Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 2, Problem 52P
A system’s output, c, is related to the system’s input, r, by the straight-line relationship,
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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?
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
If a system, * + 10x + 21x = 4f(t) is converted into a state-space model, what would
be the state (A), input (B), and output (C) matrices?
[where input = f (t) and output = x(t)]
%3D
A) A = |
[-21
l, B = | and C = [0 1]
В
-10
1
B) A = 21
ol, B =
and C = [1 0]
%3D
C) A =
= Al and C = [1 0]
В
%3D
-21
D) None of the above
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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- 38. Given the rotational system shown in Figure P2.24, find the transfer function, G(s) = 06(s)/01(s). [Section: 2.7]arrow_forwardConsider the state space representation of the following system [6]-[2][]+8-0 X2 (1) y()=[11][26] y(t) = [1 X2 u(t) Find x(t) and y(t) of this systems by u(t)= unit step function. =[7] x(0) = Xo =arrow_forwardThe state transmission matrix of the system whose state-space [3²₁] = [0²2 J]+[]u a. b. C. O 0 cosh at c. Ø(t) = [ a sinh at/a cosh a. ¢(t) = [sinhat cosh at a. Ø(t) = [a cosh at sinh at b. Ø(t) = [a [a cosh at a sinh at sinhat cosh at] sinhat/a] cosh at [/a] sinh at/a] a cosh at sinh at att cosh atarrow_forward
- 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_forwardFeedback & Control Systems State-Space Representation Write the state-space representation of the system below. Let the output of the mechanical system is x3 (t). 1 N-s/m x₁ (t) M3 = 1kg 1 N/m М1 -0000 1kg > X3 (t) 1 N-s/m 1 N/m oooo x₂ (t) M₂ 1kg 4 1 N-s/m² -1 N-s/m →f(t)arrow_forward
- O 1::09 O [Template] Ho... -> Homework For the system shown in figure below, Find the range of K for stable system. R K(s + 2) C s(s +5)(s² + 2s + 5) IIarrow_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_forward3. 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.arrow_forward
- 01(1) 18 N-m-s/rad T(t) 02(1) 1 N-m-s/rad kg-m? 3 kg-m2 3 N-m/rad 9 N-m/rad (a) Figure P2.16a OJohn Wiley & Sons, Inc. All rights reserved. The transfer function where the output Theta, is s? +5s +1 0,(s) а. Н(s)3D T(s) s' +30s +80s² +s+15 4 s' +5s +1 0,(s) b. H(s)= T(s) 25s* + 30s' +80s? + s +15 4 5s? +9s+9 0,(s) c. H(s)= T(s) 15s* +30s +95s² + s +27 5s +9s +9 0,(s) T(s) 15s +32s' +95s² +99s+27 d. H(s)= 4 Select one: O a.c O b. a O .b O d.d 立arrow_forwardFor the following state-space representation,define the:– State Vector– System Matrix– Feedforward Matrix– Input Matrix & Input Vector– Output Matrix & Output Vectorarrow_forwardThe differential equation that models a rotational mechanical system is presented below:arrow_forward
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