backstepping.zip

function [sys,x0,str,ts] = spacemodel(t,x,u,flag) switch flag, case 0, [sys,x0,str,ts]=mdlInitializeSizes; 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 sizes = simsizes; sizes.NumOutputs = 1; sizes.NumInputs = 10; sizes.DirFeedthrough = 1; sizes.NumSampleTimes = 1; sys = simsizes(sizes); x0 = []; str = []; ts = [0 0]; function sys=mdlOutputs(t,x,u) I=1.0;J=1.0;Mgl=5.0; c1=50;c2=50;c3=50;c4=50; K=1200; %K=120; qt=u(1);dqt=u(2);ddqt=u(3);dddqt=u(4);ddddqt=u(5); x(1)=u(6);x(2)=u(7);x(3)=u(8);x(4)=u(9);dx2=u(10); z1=x(1)-qt; dz1=x(2)-dqt; a1=-c1*z1; z2=x(2)-(a1+dqt); dz2=-(1/I)*(Mgl*sin(x(1))+K*(x(1)-x(3)))+c1*x(2)-c1*dqt-ddqt; a2=-(I/K)*[-(1/I)*(Mgl*sin(x(1))+K*x(1))+c1*x(2)-c1*dqt-ddqt+z1+c2*z2]; z3=x(3)-a2; S1=(-1/I)*(Mgl*cos(x(1))*x(2)+K*x(2))+c1*c2*x(2)+(c1+c2)*(-1/I)*(Mgl*sin(x(1))+K*(x(1)-x(3)))-c1*c2*dqt-(c1+c2)*ddqt-dddqt+x(2)-dqt; dz3=x(4)+(I/K)*S1; a3=-(I/K)*S1-(K/I)*z2-c3*z3; z4=x(4)-a3; S2=-(1/I)*(-Mgl*sin(x(1))*x(2)^2+Mgl*cos(x(1))*dx2+K*dx2)+c1*c2*dx2+(c1+c2)*(-1/I)*(Mgl*cos(x(1))*x(2)+K*(x(2)-x(4)))-c1*c2*ddqt-(c1+c2)*dddqt-ddddqt+dx2-ddqt; tol=-J*(-(K/J)*(x(3)-x(1))+(I/K)*S2+K/I*dz2+c3*dz3+z3+c4*z4); sys(1)=tol;