%
%   MatLab script for parameter initialization of the car
%   HGO control  simulation and experiment.
%
% Jose Paulo V. S. da Cunha
%
% Rio de Janeiro, February 04, 2004.
%

%
%                                PLANT PARAMETERS:
%

% Kp given by the V/V gain divided by the potentiometer gain (V/m):

Kp = 17.0/10.7;

% Electromechanical pole:

p1 = -15;

%
%                                SPECIFIED Kpnom:
%

Kpnom = 25.8/10.7;

%
%                          REFERENCE MODEL PARAMETERS:
%
%                            Wm(s) = Km/(s^2+a1*s+a0)
%

a1 = 5 + 10;

a0 = 5 * 10;

Km = a0;

pm = 2;

%
%                         SPECIFIED L(s) OPERATOR:
%

L = [ 1 10 ]' ;

%
%               SPECIFIED alpha(s) FOR THE HGO FEEDBACK MATRIX:
%

alpha1 = 15 + 15;

alpha0 = 15 * 15;

%
%               SPECIFIED lambda(s) FOR THE STATE FILTERS:
%

lambda0 = 10;

%
%                          INITIAL CONDITIONS:
%

xp0 = [ 0.1 ; 0 ];

xm0 = [ 0 ; 0 ];

hat_zeta0 = [ 0 ; 0 ];

xsf0 = [ 0 ];

%
%                     COMPUTATION OF SYSTEM PARAMETERS:
%

% Matrices of the plant:

Ap = [ 0 1 ;
       0 p1 ];

Bp = [ 0 ;
       Kp ];

Cp = [ 1 0 ];

% Reference model matrices:

Am = [ -a1  1 ;
       -a0  0 ];

Bm = [ 0 ;
       Km ];
 
Cm = [ 1 0 ];

% State filters state space form:

Phi = [ -lambda0 ];

Gamma = [ 1 ];

Csf = eye(1);

Dsf = zeros(1,1);

% HGO matrices:

bar_Am = [ -a1*epsilon   1 ;
           -a0*epsilon^2 0 ] / epsilon;

bar_Bm = Bm * ((epsilon^(pm-1))*Kpnom/Km);

bar_alpha_am = - [alpha1 - a1*epsilon ;
                  alpha0 - a0*epsilon^2 ] / epsilon ;

% Sliding surface matrix:

bar_S = - (inv( [ 0 1 ;
                  1 a1 ] ) * L )' * diag([1,epsilon^-1]) * (epsilon^(pm-1)) ;

% Controller coefficients:

theta_nomT = [ -1.6 , -22.56124 , -18.48031 , 20.736434 ];

c1 = 44;

hat_d = 0.4;