8. Consider the unity-feedback system of Figure P9.1, withK (s+5)whG(s):(s+2) (s+3) (s+ 7) (s + 10)G(s)=s²+25ws+wdo the following: [Section: 9.3]a. Draw the root locus.b. Find the location of the dominant poles when = 0.8.c. Find the gain at which <= 0.8.d. If the system is to be cascade-compensated to attain T₂ = 1second and <= 0.8, find the compensator pole if the compensatorzero is at -4.e. Make an argument for the validity of your second-orderapproximation.f.MAILABMLVerify the validity of your design by simulatingyour system using MATLAB or any other computer program.%OS = e−(S/√1-57) × 100TpT'S==-In (%OS/100)²+In²(%OS/100)4

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Answered: 8. Consider the unity-feedback system…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Consider the plant with transfer function G(s) connected in standard feedback configuration with the controller De(s) = K. 1) 2) = s+2 (s+1)²+1 Sketch the root locus for G(s). Explain what rules you used to plot it. (Be sure to describe the following: the number of branches, where they start and where they are going; the real-axis portion of the root locus; jw-axis crossings (if any); points of multiple roots (if any).) What conditions need to be imposed if we want our closed-loop system to have no oscillations under a step input? Explain the conditions from the root locus. + Ro Σ Dc(s) G(s) Figure 1: Control system in Problem 1.
Problem 4: For the unity (negative) feedback system configuration (i.e., similar to problems 2 and 3 above) with open loop transfer function G(s) = K(S+3), sketch the root locus showing sufficient s(s+2)' details. Next, for the same configuration, assume that we add a new pole at s = -a to the open loop transfer function G(s). Can you (without getting deep into the math) qualitatively show how the root locus changes when a = 0, or a = 1, or a = = 5 (so, there will be three plots you need to show)?
2. Sketch the general shape of the root locus for each of the open-loop pole-zero plots shown in Figure P8.2. [Section: 8.4] jo) s-plane ° ja) *s-plane (a) (b) *s-plane * 3-plane (c) (d) jav ja) s-plane splane
Q5) For unity feedback control system with forward transfer function (G(s) ): G(s) = ; By using root locus graph calculate the value K(s+5) (s+2)(s²+12s+50) of gain (K) which must be added to get the dominant root at damping ratio (-0.886) and natural frequency (w = 8 rad/sec )? www CTRICAL ENGIN
and 1) 2) LIUS S Consider the following feedback system, where K is a constant gain G(s) === 1 s3 +382 +s+1 Let K be a real number. Utilize the Routh-Hurwitz criterion to derive stability conditions for the closed-loop system. Suppose that the reference input r(t) = 1. What are the steady-state tracking errors (ess) for K = 1 and K = 3, respectively? R K G(s) Y Figure 2: Control system in Problem 2.
For the system with open loop transfer function given by R(s) K s(s + 1) (s² + 4s +13) where K is the feedback gain. Sketch the root locus a) How many asymptotes are there for this system's root locus? what are asymptote angles? What is the center of asymptotes? C(s) b) Does the root locus cross the imaginary axis? where and what is the value of K at that point? c) Is there any break away, break in points? What is the approximate values of these points?
5. A feedback system's open-loop transfer function is K G(s) = s(s+ 3)(s+ 6) 1)Sketch the system root locus. 2)Find the range of K when the system is a stable system.
Solve the following problem by hand and without the use of AI. Thank You!
Please don't provide handwritten solution ....
root locus electrical engineering Don't overthink and reject. Complete the solution as per the given transfer function. No need of quadratic equation just simplify for the exact given transfer function.
Homework: For a unity feedback system with the forward transfer function: K(s + 20) G(s) = s(s + 2)(s+3) find the range of K to make the system stable.
Problem 1. For the systems (s + 2)² 1. G₁(s) = (s+1)(s² + 1)' (s+1)(s+2) 2. G2(s) = (s - 1)(s - 2)(s - 3)' => (a) Using the root-locus rules, draw the root locus plot by hand.

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