我正在尝试对液位控制进行建模，并且正在尝试使用牛顿拉夫森方法求解隐式方程
t=(0:1:10);
x=[14 -4.32E-4 5.28E-4]; y=[14 7];
[t,x]=ode45(@PHandLiquidlevelmain,t,x) % returns x
% For this time period t ,I have x as a 11X3 double array.
% And I am trying to access that array to calculate y
y=zeros(max(size(t)),2);
cv=8.75;
pk1=6.35;
pk2=10.25;
for l=1:1:1% For output Y(1)
for k=1:1:11
if l<2
y(k,l)=y(k,l)+x(k,l);% Equation governed to calculate y(1)
end
end
end
for l=2:1:2
for k=1:1:11
if l<3
syms z;
format long;
Equa_0=((x(k,l))+(10^(z-14))+((x(k,l+1))*((1+2*(10^(z-pk2)))/(1+(10^(pk1-z))+
(10^(z-pk2)))))-(10^(-z)))
% using looping to get values of x(1,2)to x(t,2) and x(1,3) up to x(t,3)
% and using it in Equa_0 to create t equations which are need to be
% solved using Newton Raphson method
%Newton Raphson method
e = 1e-5; % setting the tolerance value
dx = e + 1;
guess = 7; % initially assumed value of z
count = 0; % setting counter to know the
% no of iterations taken
p = zeros(1,1);
while (abs(dx) > e) % initialising the iteration and
% continue until the error is less than tolerance
dx = (eval(Equa_0/(diff(Equa_0)))); % calculating dx, diff is used for
% finding the differentiation of the
% function
guess = guess - dx; % updating the value of x
count = count + 1; % incrementing the counter
p(count) =guess;
drawnow();
plot(abs(p),'r','linewidth',3);
grid;
if (count > 300)
fprintf('Error...! Solution not converging !!! \n'); % printing the
% error message
break;
end
end
if (count < 300)
fprintf('The solution = '); %printing the result
y(k,l)=y(k,l)+guess;% y(1,1) to y(t,1) is calculated
fprintf('\nNumber of iteration taken = %d\n',count);
end
end
end
end
y
输出是：
t =
0
1
2
3
4
5
6
7
8
9
10
x =
14.0000 -0.0004 0.0005
14.0001 -0.0004 0.0005
14.0001 -0.0004 0.0005
14.0002 -0.0004 0.0005
14.0002 -0.0004 0.0005
14.0003 -0.0004 0.0005
14.0003 -0.0004 0.0005
14.0003 -0.0004 0.0005
14.0004 -0.0004 0.0005
14.0004 -0.0004 0.0005
14.0005 -0.0004 0.0005
Equa_0 =
10^(z - 14) - 1/10^z + (33*(2*10^(z - 41/4) + 1))/(62500*(10^(z - 41/4) + 10^(127/20 -
z) + 1)) - 27/62500
并发生以下错误：
The following error occurred converting from sym to double:
Error using mupadmex
Error in MuPAD command: DOUBLE cannot convert the input expression into a double array.
If the input expression contains a symbolic variable, use the VPA function instead.
Error in PHmain (line 55)
p(count) =guess;
我尝试vpa了功能，但无济于事。Equa_0接受这些值x，但似乎创建了一种不同的表达式。