Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 10, Problem 4RQ
Briefly describe how to obtain the frequency response analytically.
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needs complete detailing. take N=70 b=20
a) The figure shows an oscillatory system where the
mass 'M' is required to remain stationary even if
an oscillatory force "Fo cos ot" acts on this mass
'M’. This mass 'M’ is a part of a simple harmonic
system of stiffness 'k' and also connected to
mass 'm' by a spring of stiffness 's'. If all oscillations are along the x-axis, find the
value of frequency 'o' with which the small mass 'm' should oscillate to keep the mass
'M' stationary?
Consider the following numerical values for calculations:
M=100 kg,
Fo cos ot
m
k=5 N/m,
m='B’ kg,
s='N' N/m
Solve the inverse kinematic problem for the following 6 DOF robot, using the method ofkinematic decouplingif it is known that its Denavit-Hartenberg parameters are as shown in the table inthe table
Q1: (Section A) Considering single degree undamped vibration system and
Newton's equation as follow: më +kx=0; find the solution of the displacement
equation [(t)=Cietwnt+C2e-lwn] for the case with:
Wn = 2 rad/s, x (0) = 1 mm, and x(0) = v5 mm/s.
(Section B) Given the matrix equation of motion of a two degree-of-freedom system
3m
2k
- k
= 0
X2
+
as:
-k 4k
m
Determine (a) the natural frequencies, (b) the modes shapes.
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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- A satellite single-axis amplitude control system can be represented by the block diagram is as shown in Figure 2.11. The variable k, a and b are controller parameters, andj is the spacecraft moment of inertia. Suppose the moment of inertia is J=7.8E+08 (slug-ft), and the controller parameters are k=10.8E+08, a=1.5 and b=8. Spacecraft Rotational R(s) Controller motion C(s) k(s + a) (s + b) js? Figure 2.11 A negative feedback control system a) Develop an m-file script to compute the closed loop transfer function. b) Compute and plot the step response to a 10° step input. c) The exact moment of inertia is generally unknown and any change slowly with time. Compare the step response performance of the spacecraft when J is reduced by 25% and 60%.arrow_forwardGraph/Plot the output step response from t=0 to t=10 with a 0.1-second interval.arrow_forwardThis course EHide blc Clear my choice For the shown system, Use the Routh criterion to determine the range of stability relative to the gain K. Note that K is always positive K>0. Type a, b, c, d, e or f R(s) C(s) K(s² + s) (s² –2s+ 2)(s + 2) a) K > 2 b) K > 1.236 c) 1 3.236 e) – 2 < K < 2 f) not stable for any K Answer: What's the maximum percent overshoot %OS for this system with its closed-loop poles as shown? jo j8 j6arrow_forward
- H-W Find Time response for 2S+3 Yes)= s° (s+3)arrow_forwardQ5. For a point at distance 50 m and angle 450 to the axis which of the following statements are correct? Consider an infinite baffled piston of radius 5 cm driven at 2 kHz in air with velocity 10 m/s. You may choose multiple options. a. The constant term is given by 515.03 b. The distance dependent term is given by e-jk50/50 c. The directivity term is given by j1(Ka sin 450)/sin 450 d. There is no time dependent term.arrow_forwardDerive the differential equation and find the natural frequency. (Mech. Vibration)arrow_forward
- 5. Sketch the following function in frequency domain plot: i. Y(t) = 3 sin (4лt) + 4 cos (4 лt) ii. Y(t) = 12 sin (10nt) + 5 sin (20лt) + sin (100лt)arrow_forwardConsider two robot-manipulators:• A SCARA robot with joints displacement range q1,2 = −90◦...90◦ and q3 = 0..10cm and links lengths L1,2=10 cm.• A Cartesian robot with joint displacements’ range q1,2,3 = 0..10 cm.Which statement is correct?1) The Cartesian robot has a larger workspace.2) It is not possible to judge the workspace based on the information provided.3) Both robots have revolute joints.4) The SCARA robot has a larger workspace.arrow_forwardIf characteristic equation is minimum value for k to be in order to let the system stable OK>-6 Ok>0 OK>-3 s³ + s² (K+6) + s(6K +9)+9K = 0 -3>K>-6 ,what is the 5arrow_forward
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