Systems Dynamics and Control
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AMME3500 Systems Dynamics and Control
Design Project
Weight: 20% of your total mark.
Approved Late Submissions: If you receive an approval for a submission extension, you should add a
comment along with your submission over Canvas stating your extended due date (when you submit the
work, on the top-right corner of the Canvas portal you will be able to see a button “Add Comment”).
You may also indicate your extension under the title of your report.
Late Submissions: According to our University policy, late submissions without approval will be sub-
jected to penalties: the penalty will be 5% of the total assignment mark per day; and when it is more than
ten calendar days late, a mark of zero for the assignment will be awarded.
Project Summary: This project asks you to design some of the basic components of an autonomous
car: the cruise control system and a controller for automatically changing lanes. For the parameters of
the vehicle model (masses, lengths, etc), look up or estimate numbers for your car if you own one, or the
car of a family member. This assignment draws most directly on knowledge of linearisation, second-order
systems and second-order control systems. The approach you should take is that your tutor is your boss at
your first job after graduation, and they have asked you to prepare design proposal. Therefore the report
should be of a professional standard.
1 Project Description: Cruise Control
Let a vehicle be moving in a straight line with its velocity described by v(t) at time t. We assume an
engine controller has been designed, so that the control input u is the force demanded from the engine:
Here ρ is density of air in kg/m3, CD is a dimensionless drag coefficient, and A is cross-sectional area
of the vehicle in m2 (looking from the front). Reasonable values for cD for a car are about 0.25 to 0.45
(Wikipedia has an interesting list). For your car, look up, measure, or estimate A and cD. You are asked
to complete the following design and testing tasks.
Task 1 (Linearization): Select three pairs of equilibriums (ve, ue). Linearize the system dynamics (1)
under the three pairs of equilibriums, respectively. Select initial conditions for v(0), and simulate the
three linearized dynamics to obtain three trajectories of v(t). Plot the three trajectories and explain their
similarities and differences.