Simulation of Automobile Cruise Control ENGR 1221
Designed to test skills with: simulation, graphical user interface
11/17/2021
Overview
In a previous application assignment, you studied feedback control using a PID controller. In this project,
you will apply that same control algorithm to control the speed of an automobile as it experiences a
change of grade.
Physical Model
Despite its complex machinery, the dynamics of an automobile as it travels in a straight line, with no
slipping between the wheels and the road, can be modeled by two relatively simple equations.1 The
acceleration of the vehicle is:
? =
?? − ??? cos ? −
1
2
?????
2 − ?? sin ?
?
where
• Fw is the force applied to the wheels
• m is the mass of the vehicle, including its occupants and contents
• f is the rolling resistance coefficient
• is the density of air
• CD is the drag coefficient
• A is the front cross-sectional area
• v is the speed of the vehicle
• g is the acceleration of gravity
• is the inclination angle of the road
This equation is an application of Newton’s second law in the longitudinal direction with 4 external
forces: traction, rolling resistance, drag, and gravity.
The second equation is a simplified model of the drive train that relates the variation of Fw to the
accelerator position, assuming first-order engine dynamics:
???
??
= −
??
?
+
? ?
? ??
?
where
• is the engine time constant
• k is the engine torque gain factor
• i is the gear ratio
• Rw is the wheel radius
1 Adapted from the online course, “Model-Based Automotive Systems Engineering” from Chalmers University of
Technology
https:
www.edx.org/course/model-based-automotive-systems-engineering?index=product&queryID=1032d0dd0332e300a064f9b0167cabf9&position=1
https:
www.edx.org/school/chalmersx
Simulation of Automobile Cruise Control ENGR 1221
Designed to test skills with: simulation, graphical user interface
11/17/2021
• u is the input (accelerator pedal position, given as an angle in radians)
In this simple model, all of the complex mechanics of the engine and transmission are encapsulated in
the time constant, , which represents how the engine responds when the accelerator position is
changed. The transmission of the engine torque to the wheel force is captured with the parameters k, i,
and Rw.
Conditions for Cruising at Constant Speed
At the beginning of the simulation, the vehicle can be taken as cruising at constant speed prior to
experiencing a change in inclination or set point. The necessary wheel force and accelerator input for
constant speed can be calculated by setting the acceleration and dFw/dt to 0 in the above equations.
First, the necessary wheel force is:
?? = ??? cos ? +
1
2
?????
2 + ?? sin ?
Then, the required input is
? =
????
? ?
The vehicle parameters should be user inputs to the model. A representative set of values that can be
used for testing is given in the table below.
Project Requirements
Simulation of Automobile Cruise Control ENGR 1221
Designed to test skills with: simulation, graphical user interface
11/17/2021
1. Write a simulation that calculates the position, velocity, and acceleration of the vehicle vs. time,
given the input parameters of the model.
2. Apply the PID controller model from an earlier application to control the speed of the vehicle at
a set point, with u being the input control signal. You can decide whether to include changes of
gear ratio in the simulation. In practice, an automatic transmission would downshift (increase
the gear ratio) when the vehicle hits an increase in grade or accelerates suddenly.
A note about the controller: Unlike the temperature control application, you do not want the
input signal, u, to be the output of the controller. Rather, you want the output of the
controller to be the change in u, or the difference between u and its reference value. That is,
you do NOT want this:
u = PID (…); %No!
But rather, one of the following:
u = u + PID(…)
or
u = u0 + PID (…)
where u0 is the reference input, i.e. the value that produced constant speed before
the distu
ance
The first (wrong) way would mean that when the cruising speed is reached, the accelerator is
eleased, which would not make sense. The second way continually adds (or subtracts) from the
cu
ent input based on the e
or, while the third way calculates the input signal as a difference
from the reference value based on the e
or. Either the second or third way will work, although
the control parameters may be very different. (I found that with the second way, I needed much
smaller values of P and I compared to the third way.)
3. Make a graphical user interface with App Designer that allows the user to input the vehicle and
controller parameters and displays graphs of the velocity and acceleration vs. time. The GUI
should allow the user to simulate at least the following scenarios:
a. A step change in set point speed on level road (e.g. the vehicle is cruising at, say, 55
mph, and the set point is increased to 65 mph)
. A step change in road inclination at fixed set point (e.g. the vehicle is cruising on a level
oad and encounters a sudden uphill grade.
The GUI should also display at least one text/numerical output, which could be the settling time
(time after the distu
ance at which the speed reaches and stays within 1 % of the set point),
the % overshoot, or other appropriate value.