I am looking for a problem in my implementation for steepest ascent method. My answer is in a long equation form with h in it. But I am calculating h in the loop still ther is no value of it for the answer. The solution is at the end of the function
function STPAscent(x,theta,TC)
x0 =1500;
theta0=pi/6;
i=0;
i_max=100;
ea=5;
es=1;
while (es<double(subs(ea)) && i<i_max)
fx = tan(theta0)/(2*100^2*(cos(theta0))^2) + (2*9.81*x0)/(2*100^2*(cos(theta0))^2); % derivative wrt "x"
ftheta= x0*(sin(theta0)*(100*sin(theta0)+981*x0*cos(theta0))+50)/(1000000*(cos(theta0))^4); % derivative wrt "theta"
syms h
x=x0+fx*h;
theta=theta0+ftheta*h;
f= 1000 + (x*tan(theta))/(2*100^2*(cos(theta))^2) + (9.81*x^2)/(2*100^2*(cos(theta))^2);
c=diff(f,h);
assume(h,'clear')
h=solve(c==0,h,'PrincipalValue',true);
x_new=x+fx*h;
theta_new=theta0+ftheta*h;
ea=abs((x_new-x0)/x_new)*100;
x0=x_new;
theta0=theta_new;
i=i+1;
end
fxtheta = 1000 + (x0*tan(theta0))/(2*100^2*(cos(theta0))^2) + (9.81*x0^2)/(2*100^2*(cos(theta0))^2)
simplify(fxtheta)
end
Command Window
Warning: Unable to solve symbolically. Returning a numeric
solution using vpasolve.
> In sym/solve (line 304)
In STPAscent (line 18)
fxtheta =
(981*((8836235812531391*h)/4503599627370496 + 1499.9993954193889930311396801317)^2)/(2000000*cos(pi/6 - 0.52363352427033321420523588398365)^2) + (tan(pi/6 - 0.52363352427033321420523588398365)*((8836235812531391*h)/4503599627370496 + 1499.9993954193889930311396801317))/(20000*cos(pi/6 - 0.52363352427033321420523588398365)^2) + 1000
ans =
0.0018882263675909642813601409431637*h^2 + 2.8871384744661982638760370739896*h + 2103.6241090862540686603690416302
