Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 2, Problem 10RQ
What are the component parts of the
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A dc motor develops 5 N-m of torque at a speed of 75 rad/s when 10 volts are applied. It stalls out at
this voltage with 10 N-m of torque. Find the transfer function, G(s) = 02(s)/E.(s).
N = 10
ealt) Motor
J =1 kg-m2
W= 10
N, = 20
J = 2 kg-m?
J, = 2 kg-m-
N= 20
D
Find the transfer function 8,(s) / T(s) of the given mechanical network below. Show your complete solution on a
clean sheet of paper. I should see the following
• List of torques exerted in tabular form (
• Clearly stated equations (
• Solution on how to find the transfer function from these equations
IN-m/rad
T)
02(1)
for
f I kg-m2
IN-m-s/rad
I N-m-s/rad
I N-m-s/rad
1. Consider the simplified model we discussed in class about a car on a bumpy road; see Fig. 1.
The car has a mass m supported by stiffness k and damping c. The road gives a displacement
excitation R(t) to the car. The transfer function from R(t) to the car displacement y(t) is
Hy(s) =
=
Y(s)
R(s)
=
cs+k
ms² + cs+k
(1)
Let the acceleration of the car be a(t) = ÿ(t). Determine the frequency response function
Ga(w) from R(t) to a(t). Plot |Ga(w) as a function w. Hint: Analyze |Ga(w)| for w > wn.
m
y(t)
Suspension
k₁
y(t)
Head
m
k
Air
Bearing
x(t)
k2
R(t)
Disk Surface
Figure 1: A simple model of
a car on a bumpy
road
Figure 2: Suspension in computer
hard disk drives
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Rotational Mechanical System: Find the transfer function for each rotational mechanicalnetwork shown below.arrow_forward1. Consider the simplified model we discussed in class about a car on a bumpy road. The car has a mass m supported by stiffness k and damping c. The road gives a displacement excitation R(t) to the car. The transfer function from R(t) to the car displacement y(t) is Hy(s) - Y(s) R(s) cs + k ms² + cs+k (1) (a) Determine the driving point impedance ZR(s), which is the ratio of the velocity R(t) to the force acting on the wheel from the road. (b) Engineer X is testing the car in the Vehicle Dynamics Lab of a start-up company GF.com. Because of insufficient cash flow, Engineer X only has the equipment to mea- sure ZR(s), and identify the zeros and poles of ZR(s). But eigineer X wants to find the poles of Hy(s). To do so, should Engineer X use the zeros or poles of ZR(s) instead? Explain why? m y(t) R(t) Figure 1: A simple model of a car on a bumpy roadarrow_forwardFind the transfer function of the following mechanical system given in Fig. (1). k1 In 1 k2 bi u2 m2 Fig.(1) wwarrow_forward
- The following figure shows a machine of mass m mounted on a vibration isolator. The machine (starting at rest at t=0) is subjected to a sinusoidal excitation force p(t) = P sin wt. Solve for the transfer function X(s)/P(s). Then state in words the process you would then follow to determine the force transmissibility, TR. p(t) = P sin wi m b₂arrow_forwardI need the answer as soon as possiblearrow_forwardPlease Help with this question. Show clear steps and highlight the answers.arrow_forward
- How can the Bode plot be used to analyze and design control systems in mechanical engineering applications?arrow_forwardFor the mechanical network in figure 2,(a) Draw block diagram. (b) Draw free-body diagram of mass, spring, and damper system. (c) Draw transformed free-body diagram.arrow_forward1. A force F is applied to the mass m₂ in Figure 1, where k₁ and k₂ are the spring constants, b₁ is the damping constant and b₂ is the friction coefficient, x₁ and x₂ are the displacement. Find the transfer function X₁/F. K₁ wwww no chat GPT, HAND WRITTEN PLEASE m1 X1 b₁ + K₂ No friction Figure 1 M₂ X2 Friction b₂ LL Farrow_forward
- mechanics of materials b) ?arrow_forward4 N-s/m 5 N/m 5 kg Is the spring involved in the transfer function between the force and the position, x1?arrow_forwardSolve the transfer function of the Mechanical system as shown below. Find X₁(s)/U(s) and X₂ (s)/U(s). Where x is displacement, m is mass, k is spring constant and u is force. k₁ 21 m1 -X1 k₂ ww + b m2 x2 www k3arrow_forward
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