Modeling #4 - The Cab Control Problem
The speed-of-approach algorithm employs:
an  k2  un  vn 
an  amax if k2  un  vn   amax
an  dmax if k2  un  v n    d max
ECE194
S’02
Introduction to Engineering Design
Arizona State University
1
Modeling - The Cab Control Problem
Start as before with the equation for the velocity of the leading car A:
un  us  ud  costn 
Again use the numerical approach:
x n1  x n
un 
 x n1  x n  un t
t
ECE194
S’02
Introduction to Engineering Design
Arizona State University
2
Modeling - The Cab Control Problem
Then repeat for the trailing car B:
1. Calculate the acceleration an from the speed-of-approach
algorithm
2. Calculate the velocity vn+1
vn1  v n
an 

t
vn1  vn  ant
3. Calculate the distance yn+1
yn1  yn
vn 
 yn1  yn  vnt
t
ECE194
S’02
Introduction to Engineering Design
Arizona State University
3
Modeling - The Cab Control Problem
4. Calculate the relative speed:
un1  vn1
then compute the new acceleration from the speed of approach
algorithm.
5. Increment the time, and repeat all of the calculations for both cab A
and cab B
ECE194
S’02
Introduction to Engineering Design
Arizona State University
4
Modeling - The Cab Control Problem
Note: Once again, you must limit the accelerations
With “if” statements, or some other approach, you
must stop the acceleration from exceeding the two
limits (amax and -dmax)
ECE194
S’02
Introduction to Engineering Design
Arizona State University
5