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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38. Given the rotational system shown in Figure P2.24,
find the transfer function, G(s) = 06(s)/01(s).
[Section: 2.7]
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
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 P4.8
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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- Frame {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_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_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_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_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
- For the mechanical translation system below, find the transfer function O1/T and 02/T. Use the following values. K= 2+c D1 = 1 J1 = 3+a J2 = 2+b D2 = 5 where a 2 b= 5 C = oblems. T(t) 0(1) 02(1) D1 K D2arrow_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_forwardFrame {2} is rotated with respect to frame {1} about the x-axis by an angle of 60°. the position of the origin of frame {2} as seen from frame {1} is 'D2=[9.0 7.0 9.0]". Obtain the transformation matric 'T2, which describes frame {2} relative to frame {1}. Also, find the description of point P in frame {1} if ²P = [4.0 6.0 8.0]".arrow_forward
- Find the transfer functions G(S) = 02(s) for rotational system in Figure 1. T(s) 250 N-m/rad N3 = 50 200 kg-m² T(1) 6 kg-m?) N1 = 5 0,(1) 250 N-m/rad - so90 200 kg-m² N2 = 50 Figure 1 1000 N-m-s/rad R1000 N-m-s/radarrow_forward2. (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_forwardFigure 2.2 shows a rotational mechanical system consisting of inertia elements, springs and dampers with an applied torque, T. i. Derive the transfer function of 04(s)/T(s) of the given system. ii. Explain what happen to the system if • The inertia A is reduced to half. • The elasticity of spring A, KĄ is doubled. T(t) 0Ą(t) Og(t) KB Kc KA CA CB JA JB Figure 1.2 Rotational mechanical system with applied torque, T.arrow_forward
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