Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Textbook Question
Chapter 2, Problem 41P
Given the rotational system shown in Figure P226, find the transfer function,
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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 system
The universal transfer function is found in Figure 1 and Figure 2
Find J and D (SI units) to yield 10% overshoot and settling time for 4 seconds for a step input of torque T(t)
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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- 3. For the rotational system shown below, find the transfer function, L(s) G(s): T(s) IN-m-s/rad IN-m/rad Ng = 100H Ikg-m? 00 N= 50 N- 10 N- 10 0.04 N-m-s/radarrow_forward32. 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 sairarrow_forwardFrame {2} is rotated with respect to frame {1} about x-axis by an angle of 60 degree. The position of the origin of frame {2} with respect to frame {1} is [6.0 5.0 7.0]T . Find the homogeneous transformation matrices of frame {1} with respect to frame {2}.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_forwardHand written please.arrow_forwardPlease answer it carefully. With all the steps and highlight the answers. Thanks!arrow_forward
- Please Help with this question. Show clear steps and highlight the answers.arrow_forwardPls help ASAP. Pls show all steps and calculations.arrow_forward1. Write the mathematical equations for the mechanical rotational system given. Also find the transfer function (s)/T(s) of the given system. # (Torque applied) J₂ voooooo J₂arrow_forward
- For the transfer function below, Find the time constant. 361 G(s) = s2 + 16s + 361arrow_forwardObjective: Given: Solution: Summary:arrow_forward02(s) Find the transfer functions G(S) = for rotational system in Figure 1. T(s) 250 N-m/rad N = 50 200 kg-m? T(1) fo.6 kg-m} N = 5 0,(1) 250 N-m/rad N2 = 50 200 kg-m² 1000 N-m-s/rad 1000 N-m-s/radarrow_forward
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