and1)2)LIUSSConsider the following feedback system, where K is a constant gainG(s) ===1s3 +382 +s+1Let K be a real number. Utilize the Routh-Hurwitz criterion to derivestability conditions for the closed-loop system.Suppose that the reference input r(t) = 1. What are the steady-statetracking errors (ess) for K = 1 and K = 3, respectively?RKG(s)YFigure 2: Control system in Problem 2.

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Answered: and 1) 2) LIUS S Consider the following…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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B) For a unity feedback system with the forward transfer function: G(S) K s (1+0.4 s)(1 + 0.25 s) Find the range of (K) to make the system stable (Apply Routh's stability criterion).
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?
A second order plant with unity feedback is cascaded by a proportional controller as shown. If K is 100, 1. HI. Determine its closed-loop poles Y(s)/R(s). Determine its transfer function of E(s)/R(s) Calculate the steady state error of the following block diagram for a unit step R(s) input. iv. Suggest a method to improve on the steady state error. E(s) K pito 7 (s+2)(s+5) Y(s)
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)?
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Can you also please do the simulate the step response in MATLAB for the design and report archieved PO and settling time? Thank you.
1) Consider the system below: Vehicle Controller Steering dynamics Desired Actual bearing angle bearing angle 50 1 K s2 + 10s + 50 s(s + 5) Figure 1: Simplified Block Diagram of a Self-Guiding Vehicle's Bearing Angle Control. • Find a K value that the system has minimum rise time and minimum overshoot. Let us call this proportional gain as Kopt Show each step while finding Kopt- Show the necessary graphical solutions. Simulate the system response with 3 different K values. (Kopt and two other K values close to Kopt) Show the system response (actual bearing angle) in a single graph for different K values. • Comment on the results.
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.
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Below is a very common feedback block system. It is a 1dof, and unity-feedback system. The input is the reference command R(s). This is what flows out of thin air, into the system. All other signals in the system (e.g. U, Y, etc.) will depend on R(s). R(s) a. E(s) e. K U(s) G Y(s) Write the algebraic relation between the output Y(s) and the reference R(s) in terms of G and K?. Write it in the format Y = some function of s * R b. What is the TF from R to Y, aka the closed loop TF? What is the "Loop TF" aka the "the open-loop TF"? G has zeros at ZG1, ZG2 etc. and poles at PG1, PG2 etc. C. K has zeros at ZK1, ZK2 etc. and poles at PK1, PK2 etc. What are the zeros and the poles of OLTF? What are the zeros and the poles of CLTF? d. Write the algebraic relation between the error E(s)=R-Y and the reference R(s) in terms of G and K? Write it in the format E = some function of s * R. What is the TF from R to E? Write the algebraic relation between the controller output U(s) and the reference…
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