University of Notre Dame
Aerospace and Mechanical Engineering

ME 437: Control Systems Engineering
Homework 1a

Sample Matlab Code

Have these two files in your current directory or path. To integrate the system type 'car' (assuming the first file is named car.m).

First file:

%
%   First control example: proportional control for cruise control.
%   B. Goodwine, January 14, 1999.  I called this file 'car.m'
%

b = 25;
m = 750;
lam = 0.5;
vd = 40;
kp = 100;
fe = b*vd;    % inital condition for engine 'force'

%   OutputFcn odeplot tells Matlab to plot the output
%   Outputsel [1] tells it to plot only the velocity (the
%   first component of y).
options = odeset('OutputFcn','odeplot','Outputsel',[1]);

%   In the following, t = time, and y is the state vector [v fe].
%   The [0 20] is the time range and [0 fe] are the initial conditions.
%   'proporational' tells this program to look at the file
%   'proportional.m' for the equations of motion.

[t y] = ode45('proportional', [0 20], [0 fe],options,b,m,lam,vd,kp);

Second file:

%
%   The is the 'odefile' called by ode45 to integrate the cruise control
%   equations.  To modify to add integral control, you have to add a
%   integral gain, ki, to the paramter list in the 'odefile' function.
%   You must also add ki to the ode45 function line in the car.m file.
%   The same is true later when you add derivative gain.
% 
%   I called this file 'proportional.m'
%
%   Also, you must change the form of 'out' to reflect the addition of
%   integral and/or derivative gain.
%
%   B. Goodwine, January 16, 1998.
%

function out = odefile(t,y,options,b,m,lam,vd,kp);
out = [-b/m*y(1)+y(2)/m; lam*kp*(vd - y(1)) - lam*y(2)];

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Last modified: January 16, 1998.

B. Goodwine
Spring, 2000