CONTROL SYSTEMS ENGINEERING
7th Edition
ISBN: 2819770197050
Author: NISE
Publisher: WILEY
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Textbook Question
Chapter 8, Problem 6P
For the open-loop pole-zero plot shown in Figure P8.4, sketch the root locus and find the break-in point. [Section: 8.5]
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Part A: Find the steady-state solution of the mechanical system shown below:
k
mu
E
m
G(s)
F(t)
F(t) = F sin wt
Part B: Sketch the root locus for the transfer function:
Ks
(s+ 4) (s + 3)(s + 1)
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.
R(S)
s+5
Find Closed Loop Transfer function
XIS
K
s+2
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Y(s)
Chapter 8 Solutions
CONTROL SYSTEMS ENGINEERING
Ch. 8 - Prob. 1RQCh. 8 - Prob. 2RQCh. 8 - Prob. 3RQCh. 8 - Prob. 4RQCh. 8 - Prob. 5RQCh. 8 - What are two ways to find where the root locus...Ch. 8 - Prob. 7RQCh. 8 - Prob. 8RQCh. 8 - Prob. 9RQCh. 8 - How would you determine whether or not a root...
Ch. 8 - Prob. 11RQCh. 8 - Prob. 12RQCh. 8 - Prob. 13RQCh. 8 - Prob. 1PCh. 8 - Sketch the general shape of the root locus for...Ch. 8 - Prob. 3PCh. 8 - Let Gs=Ks+23s2s+6 in Figure P8.3. [Section: 8.5]...Ch. 8 - Let Gs=Ks+12s2+2s+2 with K0 in Figure P8.3....Ch. 8 - For the open-loop pole-zero plot shown in Figure...Ch. 8 - Prob. 7PCh. 8 - Prob. 8PCh. 8 - Figure P8.5 shows open-loop poles and zeros. There...Ch. 8 - Prob. 10PCh. 8 - Prob. 11PCh. 8 - Prob. 12PCh. 8 - Prob. 13PCh. 8 - Sketch the root locus and find the range of K for...Ch. 8 - For the unity feedback system of Figure P8.3,...Ch. 8 - Prob. 16PCh. 8 - Prob. 17PCh. 8 - Given the root locus shown in Figure P8.7,...Ch. 8 - Prob. 19PCh. 8 - For the unity feedback system of Figure P8.3,...Ch. 8 - Prob. 21PCh. 8 - Prob. 22PCh. 8 - Prob. 23PCh. 8 - Prob. 24PCh. 8 - Prob. 25PCh. 8 - Prob. 26PCh. 8 - Prob. 28PCh. 8 - Prob. 29PCh. 8 - Prob. 30PCh. 8 - Prob. 31PCh. 8 - For the unity feedback system shown in Figure 8.3,...Ch. 8 - Prob. 34PCh. 8 - Prob. 35PCh. 8 - Prob. 37PCh. 8 - Prob. 38PCh. 8 - Prob. 39PCh. 8 - Prob. 41PCh. 8 - Prob. 42PCh. 8 - Prob. 45PCh. 8 - Repeat Problem 3 but sketch your root loci for...Ch. 8 - Prob. 47PCh. 8 - Prob. 49PCh. 8 - Prob. 50PCh. 8 - Prob. 51PCh. 8 - Prob. 52PCh. 8 - Prob. 53PCh. 8 - Prob. 55PCh. 8 - Prob. 57PCh. 8 - Prob. 58PCh. 8 - Prob. 59PCh. 8 - Wind turbines, such as the one shown in Figure...Ch. 8 - Prob. 62PCh. 8 - Prob. 67PCh. 8 - Prob. 68PCh. 8 - Prob. 70PCh. 8 - Prob. 72P
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- For the given close-loop system transfer function, determine its stability using Routh-Hurwitz Test for Stability.1. What is the stability of the system? (Stable, Unstable, Marginally Stable)arrow_forwardProblem 3. Find the transfer function C(s)/R(s) for the following block diagram using block diagram reduction: R(S) Gso G200 G G3()arrow_forwardQUESTION 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 5.4arrow_forward
- Given a state space model [1 1 + 0 u -1 -2 y = [1 1 0] with input u and output y. a). Derive the transfer function representation. b). Derive the differential equations representation. c). Compute the response y(t) with step control input u(t) = 1(t) and zero initial condition. d). and initial condition r(0) = [11 0]". Compute the state response r(t) with control input u(t) = 1(t)arrow_forwardHomework: Given the following transfer functions, Draw the complete Root Locus for these systēms at {K=0, 0.5, 1, 2, 3}, then find break-in points and K value? K(s +1) s' +3s + 3.25 G(s) =- K G(s) = s(s +2)arrow_forwardöialg äbäi the open - loop transfer function of the system given as in figure below, what is error steady state * for an input r(t)=1+4t+3t^2 10 (s+1) G(s) s²(5s+6) 3.6 O 5.6 O 7.6 O 10.6 Oarrow_forward
- (1) Consider the system represented by the block diagram. The closed loop transfer function T(s)-Y(s)/R(s) is (a) T(s)-50/(s+55 s+50). (b) T(s)=10/(s+50 s+55) (c) T(s)=10/(s+55 s+10). (d) None of the above. R(s)- 10 + s+5 5 Y(s)arrow_forwardroot 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.arrow_forwardFor 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?arrow_forward
- 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)arrow_forwardParameters of the following transfer function is given as: k=6, a=3.1, b=3.4, and c=2.8, determine the settling time Ts of the system response to a unit step input. (please keep four digits after decimal point) TF= k as²+bs+carrow_forwardSimplify the block diagram shown below. Then, obtain the closed-loop transfer function C(s)/R(s). H3 R(s)- G1 G2 G3 G4 > C(s) H +arrow_forward
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