Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Textbook Question
Chapter 2, Problem 44P
Given the combined translational and rotational system shown in Figure P2.29, find the transfer function. G(s) = X(s)/T(s). [Sections: 2.5; 2.6]
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32. For the rotational mechanical system with gears
shown in Figure P2.18, find the transfer function,
G(s) = 03(s)/T(s). The gears have inertia and bear-
ing friction as shown. [Section: 2.7]
T(t)
to
|N1
小D
N2
N3
2, D2
Jz, D3 03(1)
N4
J4. D4
J5. D5
FIGURE P2.18
sair
28. Find the transfer function, G(s) = X1(s)/F(s), for the
translational mechanical system shown in Figure P2.13.
[Section: 2.5]
2 N-s/m
X3(1)
2 N-s/m
(1)'x-
[4 kg
2 N-s/m
6 N/m
6 N/m
4 kg
0000 4 kg
"Frictionless
FIGURE P2.13
USE MATRIX METHOD
Consider the mechanical system shown below. The system is at rest for t < 0. The input force u is given at
t = 0. The displacement x is the output of the system and is measured from the equilibrium position.
Obtain the transfer function. You have to give the details of your work.
a) Set up the governing equations for the system.
b) Obtain the transfer function (s)/u(s)
c) Use Force-Voltage analogy to get the electrical equivalent system equations.
k3
m
"1
Chapter 2 Solutions
Control Systems Engineering
Ch. 2 - Prob. 1RQCh. 2 - Prob. 2RQCh. 2 - Prob. 3RQCh. 2 - Define the transfer function.Ch. 2 - Prob. 5RQCh. 2 - What do we call the mechanical equations written...Ch. 2 - If we understand the form the mechanical equations...Ch. 2 - Why do transfer functions for mechanical networks...Ch. 2 - What function do gears perform?Ch. 2 - What are the component parts of the mechanical...
Ch. 2 - The motor’s transfer function relates armature...Ch. 2 - Summarize the steps taken to linearize a nonlinear...Ch. 2 - Prob. 1PCh. 2 - Prob. 2PCh. 2 - Prob. 3PCh. 2 - Prob. 4PCh. 2 - Prob. 5PCh. 2 - Prob. 6PCh. 2 - Prob. 7PCh. 2 - A system is described by the following...Ch. 2 - For each of the following transfer functions,...Ch. 2 - Write the differential equation for the system...Ch. 2 - Write the differential equation that is...Ch. 2 - Prob. 12PCh. 2 - Use MATLAB to generate the MATLAB ML transfer...Ch. 2 - Repeat Problem 13 for the MATLAB following...Ch. 2 - Use MATLAB to generate the partial fraction...Ch. 2 - Use MATLAB and the Symbolic Math Symbolic Math...Ch. 2 - Prob. 17PCh. 2 - Prob. 18PCh. 2 - Prob. 19PCh. 2 - Repeat Problem 19 using nodal equations. [Section:...Ch. 2 - Prob. 22PCh. 2 - Prob. 23PCh. 2 - Prob. 24PCh. 2 - Prob. 25PCh. 2 - Prob. 26PCh. 2 - Prob. 27PCh. 2 - Prob. 28PCh. 2 - Prob. 29PCh. 2 - Write, but do not solve, the equations of motion...Ch. 2 - For the unexcited (no external force applied)...Ch. 2 - For each of the rotational mechanical systems...Ch. 2 - For the rotational mechanical system shown in...Ch. 2 - Find the transfer function, 1sTs , for the system...Ch. 2 - For the rotational mechanical system with gears...Ch. 2 - For the rotational system shown in Figure P2.21,...Ch. 2 - Prob. 37PCh. 2 - Find the transfer function, Gs=4s/Ts , for the...Ch. 2 - For the rotational system shown in Figure P2.24,...Ch. 2 - Prob. 40PCh. 2 - Given the rotational system shown in Figure P226,...Ch. 2 - In the system shown in Figure P2.27, the inertia,...Ch. 2 - Prob. 43PCh. 2 - Given the combined translational and rotational...Ch. 2 - Prob. 45PCh. 2 - The motor whose torque-speed characteristics are...Ch. 2 - A dc motor develops 55 N-m of torque at a speed of...Ch. 2 - 48. In this chapter, we derived the transfer...Ch. 2 - Prob. 49PCh. 2 - Find the series and parallel analogs for the...Ch. 2 - Find the series and parallel analogs for the...Ch. 2 - A system’s output, c, is related to the system’s...Ch. 2 - Prob. 53PCh. 2 - Consider the differential equation...Ch. 2 - 55. Many systems are piecewise linear. That is,...Ch. 2 - For the translational mechanical system with a...Ch. 2 - 57. Enzymes are large proteins that biological...Ch. 2 - Prob. 58PCh. 2 - Figure P2.36 shows a crane hoisting a load....Ch. 2 - 60. In 1978, Malthus developed a model for human...Ch. 2 - 61. In order to design an underwater vehicle that...Ch. 2 - 62. The Gompertz growth model is commonly used to...Ch. 2 - A muscle hanging from a beam is shown in Figure...Ch. 2 - A three-phase ac/dc converter supplies dc to a...Ch. 2 - Prob. 65P
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- 24. Find the transfer function, G(s) = X2(s)/F(s), for the translational mechanical system shown in Figure P2.11. (Hint: Place a zero mass at x2(t).) %3D ft) – 5 kg 10 N/m N-s/marrow_forwardQ5: Given the rotational system shown in below, find the transfer function G(s)= 01(s)/T(s) D K2 Please help ASAP. Pls show all steps and calculations. Make sure to find theta1(s)/T(s)arrow_forward02(s). T(s) Find the transfer function G(s) Tt) 1 N-m/rad 1 N-m/rad I kg-m? 1 N-m-s/rad 1 N-m-s/rad Figure: Rotational mechanical system.arrow_forward
- 26. 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_forwarda. For the translational mechanical system shown in Figure (3). 1. Write the mathematical model in a format of matrices. 2. Find the transfer function G(s) = a₁ (s)/T (s) where a is the acceleration. t 45²² +16,5 245+628²-2-05+96 M₁ = 8 kg 6 N-s/m f(t) 1 N/m 0000 4 N-s/m -x₂(1) M₂-3kg Frictionless 0000 15 N/m Frictionless Figure (3) Translational mechanical systemarrow_forwardTransfer function on translational mechanical systemarrow_forward
- For the following block diagram, determine the transfer function from the input F(s) to the output X (s). F(s) X(s) 4arrow_forwardb) Obtain the transfer function of the system. X(s)/Y(s) =? Show all intermediate operations in detail.arrow_forward25. For the system shown in Figure P4.7, do the follow- ing: [Section: 4.6] a. Find the transfer function G(s) = X(s)/F(s). b. Find $, om, %OS, T;, Тр, and T,. 28 N/m x(t) 3 kg f(t) 5 N-s/m FIGURE P4.7arrow_forward
- 3) For the mechanical system shown in Fig. 1, write the force equations at each coordinate and then determine the following transfer functions: X(s) a) ; b) U(s) Y(s) U(s) Y(s) ; c) X(s) quarter mass of the car m₂ the suspension unsprung mass. m₁ tire stiffness ground motionarrow_forward01(1) 18 N-m-s/rad T(t) 02(1) 1 N-m-s/rad kg-m? 3 kg-m2 3 N-m/rad 9 N-m/rad (a) Figure P2.16a OJohn Wiley & Sons, Inc. All rights reserved. The transfer function where the output Theta, is s? +5s +1 0,(s) а. Н(s)3D T(s) s' +30s +80s² +s+15 4 s' +5s +1 0,(s) b. H(s)= T(s) 25s* + 30s' +80s? + s +15 4 5s? +9s+9 0,(s) c. H(s)= T(s) 15s* +30s +95s² + s +27 5s +9s +9 0,(s) T(s) 15s +32s' +95s² +99s+27 d. H(s)= 4 Select one: O a.c O b. a O .b O d.d 立arrow_forwardEXAMPLE -- Consider the following transfer function: B(s) 2 + 5 + 3s + 6 + 65+ 11s +6 A(s)arrow_forward
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