CONTROL SYSTEMS ENGINEERING
7th Edition
ISBN: 2819770197050
Author: NISE
Publisher: WILEY
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Textbook Question
Chapter 6, Problem 30P
Using the Routh-Hurwitz criterion, find the value of K that will yield oscillations for the unity feedback system of Figure P6.3 with [Section: 6.4]
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Problem No. 1
1A.
100% +
1B.
Consider the translational mechanical system shown
in Figure P4.17. A 1-pound force, f(t), is applied at
t = 0. If fy = 1, find K and M such that the response
is characterized by a 4-second settling time and a
1-second peak time. Also, what is the resulting
percent overshoot? [Section: 4.6]
70)
0000
31/1
10000
K
FIGURE P4.17
Given the translational mechanical system of
Figure P4.17, where K = 1 and f(1) is a unit step.
find the values of M and ƒ, to yield a response with
17% overshoot and a settling time of 10 seconds.
[Section: 4.6]
The Routh-Hurwitz criterion to be used to determine the stability of a system with a characteristic equation given by
85 + 2s4 + 2s3 + 4s² + 11s + 10
Comment on the stability of the system.
Neutral
Stable
Unstable
Q5
Obtain Unit-Step Response of First-Order Systems: C (t).
R(S)
C(s)
Chapter 6 Solutions
CONTROL SYSTEMS ENGINEERING
Ch. 6 - Prob. 1RQCh. 6 - Prob. 2RQCh. 6 - What would happen to a physical system chat...Ch. 6 - Why are marginally stable systems considered...Ch. 6 - Prob. 5RQCh. 6 - Prob. 6RQCh. 6 - Prob. 7RQCh. 6 - Prob. 8RQCh. 6 - Prob. 9RQCh. 6 - Why do we sometimes multiply a row of a Routh...
Ch. 6 - Prob. 11RQCh. 6 - Prob. 12RQCh. 6 - 13. Does the presence of an entire row of zeros...Ch. 6 - Prob. 14RQCh. 6 - Prob. 15RQCh. 6 - Prob. 16RQCh. 6 - Tell how many roots of the following polynomial...Ch. 6 - Tell how many roots of the following polynomial...Ch. 6 - Using the Routh table, tell how many poles of the...Ch. 6 - Prob. 4PCh. 6 - Determine how many closed-loop poles lie in the...Ch. 6 - Determine how many closed-loop poles lie in the...Ch. 6 - MATLAB ML 7. Use MATLAB to find the pole location...Ch. 6 - Symbolic Math SM 8. Use MATLAB and the Symbolic...Ch. 6 - Determine whether the unity feedback system of...Ch. 6 - Use MATLAB to find the pole locations for the...Ch. 6 - Consider the unity feedback system of Figure P6.3...Ch. 6 - In the system of Figure P6.3, let Gs=Ks+1ss2s+3...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Using the Routh-Hurwitz criterion and the unity...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Repeat Problem 15 using MATLAB.Ch. 6 - Prob. 17PCh. 6 - For the system of Figure P6.4, tell how many...Ch. 6 - Using the Routh-Hurwitz criterion, tell how many...Ch. 6 - Determine if the unity feedback system of Figure...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - In the system of Figure P6.3, let Gs=Ksassb Find...Ch. 6 - For the unity feedback system of Figure P63 with...Ch. 6 - Find the range of K for stability for the unity...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - find the range of K for stability. [Section: 6.41]...Ch. 6 - Find the range of gain, K, to ensure stability in...Ch. 6 - Using the Routh-Hurwitz criterion, find the value...Ch. 6 - Use the Routh-Hurwitz criterion to find the range...Ch. 6 - Prob. 32PCh. 6 - Given the unity feedback system of Figure P63 with...Ch. 6 - Repeat Problem 33 for [Section: 6.4]...Ch. 6 - For the system shown in Figure P6.8, find the...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Using the Routh-Hurwitz criterion and the unity...Ch. 6 - Find the range of K to keep the system shown in...Ch. 6 - Prob. 43PCh. 6 - The closed-loop transfer function of a system is...Ch. 6 - Prob. 45PCh. 6 - Prob. 46PCh. 6 - An interval polynomial is of the form...Ch. 6 - A linearized model of a torque-controlled crane...Ch. 6 - The read/write head assembly arm of a computer...Ch. 6 - A system is represented in state space as...Ch. 6 - State Space SS 52. The following system in state...Ch. 6 - Prob. 54PCh. 6 - A model for an airplane’s pitch loop is shown in...Ch. 6 - Prob. 57PCh. 6 - Prob. 58PCh. 6 - Prob. 59PCh. 6 - Prob. 60PCh. 6 - Prob. 61PCh. 6 - Look-ahead information can be used to...Ch. 6 - Prob. 63PCh. 6 - It has been shown (Pounds, 2011) that an unloaded...Ch. 6 - Prob. 65PCh. 6 - The system shown in Figure P6.16 has G1s=1/ss+2s+4...Ch. 6 - Prob. 67PCh. 6 - Prob. 68PCh. 6 - Hybrid vehicle. Figure P6.l8 shows the HEV system...Ch. 6 - Prob. 70P
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- Consider in Figure 1 = 0. Iff, the translational mechanical system shown P4.17. A 1-pound force, f(t), is applied at 1, find K and M such that the response is characterized by a 4-second settling time and a 1-second peak time. Also, what is the resulting percent overshoot? [Section: 4.6] 1+ 270 Karrow_forwards)- Characteristic equation for a 5th order system is given as: s5 + 4s4 + 3s3 + s? + 2s + 10 Using Routh-Hurwiz stability criteria, determine if the system is stable or unstable (show your work)arrow_forwardConsider the following mechanical system: k m +f b d²y(t) +b- dy(t) + ky(t) = f (t) m %3D dt? dt Obtain the state space model of the system with input f (t) and output y(t). Calculate the system matrices for m = 1, k = 1 and b = 2. Check the stability by using the second method of Lyapunov. 3.arrow_forward
- The response to a unit step input (applied at time t = 0 s) of a system is shown in Figure Q2, determine the transfer function of this system from the step response graph. Amplitude 2.6 2.4 2.2 28 1.8 1.6 64 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 Step Response 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Time (sec) Figure Q2 Step response 1.2arrow_forwardA system has the following characteristic equation: s+ s+ 3s+ 2s + 2 = 0 Using the Routh-Hurwitz method, checka. How many roots are to the right of the imaginary axis?b. Is the system stable?.arrow_forwardP6. 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.arrow_forward
- 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.2arrow_forward(b) The response to a unit step input (applied at time t = 0 s) of a system is shown in Figure Q2, determine the transfer function of this system from the step response graph. Amplitude 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 Amplitude 5 Step input of 3 units was applied to a system and the response of this system is shown in Figure Q2.2. Determine the transfer function of this system. 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 o Step Response 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Time (sec) Figure Q2 Step response Step Response 2 Time (seconds) 3arrow_forwardA proposed hypersonic plane would climb to 100,000 feet, fly 3800 miles per hour, and crossthe Pacific in 2 hours. Control of the aircraft speed could be represented by the model in Figure.Find the sensitivity of the closed-loop transfer function T(s) to a small change in the parameterarrow_forward
- Look at the block diagram for the dynamic model of the hydraulically actuated system in Fig where: km = 0.2 J = 0.1 m = 5 k₂ = 3 L₂ = 2 KAP = 4 *BÖH Lu da K₁ W *ÖDDÖDDÖD D Km/J X4 QmJ/Km K₁pJ 1. Determine the controllability and observability for this system d₂ X3 X₂ Aarrow_forwardThe transfer function of a system is shown below. G (s) = S-a (8+b)(8-c) Where: a = 6, b = 5 and c = 9 %3D When you solve the step response in which R(s) = 1/s, you will get the form of c(t) as shown below: c (t) = X+Y e-bt + Z ect %3D X, Y and Z are constant values which you will obtain when you solve the response c(t). For the blank below, enter the sum of Y and Z (if negative, place a "-" sign before the value). Use FOUR decimal places. Y+Z = %3Darrow_forward6. Consider the mechanical system shown in Fig. 8. Let V(t) be the input and the acceleration of the mass be the output. Derive the state equations and the output equation using linear graphs and normal trees. B m V₁(t) Figure 8: A mechanical system with an across-variable sourcearrow_forward
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