve this question for calculating zeros we will be using this equation s plus 4 is equals to 0 and s will come as minus 4.
00:10 4 poles, 4 poles, a square plus 3s plus 9 is equals to 0 and hence here on solving this quadratic equation we will get two values of s.
00:23 It will be s is equals to minus 3 plus minus root 27 divided by 3 and here another thing here will be minus 3 divided by 2 plus minus 3 divided by 2 root 3j.
00:41 So for this pole, pole zero diagram will be like this.
00:52 We will make cartesian coordinate here like this and here 0 minus 1 minus sorry this will be positive 1 positive 2 plus 3 and between plus 3 divided by 2 root 2.
01:23 So and here it will be minus 1 minus 1 .5 and here it will be minus 2 and minus 3.
01:35 So in the cartesian coordinate this point will be somewhere over here and here we will mark this as minus 1 .5 comma 1 .5 root 3 and here in the third quadrant we will have plus 2 minus of 3 divided by 2 root 3 and here this will be the point minus 1 .5 comma minus 1 .5 root 3...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever