Non-Negative Solution with Integrator in Simulink

4 次查看（过去 30 天）
Rajmohan
Rajmohan 2024-5-7
评论： Sam Chak 2024-5-9
When solving ode in Matlab, the ode solver has an option that allows setting the solution non-negative property to be true. For instance -
x = odeset;
x.NonNegative = ones(numStates,1);
Is there an equivalent setting in Simulink? Something that can be adjusted in either model parameters or the [1/s] block?

请先登录，再回答此问题。

采纳的回答

Paul
Paul 2024-5-7
Hi Rajmohan,
Do the parameters Limit Output along with Upper and Lower Saturation Limit do what's needed? Integrator
  3 个评论
显示 1更早的评论
Paul
Paul 2024-5-8
Ran in:
"The saturation modifies the output only, it does not limit the state value"
I'm quite sure that's incorrect. I ran the equivalent of this model in Simulink, with Limit Output checked and Lower Saturation Limit set to 0 in the Integrator parameters and got the same result.
[t,x]=ode45(@(t,x) -t.*sin(t),[0 30],1,odeset('MaxStep',0.01,'NonNegative',1));
figure
plot(t,x)
Sam Chak
Sam Chak 2024-5-9
Ran in:
Hi @Rajmohan
Now that I've had the chance to test it in Simulink, I can confirm that @Paul's suggestion of setting the Lower Saturation Limit to 0 does indeed enforce the nonnegativity constraint and yield the correct solution. This option is also directly available in the Integrator Limited block. Here's a demo using the liquid level drainage system for reference.
If we don't impose the nonnegativity constraint (either mathematically or technically), the Simulink solver will terminate at 2 seconds, and the ode45 solver will provide an incorrect solution.
ode = @(t, h) - sqrt(h);
[t, h] = ode45(ode, [0 10], 1);
plot(t, h), grid on, xlabel('t'), ylabel('h(t)')
Warning: Imaginary parts of complex X and/or Y arguments ignored.
title('Solution without nonnegativity constraint')

请先登录，再进行评论。

更多回答（1 个）

Sam Chak
Sam Chak 2024-5-8
编辑：Sam Chak 2024-5-8
Ran in:
Hi @Rajmohan
I'm not familiar with all types of settings, codes, and tools in MATLAB/Simulink. Therefore, I usually resolve numerical issues using my own mathematical tricks, whenever possible.
In this case, you can attempt to address the ODE by incorporating a signum function in the Simulink model. You may find the demonstration below helpful, which is obtained from the "Nonnegative ODE Solution" article. However, I have also devised my own solution without relying on the built-in 'NonNegative' option.
Update: I have added a proper non-negative solution using the popular ReLU function in Case 4.
ode = @(t, y) - abs(y);
% Analytic solution
tspan = [0 40];
t = linspace(tspan(1), tspan(2), 1001);
y = exp(-t);
%% Case 1: Standard solution with ode45
options1 = odeset('Refine',1);
[t1, y1] = ode45(ode, tspan, 1, options1);
%% Case 2: Solution with nonnegative constraint
options2 = odeset(options1, 'NonNegative', 1);
[t2, y2] = ode45(ode, tspan, 1, options2);
%% Case 3: Solution with signum function
odefix = @(t, y) - abs(y)*sign(y);
[t3, y3] = ode45(odefix, tspan, 1, options1);
%% Case 4: Solution with ReLU function
odeReLU = @(t, y) - abs((sqrt(y.^2) + y)/2); % ReLU(x) = (√(x²) + x)/2
[t4, y4] = ode45(odeReLU, tspan, 1, options1);
%% Plot results
plot(t, y, '-', t1, y1, 'o', t2, y2, '*', t3, y3, 'x', t4, y4, 'p'), grid on, ylim([-5 2])
xlabel('t'), ylabel('y(t)')
legend('Exact solution', 'No constraints', 'Nonnegativity', 'Signum Fix', 'ReLU Fix', 'Location', 'best')
  1 个评论
Sam Chak
Sam Chak 2024-5-8
Or try using this Detect Rise Nonnegative block
  • The output is true (equal to 1) when the input signal is greater than or equal to zero, and its previous value was less than zero.
  • The output is false (equal to 0) when the input signal is less than zero, or if the input signal is nonnegative, its previous value was also nonnegative.

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Ordinary Differential Equations 的更多信息

标签

产品


版本

R2022b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by