Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Textbook Question
Chapter 10, Problem 15P
For each closed-loop system with the following performance characteristics, find the closed-loop bandwidth: [Section: 10.8]
a.
b.
c.
d.
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For the following open loop transfer functions, identify the correct Bode plot from the Bode plots given below:
Bode Plots:
Magnitude (dB)
Phase (deg)
O
50
-100
-50
-150
-90
0
-135
-180
Magnitude (dB)
a 225
Phase (deg)
-270
-20
10:2
-40
-60
-80
-100
0
-90
-180
G(s) =
-270
Transfer function:
a. 1
10-1
101
O b. 2
O c. 3
O d. 4
S
Bode Diagram
10°
Frequency (rad/s)
Bode Diagram
(₁² +s+2)(x² +58 +
Frequency (rad/s)
s+16)
101
10¹
10²
%
2)
Magnitude (dB)
Phase (deg)
Magnitude (dB)
Phase (deg)
50
-50
-100
-45
-90
-135
-180
10/2
-60
-80
-100
-120
90
0
-90
-180
-270
10:2
10¹
10"
Bode Diagram
10°
Frequency (rad/s)
Bode Diagram
10°
Frequency (rad/s)
10¹
101
10²
102
For the following open loop transfer functions, identify the correct Bode plot from the Bode plots given below:
Bode Plots:
1)
3)
Magnitude (dB)
(Bap) eseyd
50
0
-100
-50
-150
-90
-135
-180
Magnitude (dB)
-225
Phase (deg)
-270
1012
-20
-40
-60
-80
-100
0
-90
-180
-270
G(s) =
10-1
Transfer function:
10
O a. 1
O b. 2
O c. 3
O d. 4
16
Bode Diagram
TOP
Frequency (rad/s)
Bode Diagram
(s+4)(s² +1.65+4)
101
Frequency (rad/s)
10
Њ
10²
10²
N
+
Magnitude (dB)
Phase (deg)
Magnitude (dB)
Phase (deg)
50
-50
-100
-45
-90
-135
-180
10:12
-20
-40
-60
-80
-100
-120
90
0
-90
-180
-270
1012
10
10
Bode Diagram
10²
Frequency (rad/s)
Bode Diagram
10²
Frequency (rad/s)
10
10¹
10²
10²
You are tasked to enhance the performance of an analog plant using a digital controller PID. The
controller is in connected in series with the plant in a closed-loop configuration. The pulse transfer
K(z+a)
function is given as GzohGp(s) =-
Use sampling time Ts=0.6 second, K=8, a=0.78, b=-0.602
(0+z)(q+z)
and c=-0.705. Do the following:
i. Obtain the design point in z-coordinates to achieve the requirement of having a system settling
time of 3 second, and damping ratio of zeta (z=0.705).
Chapter 10 Solutions
Control Systems Engineering
Ch. 10 - Prob. 1RQCh. 10 - Prob. 2RQCh. 10 - Prob. 3RQCh. 10 - Briefly describe how to obtain the frequency...Ch. 10 - Prob. 5RQCh. 10 - Each pole of a system contributes how much of a...Ch. 10 - Prob. 7RQCh. 10 - Prob. 8RQCh. 10 - Prob. 9RQCh. 10 - What is the major difference between Bode...
Ch. 10 - Prob. 11RQCh. 10 - Prob. 12RQCh. 10 - Prob. 13RQCh. 10 - 14. What is a Nyquist diaoram?
Ch. 10 - Prob. 15RQCh. 10 - 16. When sketching a Nyquist diagram, what must be...Ch. 10 - Prob. 17RQCh. 10 - Prob. 18RQCh. 10 - Prob. 19RQCh. 10 - Prob. 20RQCh. 10 - Prob. 21RQCh. 10 - Prob. 22RQCh. 10 - Prob. 23RQCh. 10 - Prob. 24RQCh. 10 - Prob. 25RQCh. 10 - Prob. 26RQCh. 10 - Prob. 1PCh. 10 - Prob. 7PCh. 10 - Prob. 14PCh. 10 - For each closed-loop system with the following...Ch. 10 - Prob. 27PCh. 10 - For the Bode plots shown in Figure P10.10,...
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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 degarrow_forwardFor the pole plot given below, which pole will have the fastest decrease in exponential transient response? jw O Save X X X X k z y x karrow_forwardH.w 2: The open loop response, that is, the speed of the motor to a voltage input of 20V, assuming a system without damping is dw 20 = (0.02) + (0.06)w. dt If the initial speed is zero (w(0) = 0) ,and using the Runge-Kutta 4th order method, what is the speed at t = 0.8s? Assume a step size of h = 0.4s.arrow_forward
- Find the 75%, 90% and 95% response time for the following system given: 0.8Ť + T = U(t)arrow_forwardProblem-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_forwardP10. Consider a system represented by the block diagram in Fig.10. 10 Y(s) R(s) s+ 5 fig.10 The closed-loop transfer function is: 50 a. T(s) = s2 + 55s + 50 10 b. T(s) = s2 + 55s + 10 10 c. T(s)- s2 +50s + 55 d. None of the abovearrow_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_forwardK s + 0.1 $+0.5 10 s(s+1) Fig. Q7 Fig. Q7 shows a control system. Draw a Bode diagram of the open loop transfer function and determine the value of the gain K such that the phase margin is 50º. What is the gain margin of this system with this gain K.arrow_forwardFigure 1 shows an electrical system comprising a series RLC circuit and input voltagesource ein(t).(a) Derive the input-output equation with output y = I and input u = ein(t). (b) Using the derived input-output equation, drive the system transfer function G(s)that relates output to input. Use the following numerical values for the electrical systemparameters: resistance R = 2Ω, inductance L = 0.25H, and capacitance C = 0.4F. (c) Using the derived transfer function, derive the time-domain ordinary differentialequation for the input-output equation of this electrical system. (d) Draw the complete block diagram of this series RLC circuit using the derived transferfunction.arrow_forward
- what is the closed loop transfer function K Кр 1+ Tsarrow_forward2- 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_forwardGraph/Plot the output step response from t=0 to t=10 with a 0.1-second interval.arrow_forward
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