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how to calculate the differentiation by diff command ?

3 vues (au cours des 30 derniers jours)
Pallov Anand
Pallov Anand le 13 Oct 2022
Commenté : Pallov Anand le 14 Oct 2022
I need to calculate the derivative and second derivative of phid and thetad (w.r.t time) for the code given below. Can anyone plz help in calculating this?
m = 0.65;
d = 7.5*10^-7;
l = 0.23;
Jx = 7.5 * 10^-3;
Jy = 7.5 * 10^-3;
Jz = 1.3 * 10^-2;
b = 3.13 * 10^-5;
a1 = (Jy - Jz)/Jx ; b1 = 1/Jx;
a2 = (Jz - Jx)/Jy; b2 = 1/Jy;
a3 = (Jx - Jy)/Jz; b3 = 1/Jz;
g0 = 9.81;
c1 = 1; c3 = 1; c5 = 1; c7 = 1; c9 = 1; c11 = 1;
c2 = 1; c4 = 1; c6 = 1; c8 = 5; c10 = 1; c12 = 1;
x1(1) = 0; %% roll
x2(1) = 0;
x3(1) = 0; %% pitch
x4(1) = 0;
x5(1) = 0; %% yaw
x6(1) = 0;
x7(1) = 0; %% z position
x8(1) = 0;
x9(1) = 0; %% x poition
x10(1) = 0;
x11(1) = 0; %% y position
x12(1) = 0;
dt = 0.1;
t = 0:dt:60;
for n = 1: length(t)
phid(1) = 0;
thetad(1) = 0;
xd(:,n) = [phid(n); thetad(n); 0; 0; 0; 0; zdes; diff(zdes,t); xdes; diff(xdes,t); ydes; diff(ydes,t)];
xdd(:,n) = [0; 0; 0; 0; 0; 0; diff(zdes,t); diff(diff(zdes,t)); diff(xdes,t); diff(diff(xdes,t)); diff(ydes,t); diff(diff(ydes,t))];
xddd(:,n) = [0; 0; 0; 0; 0; 0; diff(diff(zdes,t)); diff(diff(diff(zdes,t))); diff(diff(xdes,t)); diff(diff(diff(xdes,t))); diff(diff(ydes,t)); diff(diff(diff(ydes,t)))];
e1(:,n) = phid(n) - x1(n);
e3(:,n) = thetad(n) - x3(n);
e5(:,n) = xd(5,n) - x5(n);
e7(:,n) = xd(7,n) - x7(n);
e9(:,n) = xd(9,n) - x9(n);
e11(:,n) = xd(11,n) - x11(n);
e2(:,n) = x2(n) - xdd(1,n) - c1*e1(n);
e4(:,n) = x4(n) - xdd(3,n) - c3*e3(n);
e6(:,n) = x6(n) - xdd(5,n) - c5*e5(n);
e8(:,n) = x8(n) - xdd(7,n) - c7*e7(n);
e10(:,n) = x10(n) - xdd(9,n) - c9*e9(n);
e12(:,n) = x12(n) - xdd(11,n) - c11*e11(n);
U1(n) = ( m / ( cos( x1(n) ) * cos(x3(n)) ) * (g0 + xdd(8,n) + e7(n) - c8*e8(n)));
Ux(n) = (m/(U1(n)))*(xdd(10,n) + e9(n) - c10*e10(n));
Uy(n) = (m/(U1(n)))*(xdd(12,n) + e11(n) - c12*e12(n));
phid(n+1) = asin(Ux(n)*sin(xd(5,n)) - Uy(n)*cos(xd(5,n)));
thetad(n+1) = asin( ( Ux(n)*sin(xd(5,n)) + Uy(n)*cos(xd(5,n))) )/sqrt(1-( Ux(n)*sin(xd(5,n) - Uy(n)*cos(xd(5,n))) )^2 ) ;
U2(n) = (1/b1)*(- a1*x4(n)*x6(n) + xdd(2,n) + (phid(n)-x1(n)) - c2*e2(n));
U3(n) = (1/b2)*(- a2*x2(n)*x6(n) + xdd(4,n) + (thetad(n) - x3(n)) - c4*e4(n));
U4(n) = (1/b3)*(- a3*x2(n)*x4(n) + xdd(5,n) + e5(n) - c6*e6(n));
x1(n+1) = x1(n) + dt * (x2(n));
x2(n+1) = x2(n) + dt * (a1*x4(n)*x6(n) + b1*U2(n));
x3(n+1) = x3(n) + dt * (x4(n));
x4(n+1) = x4(n) + dt * (a2*x2(n)*x6(n) + b2*U3(n));
x5(n+1) = x5(n) + dt * (x6(n));
x6(n+1) = x6(n) + dt * (a3*x2(n)*x4(n) + b3*U4(n));
x7(n+1) = x7(n) + dt * (x8(n));
x8(n+1) = x8(n) + dt * ((1/m)*(U1(n)*cos(x1(n)) * cos(x3(n))) - g0);
x9(n+1) = x9(n) + dt * (x10(n));
x10(n+1) = x10(n) + dt * ((Ux(n)* U1(n)) / m);
x11(n+1) = x11(n) + dt * (x12(n));
x12(n+1) = x12(n) + dt * ( (U1(n)*Uy(n))/m );
end
  6 commentaires
Torsten
Torsten le 13 Oct 2022
You just wrote down the derivatives in the problem formulation:
dphi/dt = x2
d^2phi/dt^2 = a1*x4*x6 + b1*U2
dtheta/dt = x4
d^2theta/dt^2 = a2*x2*x6 + b2*U3
What's the problem ?
Pallov Anand
Pallov Anand le 14 Oct 2022
I need to write dphid / dt instead of dphi / dt, where
phid(1) = 0;
phid(n+1) = asin(Ux(n)*sin(xd(5,n)) - Uy(n)*cos(xd(5,n)));

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Star Strider
Star Strider le 13 Oct 2022
The diff function to calcualte the derivative is part of the Symbolic Math Toolbox.
To calculate a numerical derivative, use the gradient function.

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