Assignment 3.pdf - UBC Mechanical Engineering
Assignment 3.pdf - UBC Mechanical Engineering
Assignment 3.pdf - UBC Mechanical Engineering
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through and the voltages across the elements L, C, and R by (f l , v l ), (f 2 , v 2 ) and (f 3 , v 3 ),<br />
respectively, and then proceed in the usual manner.<br />
(i) What is the system matrix and what is the input distribution matrix for your choice of<br />
state variables?<br />
(ii) What is the order of the system?<br />
(iii) Briefly explain what happens if the voltage source v(t) is replaced by a current source<br />
i(t).<br />
L<br />
v(t)<br />
C<br />
R<br />
Figure P4.3 An electrical circuit.<br />
Problem 4 (Problem 4.4 from Textbook)<br />
Consider an automobile traveling at a constant speed on a rough road, as sketched in Figure<br />
P4.4(a). The disturbance input due to road irregularities can be considered as a velocity source<br />
u(t) at the tires in the vertical direction. An approximate one-dimensional model shown in Figure<br />
P4.4(b) may be used to study the “heave” (up and down) motion of the automobile. Note that v 1<br />
and v 2 are the velocities of the lumped masses m 1 and m 2 , respectively.<br />
(a)<br />
(b)<br />
(c)<br />
(d)<br />
Briefly state what physical components of the automobile are represented by the model<br />
parameters k 1 , m 1 , k 2 , m 2 , and b 2 . Also, discuss the validity of the assumptions that are<br />
made in arriving at this model.<br />
Draw a linear graph for this model, orient it (i.e., mark the directions of the branches),<br />
and completely indicate the system variables and parameters.<br />
By following the step-by-step- procedure of writing constitutive equations, node<br />
equations and loop equations, develop a complete state-space model for this system. The<br />
outputs are v 1 and v 2 . What is the order of the system?<br />
If instead of the velocity source u(t), a force source f(t) which is applied at the same<br />
location, is considered as the system input, draw a linear graph for this modified model.<br />
Obtain the state equations for this model. What is the order of the system now?<br />
Note: In this problem you may assume that the gravitational effects are completely balanced by<br />
the initial compression of the springs with reference to which all motions are defined.
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