Question

我正在尝试模拟液位控制，我正在尝试使用newton raphson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

输出结果为：

 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

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;

我尝试了vpa功能，但无济于事。 Equa_0接受x值但似乎创建了不同类型的表达式。

Answer 1

一，您指定guess并操纵它，但不要将其推入Equa_0。在循环中计算z = guess;之前，您需要在每次迭代期间明确说出dx。

一般来说，你不应该使用符号工具箱。如果x是常量，请使用匿名函数（这将需要重写一些代码）：

Equa_0=@(z) ((x(k,l))+(10^(z-14))+((x(k,l+1))*((1+2*(10^(z-pk2)))/(1+(10^(pk1-z))+ (10^(z-pk2)))))-(10^(-z)));

编辑：我应该注意到你的代码中还有其他东西要修复，但我会留下那部分让你弄明白。

MATLAB：调试Newton Raphson方法

1 个答案: