Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 2, Problem 56P
For the translational
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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]
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
28. 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 METHOD
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. For the system below, find the transfer function fromfi to x (driving point receptance) and from f. to ä, (driving point accelerance). What is the acceleration response of mass m, if m; = 2 kg, m; = 4 kg, k, = 40 N/m, k =100 N/m, and k; = 200 N/m, fi(t) = 20 cos(3t) N and f:(r) = 0? WW m, WW m Warrow_forward3. You are working at a medical device company, and are helping to design a new needle system that pricks the skin of a patient so that a drop of blood becomes available for a glucose test. The needle tip position a can be modeled as a system with the transfer function: Position x, mm Here, f(t) is an input force. It is constrained to be a step function with amplitude 1 (e.g. f(t) = u(t). Given all the current design parameters, the response that the team is getting is shown below: 1.4 1.2 1 0.8 0.6 0.4 0.2 0 H(s) = X(s)/F(s) = 0 Kw2/20 s² + 25wns + w²/12 0.02 0.04 Step Response 0.06 0.08 Time (seconds) 0.1 0.12 0.14 Unfortunately, the problem is that the needle needs to reach a maximum position of 1.5 mm, but then after the over- shoot, retract to a position of 0.5 mm. The peak time should be exactly 0.2 seconds. Given that you can control the damping ratio , the natural frequency wn, and the gain K, write in a few sentences a proposed strategy for modifying the design to meet the…arrow_forwardConsider the mechanical system shown below. The system is at rest for t < 0. The input force u is given at t = 0. The displacement x is the output of the system and is measured from the equilibrium position. Obtain the transfer function. You have to give the details of your work. a) Set up the governing equations for the system. b) Obtain the transfer function (s)/u(s) c) Use Force-Voltage analogy to get the electrical equivalent system equations. k3 m "1arrow_forward
- on of nd 25. For the system shown in Figure P4.7, do the following: [Section: 4.6] a. Find the transfer function G(s) = X(s)/F(s). b. Find , n, %OS, Ts, Tp, Tr, and Cfinal for a unit-step input. 20 N/m oooo 2 N-s/m 5 kg x(1) FIGURE P4.7 f(1)arrow_forwarda) Suspension system of a car. Finding the transfer function F₁(s) = Y(s)/R(t) and F₂ (s) = Q(s)/R(t), consider the initial conditions equal to zero. car chassis www K₂ M₂ 1 Tire M₁ K₁ B₁ y(t)= output q(t) r(t)= input Where [r, q, y] are positions, [k1, k2] are spring constants. [B₁] coefficient of viscous friction, [M₁, M₂] masses. b) Find the answer in time q(t) of the previous system. With the following Ns values: M₁ = 1 kg, M₂ = 0 kg, k₁ = 4 N/m, k₂ = 0 N/m, B₁. = 1 Ns/m, considered m a unit step input, that is, U(s) = 1/sarrow_forward24. Find the transfer function, G(s) = X2(s)/F(s), for the translational mechanical system shown in Figure P2.11. (Hint: Place a zero mass at x2(t).) %3D ft) – 5 kg 10 N/m N-s/marrow_forward
- 25. For the system shown in Figure P4.7, do the follow- ing: [Section: 4.6] a. Find the transfer function G(s) = X(s)/F(s). b. Find $, om, %OS, T;, Тр, and T,. 28 N/m x(t) 3 kg f(t) 5 N-s/m FIGURE P4.7arrow_forwardObtain the transfer function for the mass-spring system represented by block diagram shown in Figure 1.21. Draw the simplified block diagram. X; (t) f(t) X, (t) k m D Figure 1.21 Block Diagram for mass-spring systemarrow_forwardQuestion 4: For the system given in the below figure, assume that: u(t) e(t) y(t) G(s) H(s) (a) Find the transfer function Y(s)/U(s) in the most simplified form.arrow_forward
- A translational mechanical system is shown in Figure Q1. In this system, u(t) is the displacement of the cart and the input to the system. The displacement y(t) of the mass relative to the ground is the output. Q1 (a) Determine the mathematical model of the system. (b) Using the result in Q1(a), determine a transfer function of the system. Massless Cart k m Figure Q1arrow_forward1. (25) Find the transfer function, X1(s)/F(s) For the system show in the figure. Svy = 4 N-s/m K= 5 N/m fvz = 4N-s/m fi)- M = 4 kg0000 M2 = 4 kg Svy =4 N-s/m Fv =4 N-s/marrow_forwarda. 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_forward
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Ch 2 - 2.2.2 Forced Undamped Oscillation; Author: Benjamin Drew;https://www.youtube.com/watch?v=6Tb7Rx-bCWE;License: Standard youtube license