Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 2, Problem 50P
Find the series and parallel analogs for the translational
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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
38. Given the rotational system shown in Figure P2.24,
find the transfer function, G(s) = 06(s)/01(s).
[Section: 2.7]
3. 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.
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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- Find the transfer function, G(s) = Xs(s)/F(s), for the translational mechanical network shown in Figure P2.10arrow_forwardLESSON is Transfer Function: Mechanical System - Rotational Movement SUBJECT: FEEDBACK CONTROL SYSTEM Box the final answerarrow_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
- Page 8/5 Q4: (M4) LE Velocity: V [km/hr] Wavelength: L [m] M k y(t) Model Height: H [m] The figure above shows a model of a person riding a unicycle that contains a spring under its seat. The spring constant is k = 10,600 N/m. Assume that damping is minimal, the wheel of the unicycle has no mass and is not a spring, the unicyle always stays perfectly upright, and the person is represented by a rigid mass M = kg. a) When the unicycle is being ridden at speed V = 10 km/hr over the sinusoidal bumpy terrain shown above, with bump spacing L=0.6 m and bump height H 0.05 m, what will be the steady-state peak-to-peak amplitude of the motion y(t) [m] of the person riding the unicycle? b) Recalculate the steady-state peak-to-peak amplitude of the motion for 2.5, 5, and 20 km/hr. Will the rider have difficulty reaching speeds above 5 km/hr?arrow_forward29. 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 P2.15arrow_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
- a. 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_forwardFind J and D (SI units) to yield 10% overshoot and settling time for 4 seconds for a step input of torque T(t)arrow_forwardFor the mechanical translation system below, find the force-voltage analogy and force-current analogy. Use the following values. K1 = 2 fv, = 1/2 M1 = 1+a %3D K2 = 2 fv2 = 4+b M2 = 5 K3 = 3+c fv3 = 3 a = 0 where a = 3rd digit of your student number %3D b = 5th digit of your student number b =7 C = 7th digit of your student number C = 5 For reference, the 1st digit of your student number is the leftmost number in your student number. Indicate your student number when solving problems.arrow_forward
- Answer all questions below showing revelent calculations and working with explanation where necessary. 1.Create a mathematical model for the system shown. 2.Develop a transfer function for 0(s)/Qi(s), state the constants that you have used in your transfer function. [Hint: You would also need to derive Q(s)/Qi(s) to predict a theoretical value for the increase in rotational speed ] [Note: Omega, Q=Angular speed] 3. With the use of theoretical values, determine the theoretical increase in rotational speed expected for the water wheel when the inflow is increased by a step. This should be repeated for three different step input values. Show calculations and working throughout.arrow_forwardPlease help me solve this questions.arrow_forwardLESSON is Transfer Function: Mechanical System - Rotational Movement SUBJECT: FEEDBACK CONTROL SYSTEM Box the final answerarrow_forward
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