% normsteer.m - normalized steering dynamics
% RMM, 13 Feb 07
% 
% This file contains a model for a steering control system, as
% described in Astrom and Murray, Example 5.12.  
%
% The model has been set up to allow feedback control via a
% gain-scheduled controller.  To use the file in this way, you should
% define controller gains K1, K2 and K3 as globals in the script that
% calls this file and set them to the proper values.  You will also need 
% to modify the code here to properly compute the scheduled gain from
% the parameters of the system.

function dxdt = normsteer(t, x)
global K1 K2 K3;			% include controller gains

% Compute the vehicle speed parameter
alpha = 2 + 2*sin(t/50 * 2*pi);

% Compute the reference position
yref = square(t/20 * 2*pi);

% Figure out the gain to use (replace with your gain schedule)
K = [1 1];

% Now compute the control law
u = -K * (x - [yref; 0]);

% And finally, compute the dynamics
dxdt = [0 1; 0 0] * x + [alpha; 1] * u;