how can I simulate this NMPC in close loop? i try using the matlab examples but i have a lot of parameters.

Here´s the NMPC

clc
clear all
close all

%% NMPC
 % Parámetros

Ta = 23 + 273.15;   % K
U = 10.0;           % W/m^2-K
m = 4.0/1000.0;     % kg
Cp = 0.5 * 1000.0;  % J/kg-K    
A = 12.0 / 100.0^2; % Area in m^2
alpha = 0.01;       % W % heater
eps = 0.9;          % Emissivity
sigma = 5.67e-8;    % Stefan-Boltzman

Par = [Ta;U;m;Cp;A;alpha;eps;sigma];
  
%% Crear objeto NMPC

nx = 1; %Estados
ny = 1; %Salidas
nu = 1; %entradas
nlobj = nlmpc(nx,ny,nu);
nlobj.States.Name = 'T';
nlobj.MV.Name = 'H';


nlobj.Model.StateFcn = @(x,u,Par) prediction_model_jl(x,u,Par);
% No output function specified. Assuming "y = x" in the prediction model.
nlobj.Model.IsContinuousTime = true; 
nlobj.Model.NumberOfParameters=1;

%% Restricciones NMPC
nlobj.States.Min = 0;

nlobj.MV.Min = 0;    
nlobj.MV.Max = 100;  

nlobj.MV.RateMin = -100;   
nlobj.MV.RateMax = 100;   

%% NMPC Sintonización
N=14;
Nu=10;
delta=0.69408;
lambda=0.24209;
Ts = 8;
nlobj.Ts = Ts;                                 
nlobj.PredictionHorizon = N;                  
nlobj.ControlHorizon = Nu;                
nlobj.Weights.OutputVariables = delta;
nlobj.Weights.ManipulatedVariablesRate = lambda;

here´s the prediction model

%Specify Prediction Model for Nonlinear MPC
function dTdt = prediction_model_jl(x,u,Par)
    
    % Parameters
 Ta = Par(1);   % K
 U = Par(2);           % W/m^2-K
 m = Par(3);     % kg
 Cp = Par(4);  % J/kg-K    
 A = Par(5); % Area in m^2
 alpha = Par(6);       % W / % heater
 eps = Par(7);          % Emissivity
 sigma = Par(8);    % Stefan-Boltzman       % Stefan-Boltzman
  
    % Temperatura
    T= x(1);
    
    % Entradas
    Q= u(1);  

    % Ecuaciones de los balances de energía

   dTdt = (1.0/(m*Cp))*(U*A*(Ta-T) ...
            + eps * sigma * A * (Ta^4 - T^4) ...
            + alpha*Q);
end

The same prediction model is the plant model so i want to use the nmpc in a close loop to see the answer at the end of the plant.

%Initial States
x=23+273.15;
u=0;

%% Ref signal
% Define el vector de tiempo
t = linspace(0, 10, 1000); 
initialValue = 23+273.15;
stepValue = 50;
stepTime = 5;

ref = initialValue + stepValue * (t >= stepTime);

Answer 1

[Ishu]

Hi Juan,

In my understanding you have provided the code for 'NMPC' and now you want to simulate this 'NMPC' in a closed loop. For that you can make use of "for loop" iterating over 't'.

As the 'Par' is not changing so you can directly initialize these parameters in the "prediction_model_jl()" function itself rather than passing these as arguments. You can change your function accordingly.

function dTdt = prediction_model_jl(x,u)
    
    % Parameters
  % Parámetros
Ta = 23 + 273.15;   % K
U = 10.0;           % W/m^2-K
m = 4.0/1000.0;     % kg
Cp = 0.5 * 1000.0;  % J/kg-K    
A = 12.0 / 100.0^2; % Area in m^2
alpha = 0.01;       % W % heater
eps = 0.9;          % Emissivity
sigma = 5.67e-8;    % Stefan-Boltzman
  
    % Temperatura
    T= x(1);
    
    % Entradas
    Q= u(1);  
    % Ecuaciones de los balances de energía
   dTdt = (1.0/(m*Cp))*(U*A*(Ta-T) ...
            + eps * sigma * A * (Ta^4 - T^4) ...
            + alpha*Q);
end

And also make other changes relating to this function calling.

Now you can create two vectors to store the system response

x_history = zeros(size(t));
u_history = zeros(size(t));

Simulating NMPC:

% Closed-loop simulation
for i = 1:length(t)

    
    % Update the NMPC controller
    [u, ~] = nlmpcmove(nlobj, x, u,ref(i));
    
    % Simulate the system response
    dxdt = prediction_model_jl(x, u);
    
    x_history(i) = x + dxdt*Ts;
    u_history(i) = u;

end

Plot the results:

figure;
subplot(2, 1, 1);
plot(t, ref, 'r--', 'LineWidth', 2);
hold on;
plot(t, x_history, 'k', 'LineWidth', 2);
xlabel('Time');
ylabel('Temperature (K)');
legend('Reference', 'System Response');
title('Closed-Loop System Response');

subplot(2, 1, 2);
plot(t, u_history, 'b', 'LineWidth', 2);
xlabel('Time');
ylabel('Control Input');
title('Control Input Profile');

For more information on 'nlmpc' you can refer this documentation:

https://www.mathworks.com/help/mpc/ref/nlmpc.html?searchHighlight=nlmpc&s_tid=srchtitle_support_results_1_nlmpc

Hope it helps!