%% L7_1-cruise.m - cruise control example for Lecture 7.1
%% RMM, 8 Nov 02
%%
%% This lecture uses two main examples: the cart pendulum system and the 
%% cruise control system.  For each of these, we generate the various plots
%% used in the lecture.

%%
%% Cruise controller
%%
%% This is the cruise controller that we studied in HW #2, 3, 4.  It uses
%% a modified PD control law.  The main modification is replacing the
%% integrator with a high gain, low pass filter to make the plots show
%% the features more clearly.
%% 

% Parameter definitions
m = 1000;				% mass of the car, kg
b = 50;					% damping coefficient, N sec/m
a = 0.2;				% engine lag coefficient
r = 5;					% transmission gain
Ki = 50;				% integral gain
Kp = 1000;				% proportional gain

% Dynamics
veh = tf([1/m], [1 b/m]);		% vehicle
eng = tf([r], [1 a]);			% engine
ctr = tf([Kp Ki], [1 0.01]);		% control: PI w/ LF pole
cruise = ctr*eng*veh;			% loop transfer function

%% Slide 8: Nyquist analysis (with zoom)
nyquist(cruise); print -dmeta L7_6a.wmf
nyquist(cruise, {1,1e5}); print -dmeta L7_6b.wmf

%% Slide 12: robustness analysis
lag = tf([10], [1 10]);
bode(cruise, cruise*lag); print -dmeta L7_10a.wmf
nyquist(cruise, cruise*lag); print -dmeta L7_10b.wmf
nyquist(cruise, cruise*lag, {1,1e5}); print -dmeta L7_10c.wmf

%% Slide 13: design example
lag = tf([10], [1 10]);			% sensor lag
bode(cruise, 0.25*cruise*lag, 0.25*cruise); print -dmeta L7_13a.wmf
nyquist(cruise, 0.25*cruise*lag, 0.25*cruise*lag); print -dmeta L7_13b.wmf
nyquist(0.25*cruise*lag, 0.25*cruise*lag, {0.5,1e5}); print -dmeta L7_13c.wmf

% Additional calculations
cruise1_cl = feedback(cruise, 1);	% closed loop dynamics
cruise2_cl = feedback(0.25*cruise, 1);	% closed loop with lower gain
step(cruise1_cl, cruise2_cl);		% compare step responses