Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Textbook Question
Chapter 8, Problem 32P
For the unity feedback system shown in Figure 8.3, where
a. Sketch the root locus.
b. Find the value of K that will yield a 10% overshoot.
c. Locate all non-dominant poles. What can you say about the second-order approximation that led to your answer in Part b?
d. Find the range of K that yields a stable system.
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Students have asked these similar questions
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.
Figure Q2 shows the block diagram of a
unity-feedback control system
Proportional
Controller
Plant
R(s)
C(s).
s(3s +1)
5+2s² +4
K
2.1- Determine the characteristic
equation.
2.2- Using the Routh-Hurwitz criterion to
determine the range of gain, K to ensure
stability
and marginally stability in the unity
feedback
syste
m.
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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- 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.arrow_forward5. 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.arrow_forwardQ5 Hydraulic power actuators were used to drive the dinosaurs of the movie Jurassic Park. The motions of the large monsters required high-power actuators requiring 1200 watts. One specific limb motion has dynamics represented by: y = [0 1] Design the state feedback gain matrix using the Ackermann's formula method. Where the new closed loop poles to be placed at s1,2 =-17j3.arrow_forward
- 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-For the value of K found in part (1), use the Routh method to verify whether the closed loop system is stable.arrow_forwardThe 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.arrow_forwardPlease refer to the instruction below. As7 A42 A76 x, Aer A43 A54 A65 A32 X, A45 A s0 A23 A34 A72 Fig. 8-34 Identify the (a) input node, (b) output node, (c) forward paths, (d) feedback paths, (e) self-loop. Determine the (f) loop gains of the feedback loops, (g) path gains of the forward paths.arrow_forward
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- b. Use Routh - Hurwitz stability criterion to determine the system having the following function is stable. s 3+ 3s?+ 7s +k = 0arrow_forwardand 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.arrow_forwardDetermine the 75%, 90%, and 95% response time for the system given by (assume zero initial conditions): ?̈+ 2?̇ + 4? = ?(?)arrow_forward
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