CONTROL SYSTEMS ENGINEERING
7th Edition
ISBN: 2819770197050
Author: NISE
Publisher: WILEY
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Textbook Question
Chapter 6, Problem 29P
Find the range of gain, K, to ensure stability in the unity feedback system of Figure P6.3 with [Section: 6.4]
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1 / 1
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]
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.
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?
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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- 3- Nise (4.4) A unity feedback control system has the following open-loop transfer function: G(s) = 45+¹ Find expressions for 4s+1 45² its time response when is subjected to unit impulse input.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_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
- A Block diagram of a feedback control system is shown in Figure Q3. Using the Block Diagram Reduction Method, solve for the output Y(s) when:(i) Input D(s) = 0,(ii) Input R(s) = 0,(iii) Input R(s) and D(s) are both applied (i.e., R(s) ≠ 0 , D(s) ≠ 0).arrow_forwardHomework: 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_forwardWe consider a dynamical system represented by the block diagram: Simple negative feedback: U(s) E(s) input, + with T₁(s) = T₂(s) = 3 + T,(s) 1 S T₂(s) a s²(1+s) X(S) output measurement with a 4 and Calculate the open-loop transfer function at s=6.arrow_forward
- Find the equivalent closed loop transfer function for the system R(s) E(s) Y(s) 3 K s+2 10 s+10 (Ctrl)arrow_forwardWe consider a dynamical system represented by the block diagram: Simple negative feedback: U(s) E(s) input, + with T₁(s) T₂(s) = 2 = a 1+5² T,(s) T₂(s) X(S) output measurement with a 4 and Calculate the closed-loop transfer function at s=10.arrow_forwardConsider 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_forward
- 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.arrow_forward26. For the system shown in Figure P4.8, a step torque is applied at 01 (t). Find a. The transfer function, G(s) = 02(s)/T(s). b. The percent overshoot, settling time, and peak time for 02(t). [Section: 4.6] T(t) 01(1) 02(1) ff 1.07 kg-m2 1.53 N-m-s/rad 1.92 N-m/rad FIGURE P4.8arrow_forward• The unity feedback control structure has the following block diagram: w C(s) P(s)arrow_forward
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