EBK SYSTEM DYNAMICS
3rd Edition
ISBN: 8220100254963
Author: Palm
Publisher: MCG
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Chapter 11, Problem 11.36P
The following equations are the model of the roll dynamics of a missile ([Bryson. 1975]). See Figure Pl 1.36.
![Chapter 11, Problem 11.36P, The following equations are the model of the roll dynamics of a missile ([Bryson. 1975]). See Figure , example 1](https://content.bartleby.com/tbms-images/9780073398068/Chapter-11/images/html_98068-11-11.36p_image002.jpg)
![Chapter 11, Problem 11.36P, The following equations are the model of the roll dynamics of a missile ([Bryson. 1975]). See Figure , example 2](https://content.bartleby.com/tbms-images/9780073398068/Chapter-11/images/html_98068-11-11.36p_image001.jpg)
where 5 = aileron deflection
b = aileron effectiveness constant
it = command signal to the aileron actuator
tp = roll angle, to = roll rate
Using the specific values b = 10s-1 and r = 1 s, and assuming that the state variables 5, to, and tp can be measured, develop a linear state-feedback controller to keep tp near 0. The dominant roots should be s = —10 ± 1 Oj, and the third root should be v = —20.
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A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below.
From the free body diagram, the ordinary differential equation of the vehicle is:
m * dv(t)/ dt + bv(t) = u (t)
Where:
v (m/s) is the velocity of the vehicle,
b [Ns/m] is the damping coefficient,
m [kg] is the vehicle mass,
u [N] is the engine force.
Question:
Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system):
1. What is the order of this system?
A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below.
From the free body diagram, the ordinary differential equation of the vehicle is:
m * dv(t)/ dt + bv(t) = u (t)
Where:
v (m/s) is the velocity of the vehicle,
b [Ns/m] is the damping coefficient,
m [kg] is the vehicle mass,
u [N] is the engine force.
Question:
Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system):
A. Use Laplace transform of the differential equation to determine the transfer function of the system.
Figure Q3 shows one cart with a mass that is separated from two walls by two springs and a
dashpot, where kı, k2 and ka are the first, second spring and dashpot coefficients, respectively.
The mass, m could represent an automobile system. An external force is also shown as F(t).
Only horizontal motion and forces are considered. F(t) is input and x2(t) is output.
(a)
Derive all equations related to the system
(b)
Construct the block diagram from equation in (a)
(c)
Obtain the transfer function of the system
Chapter 11 Solutions
EBK SYSTEM DYNAMICS
Ch. 11 - Prob. 11.1PCh. 11 - Prob. 11.2PCh. 11 - Prob. 11.3PCh. 11 - Sketch the root locus plot of ms~ 4- 12s + 10 = 0...Ch. 11 - Prob. 11.5PCh. 11 - Prob. 11.6PCh. 11 - Prob. 11.7PCh. 11 - PID control action is applied to the plant GPU) =...Ch. 11 - Consider the following equation where the...Ch. 11 - 11.10 In the following equation. K > 0.
j2(j+9) +...
Ch. 11 - 11.11 Consider the following equation where the...Ch. 11 - 11.12 In the following equations, identify the...Ch. 11 - Prob. 11.13PCh. 11 - Prob. 11.14PCh. 11 - Prob. 11.15PCh. 11 - Prob. 11.16PCh. 11 - Prob. 11.17PCh. 11 - Prob. 11.18PCh. 11 - Prob. 11.19PCh. 11 - Prob. 11.20PCh. 11 - Prob. 11.21PCh. 11 - Prob. 11.23PCh. 11 - Prob. 11.24PCh. 11 - Prob. 11.25PCh. 11 - Prob. 11.26PCh. 11 - Prob. 11.27PCh. 11 - Prob. 11.28PCh. 11 - Prob. 11.29PCh. 11 - Prob. 11.30PCh. 11 - Prob. 11.32PCh. 11 - Prob. 11.33PCh. 11 - Prob. 11.34PCh. 11 - Prob. 11.35PCh. 11 - The following equations are the model of the roll...Ch. 11 - Prob. 11.38P
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