chap3_5ctrl.m

机器人控制仿真程序一书的所有源代码

function [sys,x0,str,ts] = spacemodel(t,x,u,flag)

switch flag,
case 0,
    [sys,x0,str,ts]=mdlInitializeSizes;
case 1,
    sys=mdlDerivatives(t,x,u);
case 3,
    sys=mdlOutputs(t,x,u);
case {2,4,9}
    sys=[];
otherwise
    error(['Unhandled flag = ',num2str(flag)]);
end

function [sys,x0,str,ts]=mdlInitializeSizes
global c b kv kp
sizes = simsizes;
sizes.NumContStates  = 10;
sizes.NumDiscStates  = 0;
sizes.NumOutputs     = 6;
sizes.NumInputs      = 8;
sizes.DirFeedthrough = 1;
sizes.NumSampleTimes = 1;
sys = simsizes(sizes);
x0  = 0.1*ones(1,10);
str = [];
ts  = [0 0];

%c=0.60*ones(4,5);
c= [-2 -1 0 1 2;
    -2 -1 0 1 2;
    -2 -1 0 1 2;
    -2 -1 0 1 2];
b=3.0*ones(5,1);
alfa=3;
kp=[alfa^2 0;
    0 alfa^2];
kv=[2*alfa 0;
    0 2*alfa];
function sys=mdlDerivatives(t,x,u)
global c b kv kp

A=[zeros(2) eye(2);
    -kp -kv];
B=[0 0;0 0;1 0;0 1];

Q=[50 0 0 0; 
   0 50 0 0;
   0 0 50 0;
   0 0  0 50];
P=lyap(A',Q);
eig(P);

qd1=u(1);
d_qd1=0.2*0.5*pi*cos(0.5*pi*t);
qd2=u(2);
d_qd2=0.2*0.5*pi*sin(0.5*pi*t);

q1=u(3);dq1=u(4);q2=u(5);dq2=u(6);
e1=q1-qd1;
e2=q2-qd2;
de1=dq1-d_qd1;
de2=dq2-d_qd2;

th=[x(1) x(2) x(3) x(4) x(5);x(6) x(7) x(8) x(9) x(10)]';
xi=[e1;e2;de1;de2];
h=zeros(5,1);
for j=1:1:5
    h(j)=exp(-norm(xi-c(:,j))^2/(2*b(j)*b(j)));
end
gama=20;

M1=1;
if M1==1       % Adaptive Law
    S=gama*h*xi'*P*B;
elseif M1==2   % Adaptive Law with UUB
    k1=0.001;
    S=gama*h*xi'*P*B+k1*gama*norm(x)*th;
end
S=S';
for i=1:1:5
    sys(i)=S(1,i);
    sys(i+5)=S(2,i);    
end

function sys=mdlOutputs(t,x,u)
global c b kv kp
qd1=u(1);
d_qd1=0.2*0.5*pi*cos(0.5*pi*t);
dd_qd1=-0.2*(0.5*pi)^2*sin(0.5*pi*t);

qd2=u(2);
d_qd2=0.2*0.5*pi*sin(0.5*pi*t);
dd_qd2=0.2*(0.5*pi)^2*cos(0.5*pi*t);
dd_qd=[dd_qd1;dd_qd2];

q1=u(3);dq1=u(4);
q2=u(5);dq2=u(6);
ddq1=u(7);ddq2=u(8);
ddq=[ddq1;ddq2];

e1=q1-qd1;
e2=q2-qd2;
de1=dq1-d_qd1;
de2=dq2-d_qd2;
e=[e1;e2];
de=[de1;de2];

v=13.33;
q01=8.98;
q02=8.75;
g=9.8;

D0=[v+q01+2*q02*cos(q2) q01+q02*cos(q2);
    q01+q02*cos(q2) q01];
C0=[-q02*dq2*sin(q2) -q02*(dq1+dq2)*sin(q2);
     q02*dq1*sin(q2)  0];
G0=[15*g*cos(q1)+8.75*g*cos(q1+q2);
    8.75*g*cos(q1+q2)];

dq=[dq1;dq2];

tol1=D0*(dd_qd-kv*de-kp*e)+C0*dq+G0;

d_D=0.2*D0;
d_C=0.2*C0;
d_G=0.2*G0;
d1=2;d2=3;d3=6;
d=[d1+d2*norm([e1,e2])+d3*norm([de1,de2])];
%d=[20*sin(2*t);20*sin(2*t)];
f=inv(D0)*(d_D*ddq+d_C*dq+d_G+d);

xi=[e1;e2;de1;de2];
h=zeros(5,1);
for j=1:1:5
    h(j)=exp(-norm(xi-c(:,j))^2/(2*b(j)*b(j)));
end

M=3;
if M==1               %Nominal model based controller
    tol=tol1;        
elseif M==2           %Modified computed torque controller
    tol2=-D0*f;
    tol=tol1+tol2;
elseif M==3           %RBF compensated controller
    th=[x(1) x(2) x(3) x(4) x(5);x(6) x(7) x(8) x(9) x(10)]';
    fn=th'*h;
    tol2=-D0*fn;
    tol=tol1+1*tol2;
end

sys(1)=tol(1);
sys(2)=tol(2);
sys(3)=f(1);
sys(4)=fn(1);
sys(5)=f(2);
sys(6)=fn(2);