P6. The open loop transfer function of a unity feedbacksystem isK(s+2)G (s) =s(s+3)(s²+2s+10)1- Find the value of K so that the error steady statefor the unit ramp input r(t)=t is less than or equalto 0.01.2-For the value of K found in part (1), use the Routhmethod to verify whether the closed loop system isstable.

Answered: P6. The open loop transfer function of…

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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P6. The open loop transfer function of a unity feedback system is K(s+2) G(s) = s(s+3) (s²+2s+10) 1- Find the value of K so that the error steady state for the unit ramp input r(t)=t is less than or equal to 0.01.
2- Using Matlab, what are the step response curves of the closed-loop system, as shown in fig.1. the feedback represents the second-order dynamic system. (fill in the following table) For=0.4 Wn 1 3 6 9 10 R(S) 0.1 0.3 0.6 0.9 1 For w 5 rad/sec 3 Settling time Peak response 2 Wn s(s+23wn) Settling time Peak response C(s) Discuss the follow Which parameters or w occur on the rise time of the response? Which parameter increases the speed of response? Which parameters can be decreases the response amplitude? Which parameter decreases the steady error state? fig.2
Problem-3. Consider the closed loop transfer function from R(s) to C(s) as given below as given below. 85 H(s) = (s+5)(s? + 2s +17) MATLAB gives the partial fraction values of the Laplace transform C(s) to the unit step input as follows: Num: Denom: -0.5313 -5.0000 -0.2344 + 0.3906i -1.0000 + 4.0000i -0.2344 - 0.3906i -1.0000 - 4.0000i 1.0000 d) Find the overshoot and peak time by using the reduced-order transfer function Hint:Tp = e-(n{//1-§2 %OV = Wn V1- 2)
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Match the transfer function with correct Bode phase plots. G(s) = 5 $+7 G(s)=s+5 G(s) = s+10 S S G(s) = S+ 10 QUESTION 10 90 deg 00 0 deg -90 deg 180 deg B. D 90 deg @ 0 deg -90 deg 180 deg 90 deg @ 0 deg -90 deg 180 deg 90 deg @ 0 deg -90 deg 180 deg
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?
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.
QUESTION 5 An open-loop transfer function for a root locus is given as: 2K (S + 4) S(S + 2) (S + 8) Use the given transfer function to determine the following: 5.1 The open-loop poles and the zeros G(s)H(s) = Do some of the loci break away? Explain. The centre of asymptotes The asymptotic angles 5.5 The stability of the system 5.2 5.3 5.4
The open loop transfer function of a humanoid's arm control system is given as: K G(s) = 2 s(s + 2s + 2) (a) Clearly locate all poles and zeros on a linear graph paper. Provide calculations for the following: asymptote angles, centroid for asymptotes, and departure angle from complex pole. (b) Plot the complete root locus, with the locus on the real axis is clearly shown. Use the scale of 4 cm : 1 unit for both axes and choose the longer side of the graph paper as the real axis.
The Gilles & Retzbach model of a distillation column, the system model includes the dynamics of a boiler, is driven by the inputs of steam flow and the flow rate of the vapour side stream, and the measurements are the temperature changes at two different locations along the column. The state space model is given by: x = 0 00 -30.3 0.00012 -6.02 0 0 0 -3.77 00 0 -2.80 0 0 Is the system?: a. unstable b. C. not unstable x+ 6.15 0 0 0 0 3.04 0 0.052 not asymptotically stable d. asymptotically stable -1 u y = 0 0 0 0 -7.3 0 0 -25.0 X
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.

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