How to Simulate Nonlinear Model Discrete Time?

This is My Nonlinear Model

function [PositionN, VelocityN, TorqueN] = traindiscretemodel(u,Tim_step,Position,Velocity,Torque,Mass,Ca_0,Ca_1,Ca_2,Tao,R,Eta)
% Train Model

   PositionN = Position + Velocity*Tim_step;
   VelocityN = Velocity + 1/Mass *(Eta*Torque/R - (Ca_0 + Ca_1*Velocity + Ca_2*Velocity^2))*Tim_step;
   TorqueN = Torque - 1/Tao*Torque*Tim_step + 1/Tao*u*Tim_step;
    
end

This is parameters i used

clc;clear;close all;

Eta = 0.96;

% Parameter Massa
Mass = [8095;8500;8457;8500;8443;8396;8491];

Tim_step = 0.01;

R = [0.290736184319659;0.295289596853781;0.256349340814675;0.295668792806951;0.281617962311270;0.254877020249970;0.263924910943352];

Tao = [0.744417105917954;0.771737581122686;0.538096044888052;0.774012756841706;0.689707773867623;0.529262121499823;0.583549465660115];

Torquebound = [-3297.53650110286,3297.53650110286;-3517.25332991404,3517.25332991404;-1805.63954664794,1805.63954664794;-3535.78455981619,3535.78455981619;-2873.13552926226,2873.13552926226;-1748.36142518872,1748.36142518872;-2108.92205347325,2108.92205347325];

% Parameter Resistansi
Ca_0 = [5.2;5.2;5.2;5.2;5.2;5.2;5.2;];

Ca_1 = [0.038;0.038;0.038;0.038;0.038;0.038;0.038;];

Ca_2 = [0.00112;0.00112;0.00112;0.00112;0.00112;0.00112;0.00112;];

v0 = 20;

cd('G:\Ivan\Semester 10\Tugas Akhir II\matlab\Train Model Open Loop');
save parametersvalue.mat

with that discrete time model and parameters i used, I want simulated the model open loop. Can i used ode45?

Answer 1

[Jaynik]

Hi,

The ode45 function is used for solving ordinary differential equations (ODEs) and it is typically used for continuous-time models. However, the model given is a discrete-time model as it uses a time step (Tim_step) for updating the states.

For discrete-time models, you can use a simple loop to update the states at each time step. Here’s a basic example of how you can simulate your model in an open-loop fashion:

% Initial conditions
Position = 0;
Velocity = v0;
Torque = 0;

T_end = 10; % for example, simulate for 10 seconds
t = 0:Tim_step:T_end;

PositionN = zeros(size(t));
VelocityN = zeros(size(t));
TorqueN = zeros(size(t));

% Open-loop control input
u = 0; % for example, no control input

% Simulation loop
for i = 1:length(t)
    [PositionN(i), VelocityN(i), TorqueN(i)] = traindiscretemodel(u,Tim_step,Position,Velocity,Torque,Mass(1),Ca_0(1),Ca_1(1),Ca_2(1),Tao(1),R(1),Eta);
    Position = PositionN(i);
    Velocity = VelocityN(i);
    Torque = TorqueN(i);
end
plot(t, PositionN);
xlabel('Time (s)');
ylabel('Position');

This code will simulate the model for 10 seconds with no control input (u = 0). The simulation time and the control input can be adjusted as needed. Also, please make sure to use the correct parameters for your model. This is just a basic example and might need to be adjusted based on your specific needs.

Hope this helps!