Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 2, Problem 51P
Find the series and parallel analogs for the rotational
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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
2.1) A]: Find the transfer function of the following mechanical system given in Fig. (1).
k2
u2
m2
y2 Y
Fig.(1)
ww
29. Write, but do not solve, the equations of motion for
the translational mechanical system shown in Figure
P2.15. [Section: 2.5]
K = 5 N/m
M3 = 3 kg
fy =2 N-s/m-
fvz = 3 N-s/m
K2 = 4 N/m
o R)
K3 = 4 N/m
M, =4 kg-
M2 = 5 kg
fv, = 2 N-s/m
Frictionless
x1(1)
FIGURE P2.15
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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- 2. (25) For the rotational system shown in the fig- ure, write the equations of motion from which the transfer function, G(s) = 01(8)/T(s), can be found.arrow_forward3. In this problem, you are going to analyze the dynamics of a rotational mechanical system shown in Figure below (this is also covered in Lecture Notes #3 of M. Mert Ankarali [1]). In this system input the external torque t(t), and output is the angular velocity of the load wL(t). JR WR OR K JL OL WL T DL DR The state-space representation of this system is provided in the Lecture Notes #3 [1]. Find the transfer function of the dynamical system. Find another (minimal) state-space representation for the system.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
- 4. The pitch (angular motion) and bounce (up-down linear motion) of a motor vehicle is shown in Figure Q4. Write down the two equations of motion of the vehicle and hence find its frequency equation. (a) (b) Assume that the mass of the vehicle is 1,000 kg, radius of gyration is 0.9 m, spring stiffnesses kr = 18 kN/m and kr = 22 kN/m, distances Iı = 1.0 m and l2 = 1.5 m, determine the two natural frequencies and mode shapes of the system. Bounce Pitch C.G.I Figure Q4arrow_forwardRotational Mechanical System: Find the transfer function for each rotational mechanicalnetwork shown belowarrow_forwardJ 1. Using Lagrangian mechanics, derive the equations of motion of a cart with two tires under the cart shown in Figure P.4.1.arrow_forward
- 30. For each of the rotational mechanical systems shown in Figure P2.16, write, but do not solve, the equations of motion. [Section: 2.6] O(1) 8 N-m-s/rad A I N-m-s/rad O 3 kg-m? 9 N-m/rad 3 N-m/rad (a)arrow_forwardFigure Q3 shows one cart with a mass that is separated from two walls by two springs and a dashpot, where kı, k2 and ka are the first, second spring and dashpot coefficients, respectively. The mass, m could represent an automobile system. An external force is also shown as F(t). Only horizontal motion and forces are considered. F(t) is input and x2(t) is output. (a) Derive all equations related to the system (b) Construct the block diagram from equation in (a) (c) Obtain the transfer function of the systemarrow_forwardFind the transfer function, G(s) = X3(s)/F(s), for the translational mechanical system shown in Figure P2.13. Step-by-step procedure is highly appreciated.arrow_forward
- Q1 A mechanical system with a rotating wheel of mass Mw (uniform mass distribution) is shown in Figure Q1. Springs and dampers are connected to wheel using a flexible cable without skip on wheel. (a) Determine all the mathematical modeling equations of the system for the translational and rotational motion. (b) Using the result in Q1(a), determine the translational motion equation in term of ? as a function of input motion ?. (c) By referring to standard second-order system form, determine the expressions for natural frequency and damping ratio of the system.arrow_forward28. 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 METHODarrow_forward*1(1) fv, K1 K2 M2 oll fv (a) F(s) X,(8) G(s) (b) Figure 1 Given in Figure 1 (a) Two-degree-of freedom translational mechanical system and (b) Block diagram, find the transfer function of G(s) = *:6 F(s)arrow_forward
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